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RROMPy/rrompy/hfengines/fenics_engines/linear_elasticity_problem_engine.py
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linear_elasticity_problem_engine.py
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# Copyright (C) 2018-2020 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 rrompy.hfengines.base.linear_affine_engine import LinearAffineEngine
from rrompy.hfengines.base.vector_fenics_engine_base import \
VectorFenicsEngineBase
from rrompy.utilities.base.types import paramVal
from rrompy.solver.fenics import (fenZERO, fenZEROS, fenONE,
elasticNormMatrix, elasticDualNormMatrix)
from rrompy.utilities.base import verbosityManager as vbMng
from rrompy.parameter import checkParameter
from rrompy.solver.fenics import fenics2Sparse, fenics2Vector
__all__ = ['LinearElasticityProblemEngine']
class LinearElasticityProblemEngine(LinearAffineEngine,
VectorFenicsEngineBase):
"""
Solver for generic linear elasticity problems.
- div(lambda_ * div(u) * I + 2 * mu_ * epsilon(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.
cs: Numpy array representation of cs.
energyNormMatrix: Scipy sparse matrix representing inner product over
V.
energyNormDualMatrix: Scipy sparse matrix representing dual inner
product between Riesz representers V-V.
degree_threshold: Threshold for ufl expression interpolation degree.
lambda_: Value of lambda_.
mu_: Value of mu_.
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).
dsToBeSet: Whether ds needs to be set.
"""
_energyDualNormCompress = None
def __init__(self, mu0 : paramVal = [], degree_threshold : int = np.inf,
verbosity : int = 10, timestamp : bool = True):
super().__init__(degree_threshold = degree_threshold,
verbosity = verbosity, timestamp = timestamp)
self._affinePoly = True
self.lambda_ = fenONE
self.mu_ = fenONE
self.mu0 = checkParameter(mu0)
self.npar = self.mu0.shape[1]
self.RobinDatumH = fenZERO
@property
def V(self):
"""Value of V."""
return self._V
@V.setter
def V(self, V):
VectorFenicsEngineBase.V.fset(self, V)
self.forcingTerm = fenZEROS(self.V.mesh().topology().dim())
self.DirichletDatum = fenZEROS(self.V.mesh().topology().dim())
self.NeumannDatum = fenZEROS(self.V.mesh().topology().dim())
self.RobinDatumG = fenZEROS(self.V.mesh().topology().dim())
self.dsToBeSet = True
@property
def lambda_(self):
"""Value of lambda_."""
return self._lambda_
@lambda_.setter
def lambda_(self, lambda_):
self.resetAs()
if not isinstance(lambda_, (list, tuple,)):
lambda_ = [lambda_, fenZERO]
self._lambda_ = lambda_
@property
def mu_(self):
"""Value of mu_."""
return self._mu_
@mu_.setter
def mu_(self, mu_):
self.resetAs()
if not isinstance(mu_, (list, tuple,)):
mu_ = [mu_, fenZERO]
self._mu_ = mu_
@property
def forcingTerm(self):
"""Value of f."""
return self._forcingTerm
@forcingTerm.setter
def forcingTerm(self, forcingTerm):
self.resetbs()
if not isinstance(forcingTerm, (list, tuple,)):
forcingTerm = [forcingTerm,
fenZEROS(self.V.mesh().topology().dim())]
self._forcingTerm = forcingTerm
@property
def DirichletDatum(self):
"""Value of u0."""
return self._DirichletDatum
@DirichletDatum.setter
def DirichletDatum(self, DirichletDatum):
self.resetbs()
if not isinstance(DirichletDatum, (list, tuple,)):
DirichletDatum = [DirichletDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._DirichletDatum = DirichletDatum
@property
def NeumannDatum(self):
"""Value of g1."""
return self._NeumannDatum
@NeumannDatum.setter
def NeumannDatum(self, NeumannDatum):
self.resetbs()
if not isinstance(NeumannDatum, (list, tuple,)):
NeumannDatum = [NeumannDatum,
fenZEROS(self.V.mesh().topology().dim())]
self._NeumannDatum = NeumannDatum
@property
def RobinDatumG(self):
"""Value of g2."""
return self._RobinDatumG
@RobinDatumG.setter
def RobinDatumG(self, RobinDatumG):
self.resetbs()
if not isinstance(RobinDatumG, (list, tuple,)):
RobinDatumG = [RobinDatumG,
fenZEROS(self.V.mesh().topology().dim())]
self._RobinDatumG = RobinDatumG
@property
def RobinDatumH(self):
"""Value of h."""
return self._RobinDatumH
@RobinDatumH.setter
def RobinDatumH(self, RobinDatumH):
self.resetAs()
if not isinstance(RobinDatumH, (list, tuple,)):
RobinDatumH = [RobinDatumH, fenZERO]
self._RobinDatumH = RobinDatumH
@property
def DirichletBoundary(self):
"""Function handle to DirichletBoundary."""
return self.BCManager.DirichletBoundary
@DirichletBoundary.setter
def DirichletBoundary(self, DirichletBoundary):
self.resetAs()
self.resetbs()
self.BCManager.DirichletBoundary = DirichletBoundary
@property
def NeumannBoundary(self):
"""Function handle to NeumannBoundary."""
return self.BCManager.NeumannBoundary
@NeumannBoundary.setter
def NeumannBoundary(self, NeumannBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.NeumannBoundary = NeumannBoundary
@property
def RobinBoundary(self):
"""Function handle to RobinBoundary."""
return self.BCManager.RobinBoundary
@RobinBoundary.setter
def RobinBoundary(self, RobinBoundary):
self.resetAs()
self.resetbs()
self.dsToBeSet = True
self.BCManager.RobinBoundary = RobinBoundary
def buildEnergyNormForm(self):
"""
Build sparse matrix (in CSR format) representative of scalar product.
"""
vbMng(self, "INIT", "Assembling energy matrix.", 20)
self._energyNormMatrix = elasticNormMatrix(self.V, self.lambda_[0],
self.mu_[0])
vbMng(self, "DEL", "Done assembling energy matrix.", 20)
def buildEnergyNormDualForm(self):
"""
Build sparse matrix (in CSR format) representative of dual scalar
product without duality.
"""
vbMng(self, "INIT", "Assembling energy dual matrix.", 20)
self._energyNormDualMatrix = elasticDualNormMatrix(
self.V, self.lambda_[0], self.mu_[0],
compressRank = self._energyDualNormCompress)
vbMng(self, "DEL", "Done assembling energy dual matrix.", 20)
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)
def buildb(self):
"""Build terms of operator of linear system."""
if self.thbs[0] is None:
self.thbs = self.getMonomialWeights(self.nbs)
if self.bs[0] is None:
self.autoSetDS()
vbMng(self, "INIT", "Assembling forcing term b0.", 20)
u0Re, u0Im = self.DirichletDatum
fRe, fIm = self.forcingTerm
g1Re, g1Im = self.NeumannDatum
g2Re, g2Im = self.RobinDatumG
termNames = ["forcingTerm", "NeumannDatum", "RobinDatumG"]
parsRe = self.iterReduceQuadratureDegree(zip([fRe, g1Re, g2Re],
[x + "Real" for x in termNames]))
parsIm = self.iterReduceQuadratureDegree(zip([fIm, g1Im, g2Im],
[x + "Imag" for x in termNames]))
L0Re = (fen.inner(fRe, self.v) * fen.dx
+ fen.inner(g1Re, self.v) * self.ds(0)
+ fen.inner(g2Re, self.v) * self.ds(1))
L0Im = (fen.inner(fIm, self.v) * fen.dx
+ fen.inner(g1Im, self.v) * self.ds(0)
+ fen.inner(g2Im, self.v) * self.ds(1))
DBCR = fen.DirichletBC(self.V, u0Re, self.DirichletBoundary)
DBCI = fen.DirichletBC(self.V, u0Im, self.DirichletBoundary)
self.bs[0] = (fenics2Vector(L0Re, parsRe, DBCR, 1)
+ 1.j * fenics2Vector(L0Im, parsIm, DBCI, 1))
vbMng(self, "DEL", "Done assembling forcing term.", 20)
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