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linear_elasticity_helmholtz_problem_engine_damped.py
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Sun, Apr 28, 19:05
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text/x-python
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Tue, Apr 30, 19:05 (2 d)
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R6746 RationalROMPy
linear_elasticity_helmholtz_problem_engine_damped.py
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# Copyright (C) 2018 by the RROMPy authors
#
# This file is part of RROMPy.
#
# RROMPy is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# RROMPy is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with RROMPy. If not, see <http://www.gnu.org/licenses/>.
#
import
numpy
as
np
import
fenics
as
fen
from
.linear_elasticity_helmholtz_problem_engine
import
\
LinearElasticityHelmholtzProblemEngine
from
rrompy.utilities.base.types
import
paramVal
from
rrompy.solver.fenics
import
fenZERO
,
fenZEROS
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.solver.fenics
import
fenics2Sparse
__all__
=
[
'LinearElasticityHelmholtzProblemEngineDamped'
]
class
LinearElasticityHelmholtzProblemEngineDamped
(
LinearElasticityHelmholtzProblemEngine
):
"""
Solver for generic linear elasticity Helmholtz problems with parametric
wavenumber.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(u))
- rho_ * (mu^2 - i * eta * mu) * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu + h u = g2 on \Gamma_R
Attributes:
verbosity: Verbosity level.
BCManager: Boundary condition manager.
V: Real vector FE space.
u: Generic vector trial functions for variational form evaluation.
v: Generic vector test functions for variational form evaluation.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing inner product
over V'.
dualityMatrix: Scipy sparse matrix representing duality V-V'.
energyNormPartialDualMatrix: Scipy sparse matrix representing dual
inner product between Riesz representers V-V.
degree_threshold: Threshold for ufl expression interpolation degree.
omega: Value of omega.
lambda_: Value of lambda_.
mu_: Value of mu_.
eta: Value of eta.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
RobinDatumH: Value of h.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
ds: Boundary measure 2-tuple (resp. for Neumann and Robin boundaries).
A0: Scipy sparse array representation (in CSC format) of A0.
A1: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
dsToBeSet: Whether ds needs to be set.
"""
def
__init__
(
self
,
mu0
:
paramVal
=
[
0.
],
degree_threshold
:
int
=
np
.
inf
,
homogeneized
:
bool
=
False
,
verbosity
:
int
=
10
,
timestamp
:
bool
=
True
):
super
()
.
__init__
(
mu0
=
[
mu0
],
degree_threshold
=
degree_threshold
,
homogeneized
=
homogeneized
,
verbosity
=
verbosity
,
timestamp
=
timestamp
)
self
.
_affinePoly
=
True
self
.
nAs
=
3
self
.
eta
=
fenZERO
self
.
rescalingExp
=
[
1.
]
@property
def
eta
(
self
):
"""Value of eta."""
return
self
.
_eta
@eta.setter
def
eta
(
self
,
eta
):
self
.
resetAs
()
if
not
isinstance
(
eta
,
(
list
,
tuple
,)):
eta
=
[
eta
,
fenZERO
]
self
.
_eta
=
eta
def
buildA
(
self
):
"""Build terms of operator of linear system."""
if
self
.
thAs
[
0
]
is
None
:
self
.
thAs
=
self
.
getMonomialWeights
(
self
.
nAs
)
if
self
.
As
[
0
]
is
None
:
self
.
autoSetDS
()
vbMng
(
self
,
"INIT"
,
"Assembling operator term A0."
,
20
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZEROS
(
self
.
V
.
mesh
()
.
topology
()
.
dim
()),
self
.
DirichletBoundary
)
lambda_Re
,
lambda_Im
=
self
.
lambda_
mu_Re
,
mu_Im
=
self
.
mu_
hRe
,
hIm
=
self
.
RobinDatumH
termNames
=
[
"lambda_"
,
"mu_"
,
"RobinDatumH"
]
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
(
[
lambda_Re
,
mu_Re
,
hRe
],
[
x
+
"Real"
for
x
in
termNames
]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
(
[
lambda_Im
,
mu_Re
,
hIm
],
[
x
+
"Imag"
for
x
in
termNames
]))
epsilon
=
lambda
u
:
0.5
*
(
fen
.
grad
(
u
)
+
fen
.
nabla_grad
(
u
))
sigma
=
lambda
u
,
l_
,
m_
:
(
l_
*
fen
.
div
(
u
)
*
fen
.
Identity
(
u
.
geometric_dimension
())
+
2.
*
m_
*
epsilon
(
u
))
a0Re
=
(
fen
.
inner
(
sigma
(
self
.
u
,
lambda_Re
,
mu_Re
),
epsilon
(
self
.
v
))
*
fen
.
dx
+
hRe
*
fen
.
inner
(
self
.
u
,
self
.
v
)
*
self
.
ds
(
1
))
a0Im
=
(
fen
.
inner
(
sigma
(
self
.
u
,
lambda_Im
,
mu_Im
),
epsilon
(
self
.
v
))
*
fen
.
dx
+
hIm
*
fen
.
inner
(
self
.
u
,
self
.
v
)
*
self
.
ds
(
1
))
self
.
As
[
0
]
=
(
fenics2Sparse
(
a0Re
,
parsRe
,
DirichletBC0
,
1
)
+
1.j
*
fenics2Sparse
(
a0Im
,
parsIm
,
DirichletBC0
,
0
))
vbMng
(
self
,
"DEL"
,
"Done assembling operator term."
,
20
)
if
self
.
As
[
1
]
is
None
:
vbMng
(
self
,
"INIT"
,
"Assembling operator term A1."
,
20
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZEROS
(
self
.
V
.
mesh
()
.
topology
()
.
dim
()),
self
.
DirichletBoundary
)
rho_Re
,
rho_Im
=
self
.
rho_
eta_Re
,
eta_Im
=
self
.
eta
termNames
=
[
"rho_"
,
"eta"
]
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
rho_Re
,
eta_Re
],
[
x
+
"Real"
for
x
in
termNames
]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
rho_Im
,
eta_Im
],
[
x
+
"Imag"
for
x
in
termNames
]))
a1Re
=
-
((
eta_Re
*
rho_Im
+
eta_Im
*
rho_Re
)
*
fen
.
inner
(
self
.
u
,
self
.
v
))
*
fen
.
dx
a1Im
=
((
eta_Re
*
rho_Re
-
eta_Im
*
rho_Im
)
*
fen
.
inner
(
self
.
u
,
self
.
v
))
*
fen
.
dx
self
.
As
[
1
]
=
(
fenics2Sparse
(
a1Re
,
parsRe
,
DirichletBC0
,
0
)
+
1.j
*
fenics2Sparse
(
a1Im
,
parsIm
,
DirichletBC0
,
0
))
vbMng
(
self
,
"DEL"
,
"Done assembling operator term."
,
20
)
if
self
.
As
[
2
]
is
None
:
vbMng
(
self
,
"INIT"
,
"Assembling operator term A2."
,
20
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZEROS
(
self
.
V
.
mesh
()
.
topology
()
.
dim
()),
self
.
DirichletBoundary
)
rho_Re
,
rho_Im
=
self
.
rho_
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
rho_Re
],
[
"rho_Real"
]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
rho_Im
],
[
"rho_Imag"
]))
a2Re
=
-
rho_Re
*
fen
.
inner
(
self
.
u
,
self
.
v
)
*
fen
.
dx
a2Im
=
-
rho_Im
*
fen
.
inner
(
self
.
u
,
self
.
v
)
*
fen
.
dx
self
.
As
[
2
]
=
(
fenics2Sparse
(
a2Re
,
parsRe
,
DirichletBC0
,
0
)
+
1.j
*
fenics2Sparse
(
a2Im
,
parsIm
,
DirichletBC0
,
0
))
vbMng
(
self
,
"DEL"
,
"Done assembling operator term."
,
20
)
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