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import numpy as nm
from sfepy.linalg import dot_sequences
from sfepy.terms.terms import Term, terms
class DivGradTerm(Term):
r"""
Diffusion term.
:Definition:
.. math::
\int_{\Omega} \nu\ \nabla \ul{v} : \nabla \ul{u} \mbox{ , }
\int_{\Omega} \nu\ \nabla \ul{u} : \nabla \ul{w} \\
\int_{\Omega} \nabla \ul{v} : \nabla \ul{u} \mbox{ , }
\int_{\Omega} \nabla \ul{u} : \nabla \ul{w}
:Arguments 1:
- material : :math:`\nu` (viscosity, optional)
- virtual : :math:`\ul{v}`
- state : :math:`\ul{u}`
:Arguments 2:
- material : :math:`\nu` (viscosity, optional)
- parameter_1 : :math:`\ul{u}`
- parameter_2 : :math:`\ul{w}`
"""
name = 'dw_div_grad'
arg_types = (('opt_material', 'virtual', 'state'),
('opt_material', 'parameter_1', 'parameter_2'))
arg_shapes = {'opt_material' : '1, 1', 'virtual' : ('D', 'state'),
'state' : 'D', 'parameter_1' : 'D', 'parameter_2' : 'D'}
modes = ('weak', 'eval')
function = staticmethod(terms.term_ns_asm_div_grad)
def d_div_grad(self, out, grad1, grad2, mat, vg, fmode):
sh = grad1.shape
g1 = grad1.reshape((sh[0], sh[1], sh[2] * sh[3]))
g2 = grad2.reshape((sh[0], sh[1], sh[2] * sh[3]))
aux = mat *
|
dot_sequences(g1[..., None], g2, 'ATB')
|
sfepy.linalg.dot_sequences
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh =
|
Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
|
sfepy.discrete.fem.Mesh.from_file
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain =
|
FEDomain('domain', mesh)
|
sfepy.discrete.fem.FEDomain
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 =
|
Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
|
sfepy.discrete.fem.Field.from_args
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 =
|
Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
|
sfepy.discrete.fem.Field.from_args
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 =
|
EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
|
sfepy.discrete.conditions.EssentialBC
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity =
|
Material(name='viscosity', value=1.25e-3)
|
sfepy.discrete.Material
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 =
|
FieldVariable('u', 'unknown', field_1)
|
sfepy.discrete.FieldVariable
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 =
|
FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
|
sfepy.discrete.FieldVariable
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 =
|
FieldVariable(name='p', kind='unknown', field=field_2)
|
sfepy.discrete.FieldVariable
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 =
|
FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
|
sfepy.discrete.FieldVariable
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 =
|
Integral('i1', order=2)
|
sfepy.discrete.Integral
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 =
|
Integral('i2', order=3)
|
sfepy.discrete.Integral
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 =
|
Equation('balance', t1+t2-t3)
|
sfepy.discrete.Equation
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 =
|
Equation('incompressibility', t4)
|
sfepy.discrete.Equation
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs =
|
Equations([eq1,eq2])
|
sfepy.discrete.Equations
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls =
|
ScipyDirect({})
|
sfepy.solvers.ls.ScipyDirect
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status =
|
IndexedStruct()
|
sfepy.base.base.IndexedStruct
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls =
|
Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)
|
sfepy.solvers.nls.Newton
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)
pb =
|
Problem('Navier-Stokes', equations=eqs)
|
sfepy.discrete.Problem
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)
pb = Problem('Navier-Stokes', equations=eqs)
pb.set_bcs(ebcs=Conditions([ebc_1, ebc_2, ebc_3]))
pb.set_solver(nls)
status =
|
IndexedStruct()
|
sfepy.base.base.IndexedStruct
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)
pb = Problem('Navier-Stokes', equations=eqs)
pb.set_bcs(ebcs=Conditions([ebc_1, ebc_2, ebc_3]))
pb.set_solver(nls)
status = IndexedStruct()
state = pb.solve(status=status, save_results=True)
out = state.create_output_dict()
pb.save_state('Navier_Stokes.vtk', out=out)
view =
|
Viewer('Navier_Stokes.vtk')
|
sfepy.postprocess.viewer.Viewer
|
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Dec 28 09:33:53 2020
@author: dhulls
"""
from __future__ import print_function
from __future__ import absolute_import
from argparse import ArgumentParser
import numpy as nm
import sys
sys.path.append('.')
from sfepy.base.base import IndexedStruct, Struct
from sfepy.discrete import (FieldVariable, Material, Integral, Function,
Equation, Equations, Problem)
from sfepy.discrete.fem import Mesh, FEDomain, Field
from sfepy.terms import Term
from sfepy.discrete.conditions import Conditions, EssentialBC, InitialCondition
from sfepy.solvers.ls import ScipyDirect
from sfepy.solvers.nls import Newton
from sfepy.postprocess.viewer import Viewer
from sfepy.postprocess.probes_vtk import ProbeFromFile, Probe
import numpy as np
helps = {
'show' : 'show the results figure',
}
from sfepy import data_dir
parser = ArgumentParser()
parser.add_argument('--version', action='version', version='%(prog)s')
parser.add_argument('-s', '--show',
action="store_true", dest='show',
default=False, help=helps['show'])
options = parser.parse_args()
mesh = Mesh.from_file(data_dir + '/meshes/3d/fluid_mesh.inp')
domain = FEDomain('domain', mesh)
omega = domain.create_region('Omega', 'all')
field_1 = Field.from_args(name='3_velocity', dtype=nm.float64, shape=3, region=omega, approx_order=1)
field_2 = Field.from_args(name='pressure', dtype=nm.float64, shape=1, region=omega, approx_order=1)
region_0 = domain.create_region(name='Walls1', select='vertices in (y < -0.049)', kind='facet')
region_1 = domain.create_region(name='Walls2', select='vertices in (y > 0.049)', kind='facet')
region_2 = domain.create_region(name='Inlet', select='vertices in (x < -0.499)', kind='facet')
region_3 = domain.create_region(name='Outlet', select='vertices in (x > -0.499)', kind='facet')
ebc_1 = EssentialBC(name='Walls1', region=region_0, dofs={'u.[0,1,2]' : 0.0})
ebc_2 = EssentialBC(name='Walls2', region=region_1, dofs={'u.[0,1,2]' : 0.0})
ebc_3 = EssentialBC(name='Inlet', region=region_2, dofs={'u.0' : 1.0, 'u.[1,2]' : 0.0})
ebc_4 = EssentialBC(name='Outlet', region=region_3, dofs={'p':0.0, 'u.[1,2]' : 0.0})
viscosity = Material(name='viscosity', value=1.25e-3)
variable_1 = FieldVariable('u', 'unknown', field_1)
variable_2 = FieldVariable(name='v', kind='test', field=field_1, primary_var_name='u')
variable_3 = FieldVariable(name='p', kind='unknown', field=field_2)
variable_4 = FieldVariable(name='q', kind='test', field=field_2, primary_var_name='p')
integral_1 = Integral('i1', order=2)
integral_2 = Integral('i2', order=3)
t1 = Term.new(name='dw_div_grad(viscosity.value, v, u)',
integral=integral_2, region=omega, viscosity=viscosity, v=variable_2, u=variable_1)
t2 = Term.new(name='dw_convect(v, u)',
integral=integral_2, region=omega, v=variable_2, u=variable_1)
t3 = Term.new(name='dw_stokes(v, p)',
integral=integral_1, region=omega, v=variable_2, p=variable_3)
t4 = Term.new(name='dw_stokes(u, q)',
integral=integral_1, region=omega, u=variable_1, q=variable_4)
eq1 = Equation('balance', t1+t2-t3)
eq2 = Equation('incompressibility', t4)
eqs = Equations([eq1,eq2])
ls = ScipyDirect({})
nls_status = IndexedStruct()
nls = Newton({'i_max' : 20, 'eps_a' : 1e-8, 'eps_r' : 1.0, 'macheps' : 1e-16, 'lin_red' : 1e-2, 'ls_red' : 0.1, 'ls_red_warp' : 0.001, 'ls_on' : 0.99999, 'ls_min' : 1e-5, 'check' : 0, 'delta' : 1e-6}, lin_solver=ls, status=nls_status)
pb = Problem('Navier-Stokes', equations=eqs)
pb.set_bcs(ebcs=
|
Conditions([ebc_1, ebc_2, ebc_3])
|
sfepy.discrete.conditions.Conditions
|
r"""
Piezo-elasticity problem - linear elastic material with piezoelectric
effects.
Find :math:`\ul{u}`, :math:`\phi` such that:
.. math::
- \omega^2 \int_{Y} \rho\ \ul{v} \cdot \ul{u}
+ \int_{Y} D_{ijkl}\ e_{ij}(\ul{v}) e_{kl}(\ul{u})
- \int_{Y_2} g_{kij}\ e_{ij}(\ul{v}) \nabla_k \phi
= 0
\;, \quad \forall \ul{v} \;,
\int_{Y_2} g_{kij}\ e_{ij}(\ul{u}) \nabla_k \psi
+ \int_{Y} K_{ij} \nabla_i \psi \nabla_j \phi
= 0
\;, \quad \forall \psi \;,
where
.. math::
D_{ijkl} = \mu (\delta_{ik} \delta_{jl}+\delta_{il} \delta_{jk}) +
\lambda \ \delta_{ij} \delta_{kl}
\;.
"""
import os
import numpy as nm
from sfepy import data_dir
from sfepy.discrete.fem import MeshIO
filename_mesh = data_dir + '/meshes/2d/special/circle_in_square.mesh'
## filename_mesh = data_dir + '/meshes/2d/special/circle_in_square_small.mesh'
## filename_mesh = data_dir + '/meshes/3d/special/cube_sphere.mesh'
## filename_mesh = data_dir + '/meshes/2d/special/cube_cylinder.mesh'
omega = 1
omega_squared = omega**2
conf_dir = os.path.dirname(__file__)
io =
|
MeshIO.any_from_filename(filename_mesh, prefix_dir=conf_dir)
|
sfepy.discrete.fem.MeshIO.any_from_filename
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids = nm.unique(cgroups)
for mat_id in mat_ids:
idxs = nm.where(cgroups == mat_id)[0]
imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,
coors, ngroups,
[conns[idxs]], [cgroups[idxs]], [desc])
fbase, fext = op.splitext(filename_out)
ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)
io = MeshIO.for_format(ifilename_out, format=options.format,
writable=True)
output('writing %s...' % ifilename_out)
imesh.write(ifilename_out, io=io)
output('...done')
io = MeshIO.for_format(filename_out, format=options.format,
writable=True)
cell_types = ', '.join(supported_cell_types[io.format])
|
output('writing [%s] %s...' % (cell_types, filename_out))
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids = nm.unique(cgroups)
for mat_id in mat_ids:
idxs = nm.where(cgroups == mat_id)[0]
imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,
coors, ngroups,
[conns[idxs]], [cgroups[idxs]], [desc])
fbase, fext = op.splitext(filename_out)
ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)
io = MeshIO.for_format(ifilename_out, format=options.format,
writable=True)
output('writing %s...' % ifilename_out)
imesh.write(ifilename_out, io=io)
output('...done')
io = MeshIO.for_format(filename_out, format=options.format,
writable=True)
cell_types = ', '.join(supported_cell_types[io.format])
output('writing [%s] %s...' % (cell_types, filename_out))
mesh.write(filename_out, io=io)
|
output('...done')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
|
output('Supported readable mesh formats:')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
|
output('--------------------------------')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
|
output_mesh_formats('r')
|
sfepy.discrete.fem.meshio.output_mesh_formats
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
|
output('')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
|
output('Supported writable mesh formats:')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
|
output('--------------------------------')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
|
output_mesh_formats('w')
|
sfepy.discrete.fem.meshio.output_mesh_formats
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh =
|
Mesh.from_file(root + '.1.vtk')
|
sfepy.discrete.fem.Mesh.from_file
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
|
remove_files(dirname)
|
sfepy.base.ioutils.remove_files
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh =
|
Mesh.from_file(filename_in)
|
sfepy.discrete.fem.Mesh.from_file
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh =
|
Mesh.from_data(mesh.name, *data)
|
sfepy.discrete.fem.Mesh.from_data
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain =
|
FEDomain(mesh.name, mesh)
|
sfepy.discrete.fem.FEDomain
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids =
|
nm.unique(cgroups)
|
sfepy.base.base.nm.unique
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option =
|
nm.array(option, dtype=nm.float64, ndmin=1)
|
sfepy.base.base.nm.array
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh =
|
Mesh.from_file(filename_in)
|
sfepy.discrete.fem.Mesh.from_file
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain =
|
FEDomain(mesh.name, mesh)
|
sfepy.discrete.fem.FEDomain
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
|
output('refine %d...' % ii)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
|
output('initial mesh: %d elements' % nelo)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns =
|
elems_q2t(conns)
|
sfepy.mesh.mesh_tools.elems_q2t
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups =
|
nm.repeat(mesh.cmesh.cell_groups, nn)
|
sfepy.base.base.nm.repeat
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
|
output('new mesh: %d elements' % new_conns.shape[0])
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids = nm.unique(cgroups)
for mat_id in mat_ids:
idxs = nm.where(cgroups == mat_id)[0]
imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,
coors, ngroups,
[conns[idxs]], [cgroups[idxs]], [desc])
fbase, fext = op.splitext(filename_out)
ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)
io = MeshIO.for_format(ifilename_out, format=options.format,
writable=True)
|
output('writing %s...' % ifilename_out)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids = nm.unique(cgroups)
for mat_id in mat_ids:
idxs = nm.where(cgroups == mat_id)[0]
imesh = Mesh.from_data(mesh.name + '_matid_%d' % mat_id,
coors, ngroups,
[conns[idxs]], [cgroups[idxs]], [desc])
fbase, fext = op.splitext(filename_out)
ifilename_out = '%s_matid_%d%s' % (fbase, mat_id, fext)
io = MeshIO.for_format(ifilename_out, format=options.format,
writable=True)
output('writing %s...' % ifilename_out)
imesh.write(ifilename_out, io=io)
|
output('...done')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
|
output('bad %s! (%s)' % (name, option))
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr =
|
nm.eye(mesh.dim, dtype=nm.float64)
|
sfepy.base.base.nm.eye
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr =
|
nm.diag(scale)
|
sfepy.base.base.nm.diag
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[
|
nm.eye(mesh.dim, dtype=nm.float64)
|
sfepy.base.base.nm.eye
|
#!/usr/bin/env python
"""
Convert a mesh file from one SfePy-supported format to another.
Examples::
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s2.5
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.vtk -s0.5,2,1 -c 0
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new.mesh --remesh='q2/0 a1e-8 O9/7 V'
$ ./script/convert_mesh.py meshes/3d/cylinder.mesh new2.mesh --remesh='rq2/0 a1e-8 O9/7 V'
"""
from __future__ import absolute_import
import sys
import os.path as op
from six.moves import range
sys.path.append('.')
from argparse import ArgumentParser, RawDescriptionHelpFormatter
from sfepy.base.base import nm, output
from sfepy.base.ioutils import remove_files
from sfepy.discrete.fem import Mesh, FEDomain
from sfepy.discrete.fem.meshio import (output_mesh_formats, MeshIO,
supported_cell_types)
from sfepy.discrete.fem.mesh import fix_double_nodes
from sfepy.mesh.mesh_tools import elems_q2t
helps = {
'scale' : 'scale factor (float or comma-separated list for each axis)'
' [default: %(default)s]',
'center' : 'center of the output mesh (0 for origin or'
' comma-separated list for each axis) applied after scaling'
' [default: %(default)s]',
'refine' : 'uniform refinement level [default: %(default)s]',
'format' : 'output mesh format (overrides filename_out extension)',
'list' : 'list supported readable/writable output mesh formats',
'merge' : 'remove duplicate vertices',
'tri-tetra' : 'convert elements: quad->tri, hexa->tetra',
'2d' : 'force a 2D mesh by removing the z coordinates - assumes a 3D mesh'
' in the xy plane',
'save-per-mat': 'extract cells by material id and save them into'
' separate mesh files with a name based on filename_out and the id'
' numbers (preserves original mesh vertices)',
'remesh' : """when given, remesh the given mesh using tetgen.
The options can be the following, separated by spaces, in this order: 1.
"r" causes remeshing of the mesh volume - if not present the mesh surface
is extracted and used for the volume mesh generation. 2.
"q[<float>/<float>]" (required) - the two numbers after "q" are a maximum
radius-edge ratio bound and a minimum dihedral angle bound. 3. "a<float>"
(optional) - the number imposes a maximum volume constraint on all
tetrahedra. 4. O[<0-9>/<0-7>] - the two numbers correspond to a mesh
optimization level and a choice of optimizing operations. 5. "V"
(optional) - if present, mesh statistics are printed. Consult the tetgen
documentation for details.""",
}
def _parse_val_or_vec(option, name, parser):
if option is not None:
try:
try:
option = float(option)
except ValueError:
option = [float(ii) for ii in option.split(',')]
option = nm.array(option, dtype=nm.float64, ndmin=1)
except:
output('bad %s! (%s)' % (name, option))
parser.print_help()
sys.exit(1)
return option
def main():
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('-s', '--scale', metavar='scale',
action='store', dest='scale',
default=None, help=helps['scale'])
parser.add_argument('-c', '--center', metavar='center',
action='store', dest='center',
default=None, help=helps['center'])
parser.add_argument('-r', '--refine', metavar='level',
action='store', type=int, dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-f', '--format', metavar='format',
action='store', type=str, dest='format',
default=None, help=helps['format'])
parser.add_argument('-l', '--list', action='store_true',
dest='list', help=helps['list'])
parser.add_argument('-m', '--merge', action='store_true',
dest='merge', help=helps['merge'])
parser.add_argument('-t', '--tri-tetra', action='store_true',
dest='tri_tetra', help=helps['tri-tetra'])
parser.add_argument('-2', '--2d', action='store_true',
dest='force_2d', help=helps['2d'])
parser.add_argument('--save-per-mat', action='store_true',
dest='save_per_mat', help=helps['save-per-mat'])
parser.add_argument('--remesh', metavar='options',
action='store', dest='remesh',
default=None, help=helps['remesh'])
parser.add_argument('filename_in')
parser.add_argument('filename_out')
options = parser.parse_args()
if options.list:
output('Supported readable mesh formats:')
output('--------------------------------')
output_mesh_formats('r')
output('')
output('Supported writable mesh formats:')
output('--------------------------------')
output_mesh_formats('w')
sys.exit(0)
scale = _parse_val_or_vec(options.scale, 'scale', parser)
center = _parse_val_or_vec(options.center, 'center', parser)
filename_in = options.filename_in
filename_out = options.filename_out
if options.remesh:
import tempfile
import shlex
import subprocess
dirname = tempfile.mkdtemp()
is_surface = options.remesh.startswith('q')
if is_surface:
mesh = Mesh.from_file(filename_in)
domain = FEDomain(mesh.name, mesh)
region = domain.create_region('surf', 'vertices of surface',
'facet')
surf_mesh = Mesh.from_region(region, mesh,
localize=True, is_surface=True)
filename = op.join(dirname, 'surf.mesh')
surf_mesh.write(filename, io='auto')
else:
import shutil
shutil.copy(filename_in, dirname)
filename = op.join(dirname, op.basename(filename_in))
qopts = ''.join(options.remesh.split()) # Remove spaces.
command = 'tetgen -BFENkACp%s %s' % (qopts, filename)
args = shlex.split(command)
subprocess.call(args)
root, ext = op.splitext(filename)
mesh = Mesh.from_file(root + '.1.vtk')
remove_files(dirname)
else:
mesh = Mesh.from_file(filename_in)
if options.force_2d:
data = list(mesh._get_io_data())
data[0] = data[0][:, :2]
mesh = Mesh.from_data(mesh.name, *data)
if scale is not None:
if len(scale) == 1:
tr = nm.eye(mesh.dim, dtype=nm.float64) * scale
elif len(scale) == mesh.dim:
tr = nm.diag(scale)
else:
raise ValueError('bad scale! (%s)' % scale)
mesh.transform_coors(tr)
if center is not None:
cc = 0.5 * mesh.get_bounding_box().sum(0)
shift = center - cc
tr = nm.c_[nm.eye(mesh.dim, dtype=nm.float64), shift[:, None]]
mesh.transform_coors(tr)
if options.refine > 0:
domain = FEDomain(mesh.name, mesh)
output('initial mesh: %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
for ii in range(options.refine):
output('refine %d...' % ii)
domain = domain.refine()
output('... %d nodes %d elements'
% (domain.shape.n_nod, domain.shape.n_el))
mesh = domain.mesh
if options.tri_tetra > 0:
conns = None
for k, new_desc in [('3_8', '3_4'), ('2_4', '2_3')]:
if k in mesh.descs:
conns = mesh.get_conn(k)
break
if conns is not None:
nelo = conns.shape[0]
output('initial mesh: %d elements' % nelo)
new_conns = elems_q2t(conns)
nn = new_conns.shape[0] // nelo
new_cgroups = nm.repeat(mesh.cmesh.cell_groups, nn)
output('new mesh: %d elements' % new_conns.shape[0])
mesh = Mesh.from_data(mesh.name, mesh.coors,
mesh.cmesh.vertex_groups,
[new_conns], [new_cgroups], [new_desc])
if options.merge:
desc = mesh.descs[0]
coor, ngroups, conns = fix_double_nodes(mesh.coors,
mesh.cmesh.vertex_groups,
mesh.get_conn(desc), 1e-9)
mesh = Mesh.from_data(mesh.name + '_merged',
coor, ngroups,
[conns], [mesh.cmesh.cell_groups], [desc])
if options.save_per_mat:
desc = mesh.descs[0]
conns, cgroups = mesh.get_conn(desc), mesh.cmesh.cell_groups
coors, ngroups = mesh.coors, mesh.cmesh.vertex_groups
mat_ids = nm.unique(cgroups)
for mat_id in mat_ids:
idxs =
|
nm.where(cgroups == mat_id)
|
sfepy.base.base.nm.where
|
# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable
# double porous media.
# The mathematical model is described in:
#
#<NAME>., <NAME>., <NAME>.
#The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling.
# Computers and Mathematics with applications, 78(9):3044-3066, 2019,
# https://doi.org/10.1016/j.camwa.2019.04.004
#
# Run simulation:
#
# ./simple.py example_perfusion_BDB/perf_BDB_mac.py
#
# The results are stored in `example_perfusion_BDB/results/macro` directory.
#
import numpy as nm
from sfepy.homogenization.micmac import get_homog_coefs_linear
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete.fem.mesh import Mesh
import os.path as osp
material_cache = {}
data_dir = 'example_perfusion_BDB'
def coefs2qp(coefs, nqp):
out = {}
for k, v in coefs.items():
if type(v) not in [nm.ndarray, float]:
continue
if type(v) is nm.ndarray:
if len(v.shape) >= 3:
out[k] = v
out[k] = nm.tile(v, (nqp, 1, 1))
return out
# Get raw homogenized coefficients, recalculate them if necessary
def get_raw_coefs(problem):
if 'raw_coefs' not in material_cache:
micro_filename = material_cache['meso_filename']
coefs_filename = 'coefs_meso'
coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'),
coefs_filename) + '.h5'
coefs = get_homog_coefs_linear(0, 0, None,
micro_filename=micro_filename, coefs_filename=coefs_filename)
coefs['B'] = coefs['B'][:, nm.newaxis]
material_cache['raw_coefs'] = coefs
return material_cache['raw_coefs']
#Get homogenized coefficients in quadrature points
def get_homog(coors,pb, mode, **kwargs):
if not (mode == 'qp'):
return
nqp = coors.shape[0]
coefs=get_raw_coefs(pb)
for k in coefs.keys():
v = coefs[k]
if type(v) is nm.ndarray:
if len(v.shape) == 0:
coefs[k] = v.reshape((1, 1))
elif len(v.shape) == 1:
coefs[k] = v[:, nm.newaxis]
elif isinstance(v, float):
coefs[k] = nm.array([[v]])
out = coefs2qp(coefs, nqp)
return out
#Definition of dirichlet boundary conditions
def get_ebc( coors, amplitude, cg1, cg2,const=False):
"""
Define the essential boundary conditions as a function of coordinates
`coors` of region nodes.
"""
y = coors[:, 1] - cg1
z = coors[:, 2] - cg2
val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2)))
if const:
val=nm.ones_like(y) *amplitude
return val
#Returns value of \phi_c\bar{w}^{mes} as a material function
def get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False):
if mode == 'qp':
val = get_ebc( coors, amplitude, cg1, cg2,konst)
phic = get_raw_coefs(pb)['vol']["fraction_Zc"]
v_w1 = val[:, nm.newaxis, nm.newaxis]
return {'val': v_w1*phic}
#Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/
def define_bc(cg1,cg2, val_in=1e2, val_out=1e2):
funs = {
'w_in': (lambda ts, coor, bc, problem, **kwargs:
get_ebc( coor, val_in, cg1, cg2),),
'w_out': (lambda ts, coor, bc, problem, **kwargs:
get_ebc( coor, val_out, cg1, cg2),),
'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs:
get_ebc_mat( coor, problem, mode, val_in,
cg1, cg2),),
'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs:
get_ebc_mat( coor, problem, mode, val_out,
cg1, cg2),),
}
mats = {
'w_in': 'w_in_mat',
'w_out': 'w_out_mat',
}
ebcs = {
'fix_u_in': ('In', {'u.all': 0.0}),
'fix_u_out': ('Out', {'u.all': 0.0}),
'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}),
'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}),
'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}),
'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}),
'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}),
'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}),
}
lcbcs = {
'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value')
}
return ebcs, funs, mats, lcbcs
#Definition of macroscopic problem
def define(filename_mesh=None,cg1=None, cg2=None):
if filename_mesh is None:
filename_mesh = osp.join(data_dir, 'macro_perf.vtk')
cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity
mesh =
|
Mesh.from_file(filename_mesh)
|
sfepy.discrete.fem.mesh.Mesh.from_file
|
# This example implements macroscopic homogenized model of Biot-Darcy-Brinkman model of flow in deformable
# double porous media.
# The mathematical model is described in:
#
#<NAME>., <NAME>., <NAME>.
#The Biot-Darcy-Brinkman model of flow in deformable double porous media; homogenization and numerical modelling.
# Computers and Mathematics with applications, 78(9):3044-3066, 2019,
# https://doi.org/10.1016/j.camwa.2019.04.004
#
# Run simulation:
#
# ./simple.py example_perfusion_BDB/perf_BDB_mac.py
#
# The results are stored in `example_perfusion_BDB/results/macro` directory.
#
import numpy as nm
from sfepy.homogenization.micmac import get_homog_coefs_linear
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete.fem.mesh import Mesh
import os.path as osp
material_cache = {}
data_dir = 'example_perfusion_BDB'
def coefs2qp(coefs, nqp):
out = {}
for k, v in coefs.items():
if type(v) not in [nm.ndarray, float]:
continue
if type(v) is nm.ndarray:
if len(v.shape) >= 3:
out[k] = v
out[k] = nm.tile(v, (nqp, 1, 1))
return out
# Get raw homogenized coefficients, recalculate them if necessary
def get_raw_coefs(problem):
if 'raw_coefs' not in material_cache:
micro_filename = material_cache['meso_filename']
coefs_filename = 'coefs_meso'
coefs_filename = osp.join(problem.conf.options.get('output_dir', '.'),
coefs_filename) + '.h5'
coefs = get_homog_coefs_linear(0, 0, None,
micro_filename=micro_filename, coefs_filename=coefs_filename)
coefs['B'] = coefs['B'][:, nm.newaxis]
material_cache['raw_coefs'] = coefs
return material_cache['raw_coefs']
#Get homogenized coefficients in quadrature points
def get_homog(coors,pb, mode, **kwargs):
if not (mode == 'qp'):
return
nqp = coors.shape[0]
coefs=get_raw_coefs(pb)
for k in coefs.keys():
v = coefs[k]
if type(v) is nm.ndarray:
if len(v.shape) == 0:
coefs[k] = v.reshape((1, 1))
elif len(v.shape) == 1:
coefs[k] = v[:, nm.newaxis]
elif isinstance(v, float):
coefs[k] = nm.array([[v]])
out = coefs2qp(coefs, nqp)
return out
#Definition of dirichlet boundary conditions
def get_ebc( coors, amplitude, cg1, cg2,const=False):
"""
Define the essential boundary conditions as a function of coordinates
`coors` of region nodes.
"""
y = coors[:, 1] - cg1
z = coors[:, 2] - cg2
val = amplitude*((cg1**2 - (abs(y)**2))+(cg2**2 - (abs(z)**2)))
if const:
val=nm.ones_like(y) *amplitude
return val
#Returns value of \phi_c\bar{w}^{mes} as a material function
def get_ebc_mat( coors,pb, mode, amplitude, cg1, cg2,konst=False):
if mode == 'qp':
val = get_ebc( coors, amplitude, cg1, cg2,konst)
phic = get_raw_coefs(pb)['vol']["fraction_Zc"]
v_w1 = val[:, nm.newaxis, nm.newaxis]
return {'val': v_w1*phic}
#Definition of boundary conditions for numerical example at http://sfepy.org/sfepy_examples/example_perfusion_BDB/
def define_bc(cg1,cg2, val_in=1e2, val_out=1e2):
funs = {
'w_in': (lambda ts, coor, bc, problem, **kwargs:
get_ebc( coor, val_in, cg1, cg2),),
'w_out': (lambda ts, coor, bc, problem, **kwargs:
get_ebc( coor, val_out, cg1, cg2),),
'w_in_mat': (lambda ts,coor, problem, mode=None, **kwargs:
get_ebc_mat( coor, problem, mode, val_in,
cg1, cg2),),
'w_out_mat': (lambda ts,coor, problem, mode=None, **kwargs:
get_ebc_mat( coor, problem, mode, val_out,
cg1, cg2),),
}
mats = {
'w_in': 'w_in_mat',
'w_out': 'w_out_mat',
}
ebcs = {
'fix_u_in': ('In', {'u.all': 0.0}),
'fix_u_out': ('Out', {'u.all': 0.0}),
'w_in': ('In', {'w.0': 'w_in','w.[1,2]': 0.0}),
'w_out': ('Out', {'w.0': 'w_out','w.[1,2]': 0.0}),
'wB_dirichlet':('Bottom',{'w.2' :0.0,'u.2':0.0}),
'WT_dirichlet':('Top',{'w.2' :0.0,'u.2':0.0}),
'wN_dirichlet':('Near',{'w.1' :0.0,'u.1':0.0}),
'wF_dirichlet':('Far',{'w.1' :0.0,'u.1':0.0}),
}
lcbcs = {
'imv': ('Omega', {'ls.all' : None}, None, 'integral_mean_value')
}
return ebcs, funs, mats, lcbcs
#Definition of macroscopic problem
def define(filename_mesh=None,cg1=None, cg2=None):
if filename_mesh is None:
filename_mesh = osp.join(data_dir, 'macro_perf.vtk')
cg1, cg2 = 0.0015, 0.0015 # y and z coordinates of center of gravity
mesh = Mesh.from_file(filename_mesh)
poroela_mezo_file = osp.join(data_dir,'perf_BDB_mes.py')
material_cache['meso_filename']=poroela_mezo_file
bbox = mesh.get_bounding_box()
regions =
|
define_box_regions(mesh.dim, bbox[0], bbox[1], eps=1e-6)
|
sfepy.homogenization.utils.define_box_regions
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io =
|
MeshIO.any_from_filename(filename_mesh)
|
sfepy.discrete.fem.MeshIO.any_from_filename
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
|
per.set_accuracy(mesh_eps)
|
sfepy.discrete.fem.periodic.set_accuracy
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] =
|
Struct(name='density', mode='cell', data=density)
|
sfepy.base.base.Struct
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
|
output('average p-wave speed:', cp)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
|
output('average shear wave speed:', cs)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf =
|
ProblemConf.from_dict(define_dict, mod)
|
sfepy.base.conf.ProblemConf.from_dict
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb =
|
Problem.from_conf(conf)
|
sfepy.discrete.Problem.from_conf
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
|
output('scaling factor of periodic cell mesh coordinates:', scaling)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
|
output('new mesh size with applied unit multipliers:', scaling * size)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
|
output('1. Brillouin zone size:', bzone * scaling0)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
|
output('1. Brillouin zone size with applied unit multipliers:', bzone)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf =
|
dict_from_string(options.solver_conf)
|
sfepy.base.conf.dict_from_string
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs =
|
dict_from_string(options.define_kwargs)
|
sfepy.base.conf.dict_from_string
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
|
ensure_path(filename)
|
sfepy.base.ioutils.ensure_path
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
|
output('material parameters with applied unit multipliers:')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
|
output(pars)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
output('wave number range with applied unit multipliers:', rng)
else:
if options.stepper == 'brillouin':
raise ValueError('Cannot use "brillouin" stepper in kappa mode!')
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['frequency', 'frequency'],
options.unit_multipliers)
output('frequency range with applied unit multipliers:', rng)
pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,
options)
dim = pb.domain.shape.dim
if dim != 2:
options.plane = 'strain'
if options.save_regions:
pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))
if options.save_materials:
save_materials(output_dir, pb, options)
conf = pb.solver_confs['eig']
eig_solver =
|
Solver.any_from_conf(conf)
|
sfepy.solvers.Solver.any_from_conf
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper =
|
TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
|
sfepy.solvers.ts.TimeStepper
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
|
output_array_stats(mtx.data, 'nonzeros in %s' % key)
|
sfepy.linalg.utils.output_array_stats
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
|
output('symmetry checks:')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
|
output('eigs, omegas:')
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod =
|
import_file(options.conf)
|
sfepy.base.base.import_file
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
|
output('wave number range with applied unit multipliers:', rng)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
output('wave number range with applied unit multipliers:', rng)
else:
if options.stepper == 'brillouin':
raise ValueError('Cannot use "brillouin" stepper in kappa mode!')
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['frequency', 'frequency'],
options.unit_multipliers)
|
output('frequency range with applied unit multipliers:', rng)
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
|
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
|
sfepy.base.base.Struct.__init__
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix =
|
get_print_info(self.n_step)
|
sfepy.solvers.ts.get_print_info
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts =
|
TimeStepper(0, bzone[0], dt=None, n_step=num)
|
sfepy.solvers.ts.TimeStepper
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts =
|
TimeStepper(0, bzone[1], dt=None, n_step=num)
|
sfepy.solvers.ts.TimeStepper
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts =
|
TimeStepper(0, 1, dt=None, n_step=num)
|
sfepy.solvers.ts.TimeStepper
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(
|
convert_complex_output(aux2)
|
sfepy.discrete.fem.meshio.convert_complex_output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key),
|
max_diff_csr(mtx, mtx.T)
|
sfepy.linalg.utils.max_diff_csr
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key),
|
max_diff_csr(mtx, mtx.H)
|
sfepy.linalg.utils.max_diff_csr
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:',
|
max_diff_csr(mtx_a, mtx_a.H)
|
sfepy.linalg.utils.max_diff_csr
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
output('wave number range with applied unit multipliers:', rng)
else:
if options.stepper == 'brillouin':
raise ValueError('Cannot use "brillouin" stepper in kappa mode!')
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['frequency', 'frequency'],
options.unit_multipliers)
output('frequency range with applied unit multipliers:', rng)
pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,
options)
dim = pb.domain.shape.dim
if dim != 2:
options.plane = 'strain'
if options.save_regions:
pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))
if options.save_materials:
save_materials(output_dir, pb, options)
conf = pb.solver_confs['eig']
eig_solver = Solver.any_from_conf(conf)
n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs)
get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1)))
plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'}
for ii in range(options.n_eigs)]
get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1)))
plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'}
for ii in range(dim)]
log_names = []
log_plot_kwargs = []
if options.log_std_waves:
std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun(
pb, options)
else:
std_wave_fun = None
stepper = get_stepper(rng, pb, options)
if options.mode == 'omega':
eigenshapes_filename = os.path.join(output_dir,
'frequency-eigenshapes-%s.vtk'
% stepper.suffix)
if options.stepper == 'linear':
log = Log([[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)],
[r'$\omega_{%d}$'
% ii for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * options.n_eigs,
['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear', 'linear'],
xlabels=[r'$\kappa$', r'$\kappa$'],
ylabels=[r'eigenvalues $\lambda_i$',
r'frequencies $\omega_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'frequencies.txt'),
aggregate=1000, sleep=0.1)
else:
log = Log([[r'$\kappa_{%d}$'% ii for ii in range(dim)],
[r'$\omega_{%d}$'
% ii for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs_dim,
plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * dim,
['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear', 'linear'],
xlabels=[r'', r''],
ylabels=[r'wave vector $\kappa$',
r'frequencies $\omega_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'frequencies.txt'),
aggregate=1000, sleep=0.1)
for aux in stepper:
if options.stepper == 'linear':
iv, wmag = aux
else:
iv, wmag, wdir = aux
|
output('step %d: wave vector %s' % (iv, wmag * wdir))
|
sfepy.base.base.output
|
#!/usr/bin/env python
"""
Dispersion analysis of a heterogeneous finite scale periodic cell.
The periodic cell mesh has to contain two subdomains Y1 (with the cell ids 1),
Y2 (with the cell ids 2), so that different material properties can be defined
in each of the subdomains (see ``--pars`` option). The command line parameters
can be given in any consistent unit set, for example the basic SI units. The
``--unit-multipliers`` option can be used to rescale the input units to ones
more suitable to the simulation, for example to prevent having different
matrix blocks with large differences of matrix entries magnitudes. The results
are then in the rescaled units.
Usage Examples
--------------
Default material parameters, a square periodic cell with a spherical inclusion,
logs also standard pressure dilatation and shear waves, no eigenvectors::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only
As above, with custom eigenvalue solver parameters, and different number of
eigenvalues, mesh size and units used in the calculation::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --solver-conf="kind='eig.scipy', method='eigsh', tol=1e-10, maxiter=1000, which='LM', sigma=0" --log-std-waves -n 5 --range=0,640,101 --mode=omega --unit-multipliers=1e-6,1e-2,1e-3 --mesh-size=1e-2 --eigs-only
Default material parameters, a square periodic cell with a square inclusion,
and a very small mesh to allow comparing the omega and kappa modes (full matrix
solver required!)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_2m.mesh --solver-conf="kind='eig.qevp', method='companion', mode='inverted', solver={kind='eig.scipy', method='eig'}" --log-std-waves -n 500 --range=0,4000000,1001 --mesh-size=1e-2 --mode=kappa --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/kappa
View/compare the resulting logs::
python script/plot_logs.py output/omega/frequencies.txt --no-legends -g 1 -o mode-omega.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends -o mode-kappa.png
python script/plot_logs.py output/kappa/wave-numbers.txt --no-legends --swap-axes -o mode-kappa-t.png
In contrast to the heterogeneous square periodic cell, a homogeneous
square periodic cell (the region Y2 is empty)::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/square_1m.mesh --solver-conf="kind='eig.scipy', method='eigh'" --log-std-waves -n 10 --range=0,640,101 --mesh-size=1e-2 --mode=omega --eigs-only --no-legends --unit-multipliers=1e-6,1e-2,1e-3 -o output/omega-h
python script/plot_logs.py output/omega-h/frequencies.txt --no-legends -g 1 -o mode-omega-h.png
Use the Brillouin stepper::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves -n=60 --eigs-only --no-legends --stepper=brillouin
python script/plot_logs.py output/frequencies.txt -g 0 --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-kappas.png
python script/plot_logs.py output/frequencies.txt -g 1 --no-legends --rc="'font.size':14, 'lines.linewidth' : 3, 'lines.markersize' : 4" -o brillouin-stepper-omegas.png
Additional arguments can be passed to the problem configuration's
:func:`define()` function using the ``--define-kwargs`` option. In this file,
only the mesh vertex separation parameter `mesh_eps` can be used::
python examples/linear_elasticity/dispersion_analysis.py meshes/2d/special/circle_in_square.mesh --log-std-waves --eigs-only --define-kwargs="mesh_eps=1e-10" --save-regions
"""
from __future__ import absolute_import
import os
import sys
sys.path.append('.')
import gc
from copy import copy
from argparse import ArgumentParser, RawDescriptionHelpFormatter
import numpy as nm
import matplotlib.pyplot as plt
from sfepy.base.base import import_file, output, Struct
from sfepy.base.conf import dict_from_string, ProblemConf
from sfepy.base.ioutils import ensure_path, remove_files_patterns, save_options
from sfepy.base.log import Log
from sfepy.discrete.fem import MeshIO
from sfepy.mechanics.matcoefs import stiffness_from_youngpoisson as stiffness
import sfepy.mechanics.matcoefs as mc
from sfepy.mechanics.units import apply_unit_multipliers
import sfepy.discrete.fem.periodic as per
from sfepy.discrete.fem.meshio import convert_complex_output
from sfepy.homogenization.utils import define_box_regions
from sfepy.discrete import Problem
from sfepy.mechanics.tensors import get_von_mises_stress
from sfepy.solvers import Solver
from sfepy.solvers.ts import get_print_info, TimeStepper
from sfepy.linalg.utils import output_array_stats, max_diff_csr
def apply_units(pars, unit_multipliers):
new_pars = apply_unit_multipliers(pars,
['stress', 'one', 'density',
'stress', 'one' ,'density'],
unit_multipliers)
return new_pars
def compute_von_mises(out, pb, state, extend=False, wmag=None, wdir=None):
"""
Calculate the von Mises stress.
"""
stress = pb.evaluate('ev_cauchy_stress.i.Omega(m.D, u)', mode='el_avg')
vms = get_von_mises_stress(stress.squeeze())
vms.shape = (vms.shape[0], 1, 1, 1)
out['von_mises_stress'] = Struct(name='output_data', mode='cell',
data=vms)
return out
def define(filename_mesh, pars, approx_order, refinement_level, solver_conf,
plane='strain', post_process=False, mesh_eps=1e-8):
io = MeshIO.any_from_filename(filename_mesh)
bbox = io.read_bounding_box()
dim = bbox.shape[1]
options = {
'absolute_mesh_path' : True,
'refinement_level' : refinement_level,
'allow_empty_regions' : True,
'post_process_hook' : 'compute_von_mises' if post_process else None,
}
fields = {
'displacement': ('complex', dim, 'Omega', approx_order),
}
young1, poisson1, density1, young2, poisson2, density2 = pars
materials = {
'm' : ({
'D' : {'Y1' : stiffness(dim, young=young1, poisson=poisson1,
plane=plane),
'Y2' : stiffness(dim, young=young2, poisson=poisson2,
plane=plane)},
'density' : {'Y1' : density1, 'Y2' : density2},
},),
'wave' : 'get_wdir',
}
variables = {
'u' : ('unknown field', 'displacement', 0),
'v' : ('test field', 'displacement', 'u'),
}
regions = {
'Omega' : 'all',
'Y1': 'cells of group 1',
'Y2': 'cells of group 2',
}
regions.update(define_box_regions(dim,
bbox[0], bbox[1], mesh_eps))
ebcs = {
}
if dim == 3:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_x_plane'),
'periodic_y' : (['Near', 'Far'], {'u.all' : 'u.all'},
'match_y_plane'),
'periodic_z' : (['Top', 'Bottom'], {'u.all' : 'u.all'},
'match_z_plane'),
}
else:
epbcs = {
'periodic_x' : (['Left', 'Right'], {'u.all' : 'u.all'},
'match_y_line'),
'periodic_y' : (['Bottom', 'Top'], {'u.all' : 'u.all'},
'match_x_line'),
}
per.set_accuracy(mesh_eps)
functions = {
'match_x_plane' : (per.match_x_plane,),
'match_y_plane' : (per.match_y_plane,),
'match_z_plane' : (per.match_z_plane,),
'match_x_line' : (per.match_x_line,),
'match_y_line' : (per.match_y_line,),
'get_wdir' : (get_wdir,),
}
integrals = {
'i' : 2 * approx_order,
}
equations = {
'K' : 'dw_lin_elastic.i.Omega(m.D, v, u)',
'S' : 'dw_elastic_wave.i.Omega(m.D, wave.vec, v, u)',
'R' : """1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, u, v)
- 1j * dw_elastic_wave_cauchy.i.Omega(m.D, wave.vec, v, u)""",
'M' : 'dw_volume_dot.i.Omega(m.density, v, u)',
}
solver_0 = solver_conf.copy()
solver_0['name'] = 'eig'
return locals()
def get_wdir(ts, coors, mode=None,
equations=None, term=None, problem=None, wdir=None, **kwargs):
if mode == 'special':
return {'vec' : wdir}
def set_wave_dir(pb, wdir):
materials = pb.get_materials()
wave_mat = materials['wave']
wave_mat.set_extra_args(wdir=wdir)
def save_materials(output_dir, pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
out = {}
out['young'] = Struct(name='young', mode='cell',
data=young[..., None, None])
out['poisson'] = Struct(name='poisson', mode='cell',
data=poisson[..., None, None])
out['density'] = Struct(name='density', mode='cell', data=density)
materials_filename = os.path.join(output_dir, 'materials.vtk')
pb.save_state(materials_filename, out=out)
def get_std_wave_fun(pb, options):
stiffness = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.D, u)',
mode='el_avg', copy_materials=False, verbose=False)
young, poisson = mc.youngpoisson_from_stiffness(stiffness,
plane=options.plane)
density = pb.evaluate('ev_volume_integrate_mat.2.Omega(m.density, u)',
mode='el_avg', copy_materials=False, verbose=False)
lam, mu = mc.lame_from_youngpoisson(young, poisson,
plane=options.plane)
alam = nm.average(lam)
amu = nm.average(mu)
adensity = nm.average(density)
cp = nm.sqrt((alam + 2.0 * amu) / adensity)
cs = nm.sqrt(amu / adensity)
output('average p-wave speed:', cp)
output('average shear wave speed:', cs)
log_names = [r'$\omega_p$', r'$\omega_s$']
log_plot_kwargs = [{'ls' : '--', 'color' : 'k'},
{'ls' : '--', 'color' : 'gray'}]
if options.mode == 'omega':
fun = lambda wmag, wdir: (cp * wmag, cs * wmag)
else:
fun = lambda wmag, wdir: (wmag / cp, wmag / cs)
return fun, log_names, log_plot_kwargs
def get_stepper(rng, pb, options):
if options.stepper == 'linear':
stepper = TimeStepper(rng[0], rng[1], dt=None, n_step=rng[2])
return stepper
bbox = pb.domain.mesh.get_bounding_box()
bzone = 2.0 * nm.pi / (bbox[1] - bbox[0])
num = rng[2] // 3
class BrillouinStepper(Struct):
"""
Step over 1. Brillouin zone in xy plane.
"""
def __init__(self, t0, t1, dt=None, n_step=None, step=None, **kwargs):
Struct.__init__(self, t0=t0, t1=t1, dt=dt, n_step=n_step, step=step)
self.n_digit, self.format, self.suffix = get_print_info(self.n_step)
def __iter__(self):
ts = TimeStepper(0, bzone[0], dt=None, n_step=num)
for ii, val in ts:
yield ii, val, nm.array([1.0, 0.0])
if ii == (num-2): break
ts = TimeStepper(0, bzone[1], dt=None, n_step=num)
for ii, k1 in ts:
wdir = nm.array([bzone[0], k1])
val = nm.linalg.norm(wdir)
wdir = wdir / val
yield num + ii, val, wdir
if ii == (num-2): break
wdir = nm.array([bzone[0], bzone[1]])
val = nm.linalg.norm(wdir)
wdir = wdir / val
ts = TimeStepper(0, 1, dt=None, n_step=num)
for ii, _ in ts:
yield 2 * num + ii, val * (1.0 - float(ii)/(num-1)), wdir
stepper = BrillouinStepper(0, 1, n_step=rng[2])
return stepper
def save_eigenvectors(filename, svecs, wmag, wdir, pb):
if svecs is None: return
variables = pb.get_variables()
# Make full eigenvectors (add DOFs fixed by boundary conditions).
vecs = nm.empty((variables.di.ptr[-1], svecs.shape[1]),
dtype=svecs.dtype)
for ii in range(svecs.shape[1]):
vecs[:, ii] = variables.make_full_vec(svecs[:, ii])
# Save the eigenvectors.
out = {}
state = pb.create_state()
pp_name = pb.conf.options.get('post_process_hook')
pp = getattr(pb.conf.funmod, pp_name if pp_name is not None else '',
lambda out, *args, **kwargs: out)
for ii in range(svecs.shape[1]):
state.set_full(vecs[:, ii])
aux = state.create_output_dict()
aux2 = {}
pp(aux2, pb, state, wmag=wmag, wdir=wdir)
aux.update(convert_complex_output(aux2))
out.update({key + '%03d' % ii : aux[key] for key in aux})
pb.save_state(filename, out=out)
def assemble_matrices(define, mod, pars, set_wave_dir, options, wdir=None):
"""
Assemble the blocks of dispersion eigenvalue problem matrices.
"""
define_dict = define(filename_mesh=options.mesh_filename,
pars=pars,
approx_order=options.order,
refinement_level=options.refine,
solver_conf=options.solver_conf,
plane=options.plane,
post_process=options.post_process,
**options.define_kwargs)
conf = ProblemConf.from_dict(define_dict, mod)
pb = Problem.from_conf(conf)
pb.dispersion_options = options
pb.set_output_dir(options.output_dir)
dim = pb.domain.shape.dim
# Set the normalized wave vector direction to the material(s).
if wdir is None:
wdir = nm.asarray(options.wave_dir[:dim], dtype=nm.float64)
wdir = wdir / nm.linalg.norm(wdir)
set_wave_dir(pb, wdir)
bbox = pb.domain.mesh.get_bounding_box()
size = (bbox[1] - bbox[0]).max()
scaling0 = apply_unit_multipliers([1.0], ['length'],
options.unit_multipliers)[0]
scaling = scaling0
if options.mesh_size is not None:
scaling *= options.mesh_size / size
output('scaling factor of periodic cell mesh coordinates:', scaling)
output('new mesh size with applied unit multipliers:', scaling * size)
pb.domain.mesh.coors[:] *= scaling
pb.set_mesh_coors(pb.domain.mesh.coors, update_fields=True)
bzone = 2.0 * nm.pi / (scaling * size)
output('1. Brillouin zone size:', bzone * scaling0)
output('1. Brillouin zone size with applied unit multipliers:', bzone)
pb.time_update()
pb.update_materials()
# Assemble the matrices.
mtxs = {}
for key, eq in pb.equations.iteritems():
mtxs[key] = mtx = pb.mtx_a.copy()
mtx = eq.evaluate(mode='weak', dw_mode='matrix', asm_obj=mtx)
mtx.eliminate_zeros()
output_array_stats(mtx.data, 'nonzeros in %s' % key)
output('symmetry checks:')
output('%s - %s^T:' % (key, key), max_diff_csr(mtx, mtx.T))
output('%s - %s^H:' % (key, key), max_diff_csr(mtx, mtx.H))
return pb, wdir, bzone, mtxs
def setup_n_eigs(options, pb, mtxs):
"""
Setup the numbers of eigenvalues based on options and numbers of DOFs.
"""
solver_n_eigs = n_eigs = options.n_eigs
n_dof = mtxs['K'].shape[0]
if options.mode == 'omega':
if options.n_eigs > n_dof:
n_eigs = n_dof
solver_n_eigs = None
else:
if options.n_eigs > 2 * n_dof:
n_eigs = 2 * n_dof
solver_n_eigs = None
return solver_n_eigs, n_eigs
def build_evp_matrices(mtxs, val, mode, pb):
"""
Build the matrices of the dispersion eigenvalue problem.
"""
if mode == 'omega':
mtx_a = mtxs['K'] + val**2 * mtxs['S'] + val * mtxs['R']
output('A - A^H:', max_diff_csr(mtx_a, mtx_a.H))
evp_mtxs = (mtx_a, mtxs['M'])
else:
evp_mtxs = (mtxs['S'], mtxs['R'], mtxs['K'] - val**2 * mtxs['M'])
return evp_mtxs
def process_evp_results(eigs, svecs, val, wdir, bzone, pb, mtxs, options,
std_wave_fun=None):
"""
Transform eigenvalues to either omegas or kappas, depending on `mode`.
Transform eigenvectors, if available, depending on `mode`.
Return also the values to log.
"""
if options.mode == 'omega':
omegas = nm.sqrt(eigs)
output('eigs, omegas:')
for ii, om in enumerate(omegas):
output('{:>3}. {: .10e}, {:.10e}'.format(ii, eigs[ii], om))
if options.stepper == 'linear':
out = tuple(eigs) + tuple(omegas)
else:
out = tuple(val * wdir) + tuple(omegas)
if std_wave_fun is not None:
out = out + std_wave_fun(val, wdir)
return omegas, svecs, out
else:
kappas = eigs.copy()
rks = kappas.copy()
# Mask modes far from 1. Brillouin zone.
max_kappa = 1.2 * bzone
kappas[kappas.real > max_kappa] = nm.nan
# Mask non-physical modes.
kappas[kappas.real < 0] = nm.nan
kappas[nm.abs(kappas.imag) > 1e-10] = nm.nan
out = tuple(kappas.real)
output('raw kappas, masked real part:',)
for ii, kr in enumerate(kappas.real):
output('{:>3}. {: 23.5e}, {:.10e}'.format(ii, rks[ii], kr))
if svecs is not None:
n_dof = mtxs['K'].shape[0]
# Select only vectors corresponding to physical modes.
ii = nm.isfinite(kappas.real)
svecs = svecs[:n_dof, ii]
if std_wave_fun is not None:
out = out + tuple(ii if ii <= max_kappa else nm.nan
for ii in std_wave_fun(val, wdir))
return kappas, svecs, out
helps = {
'pars' :
'material parameters in Y1, Y2 subdomains in basic units'
' [default: %(default)s]',
'conf' :
'if given, an alternative problem description file with apply_units() and'
' define() functions [default: %(default)s]',
'define_kwargs' : 'additional keyword arguments passed to define()',
'mesh_size' :
'desired mesh size (max. of bounding box dimensions) in basic units'
' - the input periodic cell mesh is rescaled to this size'
' [default: %(default)s]',
'unit_multipliers' :
'basic unit multipliers (time, length, mass) [default: %(default)s]',
'plane' :
'for 2D problems, plane strain or stress hypothesis selection'
' [default: %(default)s]',
'wave_dir' : 'the wave vector direction (will be normalized)'
' [default: %(default)s]',
'mode' : 'solution mode: omega = solve a generalized EVP for omega,'
' kappa = solve a quadratic generalized EVP for kappa'
' [default: %(default)s]',
'stepper' : 'the range stepper. For "brillouin", only the number'
' of items from --range is used'
' [default: %(default)s]',
'range' : 'the wave vector magnitude / frequency range'
' (like numpy.linspace) depending on the mode option'
' [default: %(default)s]',
'order' : 'displacement field approximation order [default: %(default)s]',
'refine' : 'number of uniform mesh refinements [default: %(default)s]',
'n_eigs' : 'the number of eigenvalues to compute [default: %(default)s]',
'eigs_only' : 'compute only eigenvalues, not eigenvectors',
'post_process' : 'post-process eigenvectors',
'solver_conf' : 'eigenvalue problem solver configuration options'
' [default: %(default)s]',
'save_regions' : 'save defined regions into'
' <output_directory>/regions.vtk',
'save_materials' : 'save material parameters into'
' <output_directory>/materials.vtk',
'log_std_waves' : 'log also standard pressure dilatation and shear waves',
'no_legends' :
'do not show legends in the log plots',
'no_show' :
'do not show the log figure',
'silent' : 'do not print messages to screen',
'clear' :
'clear old solution files from output directory',
'output_dir' :
'output directory [default: %(default)s]',
'mesh_filename' :
'input periodic cell mesh file name [default: %(default)s]',
}
def main():
# Aluminium and epoxy.
default_pars = '70e9,0.35,2.799e3, 3.8e9,0.27,1.142e3'
default_solver_conf = ("kind='eig.scipy',method='eigsh',tol=1.0e-5,"
"maxiter=1000,which='LM',sigma=0.0")
parser = ArgumentParser(description=__doc__,
formatter_class=RawDescriptionHelpFormatter)
parser.add_argument('--pars', metavar='young1,poisson1,density1'
',young2,poisson2,density2',
action='store', dest='pars',
default=default_pars, help=helps['pars'])
parser.add_argument('--conf', metavar='filename',
action='store', dest='conf',
default=None, help=helps['conf'])
parser.add_argument('--define-kwargs', metavar='dict-like',
action='store', dest='define_kwargs',
default=None, help=helps['define_kwargs'])
parser.add_argument('--mesh-size', type=float, metavar='float',
action='store', dest='mesh_size',
default=None, help=helps['mesh_size'])
parser.add_argument('--unit-multipliers',
metavar='c_time,c_length,c_mass',
action='store', dest='unit_multipliers',
default='1.0,1.0,1.0', help=helps['unit_multipliers'])
parser.add_argument('--plane', action='store', dest='plane',
choices=['strain', 'stress'],
default='strain', help=helps['plane'])
parser.add_argument('--wave-dir', metavar='float,float[,float]',
action='store', dest='wave_dir',
default='1.0,0.0,0.0', help=helps['wave_dir'])
parser.add_argument('--mode', action='store', dest='mode',
choices=['omega', 'kappa'],
default='omega', help=helps['mode'])
parser.add_argument('--stepper', action='store', dest='stepper',
choices=['linear', 'brillouin'],
default='linear', help=helps['stepper'])
parser.add_argument('--range', metavar='start,stop,count',
action='store', dest='range',
default='0,6.4,33', help=helps['range'])
parser.add_argument('--order', metavar='int', type=int,
action='store', dest='order',
default=1, help=helps['order'])
parser.add_argument('--refine', metavar='int', type=int,
action='store', dest='refine',
default=0, help=helps['refine'])
parser.add_argument('-n', '--n-eigs', metavar='int', type=int,
action='store', dest='n_eigs',
default=6, help=helps['n_eigs'])
group = parser.add_mutually_exclusive_group()
group.add_argument('--eigs-only',
action='store_true', dest='eigs_only',
default=False, help=helps['eigs_only'])
group.add_argument('--post-process',
action='store_true', dest='post_process',
default=False, help=helps['post_process'])
parser.add_argument('--solver-conf', metavar='dict-like',
action='store', dest='solver_conf',
default=default_solver_conf, help=helps['solver_conf'])
parser.add_argument('--save-regions',
action='store_true', dest='save_regions',
default=False, help=helps['save_regions'])
parser.add_argument('--save-materials',
action='store_true', dest='save_materials',
default=False, help=helps['save_materials'])
parser.add_argument('--log-std-waves',
action='store_true', dest='log_std_waves',
default=False, help=helps['log_std_waves'])
parser.add_argument('--no-legends',
action='store_false', dest='show_legends',
default=True, help=helps['no_legends'])
parser.add_argument('--no-show',
action='store_false', dest='show',
default=True, help=helps['no_show'])
parser.add_argument('--silent',
action='store_true', dest='silent',
default=False, help=helps['silent'])
parser.add_argument('-c', '--clear',
action='store_true', dest='clear',
default=False, help=helps['clear'])
parser.add_argument('-o', '--output-dir', metavar='path',
action='store', dest='output_dir',
default='output', help=helps['output_dir'])
parser.add_argument('mesh_filename', default='',
help=helps['mesh_filename'])
options = parser.parse_args()
output_dir = options.output_dir
output.set_output(filename=os.path.join(output_dir,'output_log.txt'),
combined=options.silent == False)
if options.conf is not None:
mod = import_file(options.conf)
else:
mod = sys.modules[__name__]
apply_units = mod.apply_units
define = mod.define
set_wave_dir = mod.set_wave_dir
setup_n_eigs = mod.setup_n_eigs
build_evp_matrices = mod.build_evp_matrices
save_materials = mod.save_materials
get_std_wave_fun = mod.get_std_wave_fun
get_stepper = mod.get_stepper
process_evp_results = mod.process_evp_results
options.pars = [float(ii) for ii in options.pars.split(',')]
options.unit_multipliers = [float(ii)
for ii in options.unit_multipliers.split(',')]
options.wave_dir = [float(ii)
for ii in options.wave_dir.split(',')]
aux = options.range.split(',')
options.range = [float(aux[0]), float(aux[1]), int(aux[2])]
options.solver_conf = dict_from_string(options.solver_conf)
options.define_kwargs = dict_from_string(options.define_kwargs)
if options.clear:
remove_files_patterns(output_dir,
['*.h5', '*.vtk', '*.txt'],
ignores=['output_log.txt'],
verbose=True)
filename = os.path.join(output_dir, 'options.txt')
ensure_path(filename)
save_options(filename, [('options', vars(options))],
quote_command_line=True)
pars = apply_units(options.pars, options.unit_multipliers)
output('material parameters with applied unit multipliers:')
output(pars)
if options.mode == 'omega':
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['wave_number', 'wave_number'],
options.unit_multipliers)
output('wave number range with applied unit multipliers:', rng)
else:
if options.stepper == 'brillouin':
raise ValueError('Cannot use "brillouin" stepper in kappa mode!')
rng = copy(options.range)
rng[:2] = apply_unit_multipliers(options.range[:2],
['frequency', 'frequency'],
options.unit_multipliers)
output('frequency range with applied unit multipliers:', rng)
pb, wdir, bzone, mtxs = assemble_matrices(define, mod, pars, set_wave_dir,
options)
dim = pb.domain.shape.dim
if dim != 2:
options.plane = 'strain'
if options.save_regions:
pb.save_regions_as_groups(os.path.join(output_dir, 'regions'))
if options.save_materials:
save_materials(output_dir, pb, options)
conf = pb.solver_confs['eig']
eig_solver = Solver.any_from_conf(conf)
n_eigs, options.n_eigs = setup_n_eigs(options, pb, mtxs)
get_color = lambda ii: plt.cm.viridis((float(ii) / (options.n_eigs - 1)))
plot_kwargs = [{'color' : get_color(ii), 'ls' : '', 'marker' : 'o'}
for ii in range(options.n_eigs)]
get_color_dim = lambda ii: plt.cm.viridis((float(ii) / (dim-1)))
plot_kwargs_dim = [{'color' : get_color_dim(ii), 'ls' : '', 'marker' : 'o'}
for ii in range(dim)]
log_names = []
log_plot_kwargs = []
if options.log_std_waves:
std_wave_fun, log_names, log_plot_kwargs = get_std_wave_fun(
pb, options)
else:
std_wave_fun = None
stepper = get_stepper(rng, pb, options)
if options.mode == 'omega':
eigenshapes_filename = os.path.join(output_dir,
'frequency-eigenshapes-%s.vtk'
% stepper.suffix)
if options.stepper == 'linear':
log = Log([[r'$\lambda_{%d}$' % ii for ii in range(options.n_eigs)],
[r'$\omega_{%d}$'
% ii for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs, plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * options.n_eigs,
['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear', 'linear'],
xlabels=[r'$\kappa$', r'$\kappa$'],
ylabels=[r'eigenvalues $\lambda_i$',
r'frequencies $\omega_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'frequencies.txt'),
aggregate=1000, sleep=0.1)
else:
log = Log([[r'$\kappa_{%d}$'% ii for ii in range(dim)],
[r'$\omega_{%d}$'
% ii for ii in range(options.n_eigs)] + log_names],
plot_kwargs=[plot_kwargs_dim,
plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * dim,
['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear', 'linear'],
xlabels=[r'', r''],
ylabels=[r'wave vector $\kappa$',
r'frequencies $\omega_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'frequencies.txt'),
aggregate=1000, sleep=0.1)
for aux in stepper:
if options.stepper == 'linear':
iv, wmag = aux
else:
iv, wmag, wdir = aux
output('step %d: wave vector %s' % (iv, wmag * wdir))
if options.stepper == 'brillouin':
pb, _, bzone, mtxs = assemble_matrices(
define, mod, pars, set_wave_dir, options, wdir=wdir)
evp_mtxs = build_evp_matrices(mtxs, wmag, options.mode, pb)
if options.eigs_only:
eigs = eig_solver(*evp_mtxs, n_eigs=n_eigs,
eigenvectors=False)
svecs = None
else:
eigs, svecs = eig_solver(*evp_mtxs, n_eigs=n_eigs,
eigenvectors=True)
omegas, svecs, out = process_evp_results(
eigs, svecs, wmag, wdir, bzone, pb, mtxs, options,
std_wave_fun=std_wave_fun
)
if options.stepper == 'linear':
log(*out, x=[wmag, wmag])
else:
log(*out, x=[iv, iv])
save_eigenvectors(eigenshapes_filename % iv, svecs, wmag, wdir, pb)
gc.collect()
log(save_figure=os.path.join(output_dir, 'frequencies.png'))
log(finished=True)
else:
eigenshapes_filename = os.path.join(output_dir,
'wave-number-eigenshapes-%s.vtk'
% stepper.suffix)
log = Log([[r'$\kappa_{%d}$' % ii for ii in range(options.n_eigs)]
+ log_names],
plot_kwargs=[plot_kwargs + log_plot_kwargs],
formats=[['{:.5e}'] * (options.n_eigs + len(log_names))],
yscales=['linear'],
xlabels=[r'$\omega$'],
ylabels=[r'wave numbers $\kappa_i$'],
show_legends=options.show_legends,
is_plot=options.show,
log_filename=os.path.join(output_dir, 'wave-numbers.txt'),
aggregate=1000, sleep=0.1)
for io, omega in stepper:
|
output('step %d: frequency %s' % (io, omega))
|
sfepy.base.base.output
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym =
|
dim2sym(dim)
|
sfepy.mechanics.tensors.dim2sym
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials =
|
Materials(materials)
|
sfepy.discrete.Materials
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables =
|
Variables(variables)
|
sfepy.discrete.Variables
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Test(TestCommon):
@staticmethod
def from_conf(conf, options):
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
domains = []
for filename in filename_meshes:
mesh = Mesh.from_file(filename)
domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),
mesh)
domain.create_region('Omega', 'all')
domain.create_region('Gamma', 'vertices of surface', 'facet')
domains.append(domain)
integral =
|
Integral('i', order=3)
|
sfepy.discrete.Integral
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Test(TestCommon):
@staticmethod
def from_conf(conf, options):
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
domains = []
for filename in filename_meshes:
mesh =
|
Mesh.from_file(filename)
|
sfepy.discrete.fem.Mesh.from_file
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Test(TestCommon):
@staticmethod
def from_conf(conf, options):
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
domains = []
for filename in filename_meshes:
mesh = Mesh.from_file(filename)
domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),
mesh)
domain.create_region('Omega', 'all')
domain.create_region('Gamma', 'vertices of surface', 'facet')
domains.append(domain)
integral = Integral('i', order=3)
qp_coors, qp_weights = integral.get_qp('3_8')
custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,
order='custom')
test = Test(domains=domains, integral=integral,
custom_integral=custom_integral,
conf=conf, options=options)
return test
def test_term_call_modes(self):
from sfepy.terms import term_table
ok = True
failed = []
for domain in self.domains:
self.report('domain: %s' % domain.name)
domain_geometry = list(domain.geom_els.values())[0].name
if domain.shape.dim != domain.shape.tdim:
domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)
for _, term_cls in
|
ordered_iteritems(term_table)
|
sfepy.base.base.ordered_iteritems
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat =
|
Material('m%d' % ii, values=values)
|
sfepy.discrete.Material
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Test(TestCommon):
@staticmethod
def from_conf(conf, options):
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
domains = []
for filename in filename_meshes:
mesh = Mesh.from_file(filename)
domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),
mesh)
domain.create_region('Omega', 'all')
domain.create_region('Gamma', 'vertices of surface', 'facet')
domains.append(domain)
integral = Integral('i', order=3)
qp_coors, qp_weights = integral.get_qp('3_8')
custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,
order='custom')
test = Test(domains=domains, integral=integral,
custom_integral=custom_integral,
conf=conf, options=options)
return test
def test_term_call_modes(self):
from sfepy.terms import term_table
ok = True
failed = []
for domain in self.domains:
self.report('domain: %s' % domain.name)
domain_geometry = list(domain.geom_els.values())[0].name
if domain.shape.dim != domain.shape.tdim:
domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)
for _, term_cls in ordered_iteritems(term_table):
if (domain_geometry not in term_cls.geometries) \
or ("dg" in term_cls.name) \
or (term_cls.name == "dw_ns_dot_grad_s"):
continue
vint = ('volume', 'point', 'custom')
rname = 'Omega' if term_cls.integration in vint else 'Gamma'
self.report('<-- %s ...' % term_cls.name)
if rname == 'Gamma' and domain.mesh.dim == 1:
self.report('--> 1D Gamma region: not tested!')
elif term_cls.arg_shapes:
try:
_ok = self._test_single_term(term_cls, domain, rname)
except:
_ok = False
if not _ok:
failed.append((domain.name, term_cls.name))
ok = ok and _ok
self.report('--> ok: %s' % _ok)
else:
self.report('--> not tested!')
self.report('failed:', failed)
return ok
def _test_single_term(self, term_cls, domain, rname):
from sfepy.terms import Term
from sfepy.terms.terms import get_arg_kinds
ok = True
term_call = term_cls.name + '(%s)'
arg_shapes_list = term_cls.arg_shapes
if not isinstance(arg_shapes_list, list):
arg_shapes_list = [arg_shapes_list]
if term_cls.integration != 'custom':
integral = self.integral
else:
integral = self.custom_integral
poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange')
prev_shapes = {}
for _arg_shapes in arg_shapes_list:
# Unset shapes are taken from the previous iteration.
arg_shapes = copy(prev_shapes)
arg_shapes.update(_arg_shapes)
prev_shapes = arg_shapes
self.report('arg_shapes:', arg_shapes)
arg_types = term_cls.arg_types
if not isinstance(arg_types[0], tuple):
arg_types = (arg_types,)
for iat, ats in enumerate(arg_types):
self.report('arg_types:', ats)
arg_kinds =
|
get_arg_kinds(ats)
|
sfepy.terms.terms.get_arg_kinds
|
from __future__ import absolute_import
from copy import copy
import numpy as nm
from sfepy.base.testing import TestCommon
from sfepy.base.base import ordered_iteritems
from sfepy import data_dir
filename_meshes = [data_dir + '/meshes/elements/%s_2.mesh' % geom
for geom in ['1_2', '2_3', '2_4', '3_4', '3_8', '3_2_4']]
def make_term_args(arg_shapes, arg_kinds, arg_types, ats_mode, domain,
material_value=None, poly_space_base=None):
from sfepy.base.base import basestr
from sfepy.discrete import FieldVariable, Material, Variables, Materials
from sfepy.discrete.fem import Field
from sfepy.solvers.ts import TimeStepper
from sfepy.mechanics.tensors import dim2sym
omega = domain.regions['Omega']
dim = domain.shape.dim
sym = dim2sym(dim)
def _parse_scalar_shape(sh):
if isinstance(sh, basestr):
if sh == 'D':
return dim
elif sh == 'D2':
return dim**2
elif sh == 'S':
return sym
elif sh == 'N': # General number ;)
return 1
else:
return int(sh)
else:
return sh
def _parse_tuple_shape(sh):
if isinstance(sh, basestr):
return [_parse_scalar_shape(ii.strip()) for ii in sh.split(',')]
else:
return (int(sh),)
args = {}
str_args = []
materials = []
variables = []
for ii, arg_kind in enumerate(arg_kinds):
if arg_kind != 'ts':
if ats_mode is not None:
extended_ats = arg_types[ii] + ('/%s' % ats_mode)
else:
extended_ats = arg_types[ii]
try:
sh = arg_shapes[arg_types[ii]]
except KeyError:
sh = arg_shapes[extended_ats]
if arg_kind.endswith('variable'):
shape = _parse_scalar_shape(sh[0] if isinstance(sh, tuple) else sh)
field = Field.from_args('f%d' % ii, nm.float64, shape, omega,
approx_order=1,
poly_space_base=poly_space_base)
if arg_kind == 'virtual_variable':
if sh[1] is not None:
istate = arg_types.index(sh[1])
else:
# Only virtual variable in arguments.
istate = -1
# -> Make fake variable.
var = FieldVariable('u-1', 'unknown', field)
var.set_constant(0.0)
variables.append(var)
var = FieldVariable('v', 'test', field,
primary_var_name='u%d' % istate)
elif arg_kind == 'state_variable':
var = FieldVariable('u%d' % ii, 'unknown', field)
var.set_constant(0.0)
elif arg_kind == 'parameter_variable':
var = FieldVariable('p%d' % ii, 'parameter', field,
primary_var_name='(set-to-None)')
var.set_constant(0.0)
variables.append(var)
str_args.append(var.name)
args[var.name] = var
elif arg_kind.endswith('material'):
if sh is None: # Switched-off opt_material.
continue
prefix = ''
if isinstance(sh, basestr):
aux = sh.split(':')
if len(aux) == 2:
prefix, sh = aux
if material_value is None:
material_value = 1.0
shape = _parse_tuple_shape(sh)
if (len(shape) > 1) or (shape[0] > 1):
if ((len(shape) == 2) and (shape[0] == shape[1])
and (material_value != 0.0)):
# Identity matrix.
val = nm.eye(shape[0], dtype=nm.float64)
else:
# Array.
val = nm.empty(shape, dtype=nm.float64)
val.fill(material_value)
values = {'%sc%d' % (prefix, ii)
: val}
elif (len(shape) == 1) and (shape[0] == 1):
# Single scalar as a special value.
values = {'.c%d' % ii : material_value}
else:
raise ValueError('wrong material shape! (%s)' % shape)
mat = Material('m%d' % ii, values=values)
materials.append(mat)
str_args.append(mat.name + '.' + 'c%d' % ii)
args[mat.name] = mat
elif arg_kind == 'ts':
ts = TimeStepper(0.0, 1.0, 1.0, 5)
str_args.append('ts')
args['ts'] = ts
else:
str_args.append('user%d' % ii)
args[str_args[-1]] = None
materials = Materials(materials)
variables = Variables(variables)
return args, str_args, materials, variables
class Test(TestCommon):
@staticmethod
def from_conf(conf, options):
from sfepy.discrete import Integral
from sfepy.discrete.fem import Mesh, FEDomain
domains = []
for filename in filename_meshes:
mesh = Mesh.from_file(filename)
domain = FEDomain('domain_%s' % mesh.name.replace(data_dir, ''),
mesh)
domain.create_region('Omega', 'all')
domain.create_region('Gamma', 'vertices of surface', 'facet')
domains.append(domain)
integral = Integral('i', order=3)
qp_coors, qp_weights = integral.get_qp('3_8')
custom_integral = Integral('i', coors=qp_coors, weights=qp_weights,
order='custom')
test = Test(domains=domains, integral=integral,
custom_integral=custom_integral,
conf=conf, options=options)
return test
def test_term_call_modes(self):
from sfepy.terms import term_table
ok = True
failed = []
for domain in self.domains:
self.report('domain: %s' % domain.name)
domain_geometry = list(domain.geom_els.values())[0].name
if domain.shape.dim != domain.shape.tdim:
domain_geometry = '%d_%s' % (domain.shape.dim, domain_geometry)
for _, term_cls in ordered_iteritems(term_table):
if (domain_geometry not in term_cls.geometries) \
or ("dg" in term_cls.name) \
or (term_cls.name == "dw_ns_dot_grad_s"):
continue
vint = ('volume', 'point', 'custom')
rname = 'Omega' if term_cls.integration in vint else 'Gamma'
self.report('<-- %s ...' % term_cls.name)
if rname == 'Gamma' and domain.mesh.dim == 1:
self.report('--> 1D Gamma region: not tested!')
elif term_cls.arg_shapes:
try:
_ok = self._test_single_term(term_cls, domain, rname)
except:
_ok = False
if not _ok:
failed.append((domain.name, term_cls.name))
ok = ok and _ok
self.report('--> ok: %s' % _ok)
else:
self.report('--> not tested!')
self.report('failed:', failed)
return ok
def _test_single_term(self, term_cls, domain, rname):
from sfepy.terms import Term
from sfepy.terms.terms import get_arg_kinds
ok = True
term_call = term_cls.name + '(%s)'
arg_shapes_list = term_cls.arg_shapes
if not isinstance(arg_shapes_list, list):
arg_shapes_list = [arg_shapes_list]
if term_cls.integration != 'custom':
integral = self.integral
else:
integral = self.custom_integral
poly_space_base = getattr(term_cls, 'poly_space_base', 'lagrange')
prev_shapes = {}
for _arg_shapes in arg_shapes_list:
# Unset shapes are taken from the previous iteration.
arg_shapes = copy(prev_shapes)
arg_shapes.update(_arg_shapes)
prev_shapes = arg_shapes
self.report('arg_shapes:', arg_shapes)
arg_types = term_cls.arg_types
if not isinstance(arg_types[0], tuple):
arg_types = (arg_types,)
for iat, ats in enumerate(arg_types):
self.report('arg_types:', ats)
arg_kinds = get_arg_kinds(ats)
modes = getattr(term_cls, 'modes', None)
mode = modes[iat] if modes is not None else None
if 'dw_s_dot_grad_i_s' in term_cls.name:
material_value = 0.0
else:
material_value = 1.0
aux = make_term_args(arg_shapes, arg_kinds, ats, mode, domain,
material_value=material_value,
poly_space_base=poly_space_base)
args, str_args, materials, variables = aux
self.report('args:', str_args)
name = term_call % (', '.join(str_args))
term =
|
Term.new(name, integral, domain.regions[rname], **args)
|
sfepy.terms.Term.new
|
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