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helmholtz_square_bubble_problem_engine.py
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Created
Thu, Aug 8, 23:05
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2 KB
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text/x-python
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Sat, Aug 10, 23:05 (2 d)
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blob
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19736955
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R6746 RationalROMPy
helmholtz_square_bubble_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
.helmholtz_problem_engine
import
HelmholtzProblemEngine
__all__
=
[
'HelmholtzSquareBubbleProblemEngine'
]
class
HelmholtzSquareBubbleProblemEngine
(
HelmholtzProblemEngine
):
"""
Solver for square bubble Helmholtz problems with parametric wavenumber.
- \Delta u - omega^2 * u = f in \Omega
u = 0 on \Gamma_D
with exact solution square bubble times plane wave.
"""
def
__init__
(
self
,
kappa
:
float
,
theta
:
float
,
n
:
int
,
degree_threshold
:
int
=
np
.
inf
,
verbosity
:
int
=
10
,
timestamp
:
bool
=
True
):
super
()
.
__init__
(
mu0
=
[
kappa
],
degree_threshold
=
degree_threshold
,
verbosity
=
verbosity
,
timestamp
=
timestamp
)
pi
=
np
.
pi
mesh
=
fen
.
RectangleMesh
(
fen
.
Point
(
0
,
0
),
fen
.
Point
(
pi
,
pi
),
3
*
n
,
3
*
n
)
self
.
V
=
fen
.
FunctionSpace
(
mesh
,
"P"
,
1
)
c
,
s
=
np
.
cos
(
theta
),
np
.
sin
(
theta
)
x
,
y
=
fen
.
SpatialCoordinate
(
mesh
)[:]
C
=
16.
/
pi
**
4.
bR
=
C
*
2
*
(
x
*
(
pi
-
x
)
+
y
*
(
pi
-
y
))
bI
=
C
*
2
*
kappa
*
(
c
*
(
pi
-
2
*
x
)
*
y
*
(
pi
-
y
)
+
s
*
x
*
(
pi
-
x
)
*
(
pi
-
2
*
y
))
wR
=
fen
.
cos
(
kappa
*
(
c
*
x
+
s
*
y
))
wI
=
fen
.
sin
(
kappa
*
(
c
*
x
+
s
*
y
))
self
.
forcingTerm
=
[
bR
*
wR
+
bI
*
wI
,
bI
*
wR
-
bR
*
wI
]
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