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scattering_problem_engine.py
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Tue, Feb 18, 07:09

scattering_problem_engine.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 scipy.sparse as scsp
import fenics as fen
from rrompy.utilities.base.types import Np1D, Np2D, Tuple, List
from rrompy.utilities.base.fenics import fenZERO
from .helmholtz_base_problem_engine import HelmholtzBaseProblemEngine
__all__ = ['ScatteringProblemEngine']
class ScatteringProblemEngine(HelmholtzBaseProblemEngine):
"""
Solver for scattering problems with parametric wavenumber.
- \nabla \cdot (a \nabla u) - omega^2 * n**2 * u = f in \Omega
u = u0 on \Gamma_D
\partial_nu = g1 on \Gamma_N
\partial_nu +- i k u = g2 on \Gamma_R
Attributes:
signR: Sign in ABC.
omega: Value of omega.
diffusivity: Value of a.
refractionIndex: Value of n.
forcingTerm: Value of f.
DirichletDatum: Value of u0.
NeumannDatum: Value of g1.
RobinDatumG: Value of g2.
DirichletBoundary: Function handle to \Gamma_D.
NeumannBoundary: Function handle to \Gamma_N.
RobinBoundary: Function handle to \Gamma_R.
V: Real FE space.
u: Generic trial functions for variational form evaluation.
v: Generic test functions for variational form evaluation.
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.
A2: Scipy sparse array representation (in CSC format) of A1.
b0: Numpy array representation of b0.
As: Scipy sparse array representation (in CSC format) of As.
bs: Numpy array representation of bs.
"""
signR = - 1.
def A(self, mu:complex, der : int = 0) -> Np2D:
"""Assemble (derivative of) operator of linear system."""
if der > 2 or der < 0:
d = self.V.dim()
return scsp.csr_matrix((np.zeros(0), np.zeros(0), np.zeros(d + 1)),
shape = (d, d), dtype = np.complex)
self.autoSetDS()
if der <= 0 and not hasattr(self, "A0"):
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
aRe, aIm = self.diffusivity
a0Re = aRe * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
a0Im = aIm * fen.dot(fen.grad(self.u), fen.grad(self.v)) * fen.dx
A0Re = fen.assemble(a0Re)
A0Im = fen.assemble(a0Im)
DirichletBC0.apply(A0Re)
DirichletBC0.zero(A0Im)
A0ReMat = fen.as_backend_type(A0Re).mat()
A0ImMat = fen.as_backend_type(A0Im).mat()
A0Rer, A0Rec, A0Rev = A0ReMat.getValuesCSR()
A0Imr, A0Imc, A0Imv = A0ImMat.getValuesCSR()
self.A0 = (scsp.csr_matrix((A0Rev, A0Rec, A0Rer),
shape = A0ReMat.size)
+ 1.j * scsp.csr_matrix((A0Imv, A0Imc, A0Imr),
shape = A0ImMat.size))
if der <= 1 and not hasattr(self, "A1"):
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
a1 = fen.dot(self.u, self.v) * self.ds(1)
A1 = fen.assemble(a1)
DirichletBC0.zero(A1)
A1Mat = fen.as_backend_type(A1).mat()
A1r, A1c, A1v = A1Mat.getValuesCSR()
self.A1 = self.signR * 1.j * scsp.csr_matrix((A1v, A1c, A1r),
shape = A1Mat.size)
if der <= 2 and not hasattr(self, "A2"):
DirichletBC0 = fen.DirichletBC(self.V, fenZERO,
self.DirichletBoundary)
nRe, nIm = self.refractionIndex
n2Re, n2Im = nRe * nRe - nIm * nIm, 2 * nRe * nIm
a2Re = - n2Re * fen.dot(self.u, self.v) * fen.dx
a2Im = - n2Im * fen.dot(self.u, self.v) * fen.dx
A2Re = fen.assemble(a2Re)
A2Im = fen.assemble(a2Im)
DirichletBC0.zero(A2Re)
DirichletBC0.zero(A2Im)
A2ReMat = fen.as_backend_type(A2Re).mat()
A2ImMat = fen.as_backend_type(A2Im).mat()
A2Rer, A2Rec, A2Rev = A2ReMat.getValuesCSR()
A2Imr, A2Imc, A2Imv = A2ImMat.getValuesCSR()
self.A2 = (scsp.csr_matrix((A2Rev, A2Rec, A2Rer),
shape = A2ReMat.size)
+ 1.j * scsp.csr_matrix((A2Imv, A2Imc, A2Imr),
shape = A2ImMat.size))
if der == 0:
return self.A0 + mu * self.A1 + mu**2. * self.A2
if der == 1:
return self.A1 + 2 * mu * self.A2
return self.A2
def affineBlocksA(self, mu : complex = 0.) -> Tuple[List[Np2D], callable]:
"""Assemble affine blocks of operator of linear system."""
def lambdas(x, j):
if j == 0: return np.ones(np.size(x))
if j in [1, 2]: return np.power(self.rescaling(x)
- self.rescaling(mu), j)
raise Exception("Wrong j value.")
A0 = self.A(mu, 0)
A1 = self.A(mu, 1)
return [A0, A1, self.A2], lambdas
def affineBlocksb(self, mu : complex = 0.) -> Tuple[List[Np1D], callable]:
"""Assemble affine blocks of RHS of linear system."""
def lambdas(x, j):
if j == 0: return np.ones(np.size(x))
raise Exception("Wrong j value.")
self.b(mu, 0)
return [self.b0], lambdas

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