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RROMPy/rrompy/hfengines/fenics/helmholtz_cavity_scattering_problem_engine.py
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helmholtz_cavity_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 fenics as fen
from rrompy.hfengines.fenics.scattering_problem_engine import ScatteringProblemEngine
__all__ = ['HelmholtzCavityScatteringProblemEngine']
class HelmholtzCavityScatteringProblemEngine(ScatteringProblemEngine):
"""
Solver for scattering problem inside a cavity with parametric wavenumber.
- \Delta u - omega^2 * n^2 * u = 0 in \Omega
u = 0 on \Gamma_D
\partial_nu - i k u = 0 on \Gamma_R
with exact solution a transmitted plane wave.
"""
def __init__(self, kappa:float, n:int, gamma : float = 0.,
signR : int = -1):
super().__init__()
mesh = fen.RectangleMesh(fen.Point(0,0), fen.Point(np.pi,np.pi), n, n)
self.V = fen.FunctionSpace(mesh, "P", 3)
self.RobinBoundary = (lambda x, on_boundary: on_boundary
and np.isclose(x[1], np.pi))
self.DirichletBoundary = "REST"
import sympy as sp
x, y = sp.symbols('x[0] x[1]', real=True)
wex = 4/np.pi**4 * x * y * (x - np.pi) * (y - 2 * np.pi)
phiex = signR * kappa * (x * gamma + y)
uex = wex * sp.exp(-1.j * phiex)
fex = - uex.diff(x, 2) - uex.diff(y, 2) - kappa**2 * uex
forcingTerm = [sp.printing.ccode(sp.simplify(sp.re(fex))),
sp.printing.ccode(sp.simplify(sp.im(fex)))]
self.forcingTerm = [fen.Expression(x, degree = 3) for x in forcingTerm]
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