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helmholtz_square_bubble_domain_problem_engine.py
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Tue, Apr 30, 23:09
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7 KB
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text/x-python
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Thu, May 2, 23:09 (2 d)
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R6746 RationalROMPy
helmholtz_square_bubble_domain_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
from
numpy.polynomial.polynomial
import
polyfit
as
fit
import
fenics
as
fen
from
rrompy.utilities.base.types
import
(
Np1D
,
ScOp
,
Tuple
,
List
,
FenExpr
,
paramVal
)
from
rrompy.solver.fenics
import
fenZERO
from
.helmholtz_problem_engine
import
HelmholtzProblemEngine
from
rrompy.utilities.base
import
verbosityManager
as
vbMng
from
rrompy.utilities.poly_fitting.polynomial
import
(
hashDerivativeToIdx
as
hashD
,
hashIdxToDerivative
as
hashI
)
from
rrompy.solver.fenics
import
fenics2Sparse
,
fenics2Vector
__all__
=
[
'HelmholtzSquareBubbleDomainProblemEngine'
]
class
HelmholtzSquareBubbleDomainProblemEngine
(
HelmholtzProblemEngine
):
"""
Solver for square bubble Helmholtz problems with parametric domain heigth.
- \Delta u - kappa^2 * u = f in \Omega_mu = [0,\pi] x [0,\mu\pi]
u = 0 on \Gamma_mu = \partial\Omega_mu
with exact solution square bubble times plane wave.
"""
def
__init__
(
self
,
kappa
:
float
,
theta
:
float
,
n
:
int
,
mu0
:
paramVal
=
[
1.
],
degree_threshold
:
int
=
np
.
inf
,
verbosity
:
int
=
10
,
timestamp
:
bool
=
True
):
super
()
.
__init__
(
mu0
=
mu0
,
degree_threshold
=
degree_threshold
,
verbosity
=
verbosity
,
timestamp
=
timestamp
)
self
.
nAs
,
self
.
nbs
=
3
,
15
self
.
kappa
=
kappa
self
.
theta
=
theta
self
.
forcingTermMu
=
np
.
nan
mesh
=
fen
.
RectangleMesh
(
fen
.
Point
(
0
,
0
),
fen
.
Point
(
np
.
pi
,
np
.
pi
),
3
*
n
,
3
*
n
)
self
.
V
=
fen
.
FunctionSpace
(
mesh
,
"P"
,
1
)
self
.
rescalingExp
=
[
1.
]
def
getForcingTerm
(
self
,
mu
:
paramVal
=
[])
->
Tuple
[
FenExpr
,
FenExpr
]:
"""Compute forcing term."""
vbMng
(
self
,
"INIT"
,
(
"Assembling base expression for forcing term "
"at {}."
)
.
format
(
mu
),
25
)
pi
=
np
.
pi
c
,
s
=
np
.
cos
(
self
.
theta
),
np
.
sin
(
self
.
theta
)
x
,
y
=
fen
.
SpatialCoordinate
(
self
.
V
.
mesh
())[:]
muR
,
muI
=
np
.
real
(
mu
),
np
.
imag
(
mu
)
mu2R
,
mu2I
=
np
.
real
(
mu
**
2.
),
np
.
imag
(
mu
**
2.
)
C
=
16.
/
pi
**
4.
bR
=
C
*
(
2
*
(
x
*
(
pi
-
x
)
+
y
*
(
pi
-
y
))
+
(
self
.
kappa
*
s
)
**
2.
*
(
mu2R
-
1.
)
*
x
*
(
pi
-
x
)
*
y
*
(
pi
-
y
))
bI
=
C
*
(
2
*
self
.
kappa
*
(
c
*
(
pi
-
2
*
x
)
*
y
*
(
pi
-
y
)
+
s
*
x
*
(
pi
-
x
)
*
(
pi
-
2
*
y
))
+
(
self
.
kappa
*
s
)
**
2.
*
mu2I
*
x
*
(
pi
-
x
)
*
y
*
(
pi
-
y
))
wR
=
(
fen
.
cos
(
self
.
kappa
*
(
c
*
x
+
s
*
muR
*
y
))
*
fen
.
exp
(
self
.
kappa
*
s
*
muI
*
y
))
wI
=
(
fen
.
sin
(
self
.
kappa
*
(
c
*
x
+
s
*
muR
*
y
))
*
fen
.
exp
(
self
.
kappa
*
s
*
muI
*
y
))
fRe
,
fIm
=
bR
*
wR
+
bI
*
wI
,
bI
*
wR
-
bR
*
wI
forcingTerm
=
[
mu2R
*
fRe
-
mu2I
*
fIm
+
fenZERO
,
mu2R
*
fIm
+
mu2I
*
fRe
+
fenZERO
]
vbMng
(
self
,
"DEL"
,
"Done assembling base expression."
,
25
)
return
forcingTerm
def
A
(
self
,
mu
:
paramVal
=
[],
der
:
List
[
int
]
=
0
)
->
ScOp
:
"""Assemble (derivative of) operator of linear system."""
mu
=
self
.
checkParameter
(
mu
)
if
not
hasattr
(
der
,
"__len__"
):
der
=
[
der
]
*
self
.
npar
derI
=
hashD
(
der
)
self
.
autoSetDS
()
if
derI
<=
0
and
self
.
As
[
0
]
is
None
:
vbMng
(
self
,
"INIT"
,
"Assembling operator term A0."
,
20
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
a0Re
=
fen
.
dot
(
self
.
u
.
dx
(
1
),
self
.
v
.
dx
(
1
))
*
fen
.
dx
self
.
As
[
0
]
=
fenics2Sparse
(
a0Re
,
{},
DirichletBC0
,
1
)
vbMng
(
self
,
"DEL"
,
"Done assembling operator term."
,
20
)
if
derI
<=
1
and
self
.
As
[
1
]
is
None
:
self
.
As
[
1
]
=
self
.
checkAInBounds
(
-
1
)
if
derI
<=
2
and
self
.
As
[
2
]
is
None
:
vbMng
(
self
,
"INIT"
,
"Assembling operator term A2."
,
20
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
nRe
,
nIm
=
self
.
refractionIndex
n2Re
,
n2Im
=
nRe
*
nRe
-
nIm
*
nIm
,
2
*
nRe
*
nIm
k2Re
,
k2Im
=
np
.
real
(
self
.
omega
**
2
),
np
.
imag
(
self
.
omega
**
2
)
k2n2Re
=
k2Re
*
n2Re
-
k2Im
*
n2Im
k2n2Im
=
k2Re
*
n2Im
+
k2Im
*
n2Re
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
k2n2Re
],
[
"kappaSquaredRefractionIndexSquaredReal"
]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
k2n2Im
],
[
"kappaSquaredRefractionIndexSquaredImag"
]))
a2Re
=
(
fen
.
dot
(
self
.
u
.
dx
(
0
),
self
.
v
.
dx
(
0
))
-
k2n2Re
*
fen
.
dot
(
self
.
u
,
self
.
v
))
*
fen
.
dx
a2Im
=
-
k2n2Im
*
fen
.
dot
(
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
)
return
self
.
_assembleA
(
mu
,
der
,
derI
)
def
b
(
self
,
mu
:
paramVal
=
[],
der
:
List
[
int
]
=
0
,
homogeneized
:
bool
=
False
)
->
Np1D
:
"""Assemble (derivative of) RHS of linear system."""
mu
=
self
.
checkParameter
(
mu
)
if
not
hasattr
(
der
,
"__len__"
):
der
=
[
der
]
*
self
.
npar
derI
=
hashD
(
der
)
nbsTot
=
self
.
nbsH
if
homogeneized
else
self
.
nbs
bs
=
self
.
bsH
if
homogeneized
else
self
.
bs
if
homogeneized
and
self
.
mu0
!=
self
.
mu0BC
:
self
.
liftDirichletData
(
self
.
mu0
)
bDEIMCoeffs
=
None
for
j
in
range
(
derI
,
nbsTot
):
if
bs
[
j
]
is
None
:
vbMng
(
self
,
"INIT"
,
"Assembling forcing term b{}."
.
format
(
j
),
20
)
if
bDEIMCoeffs
is
None
:
bDEIM
=
np
.
empty
((
self
.
nbs
,
self
.
spacedim
()),
dtype
=
np
.
complex
)
muDEIM
=
np
.
linspace
(
.
5
,
4.
,
self
.
nbs
)
for
jj
,
muD
in
enumerate
(
muDEIM
):
fRe
,
fIm
=
self
.
getForcingTerm
(
muD
)
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
fRe
],
[
"forcingTerm{}Real"
.
format
(
jj
)]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
fIm
],
[
"forcingTerm{}Imag"
.
format
(
jj
)]))
LR
=
fen
.
dot
(
fRe
,
self
.
v
)
*
fen
.
dx
LI
=
fen
.
dot
(
fIm
,
self
.
v
)
*
fen
.
dx
DBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
bDEIM
[
jj
]
=
(
fenics2Vector
(
LR
,
parsRe
,
DBC0
,
1
)
+
1.j
*
fenics2Vector
(
LI
,
parsIm
,
DBC0
,
1
))
bDEIMCoeffs
=
fit
(
muDEIM
,
bDEIM
,
self
.
nbs
-
1
)
b
=
bDEIMCoeffs
[
j
]
if
homogeneized
:
Ader
=
self
.
A
(
0
,
hashI
(
j
,
self
.
npar
))
b
-=
Ader
.
dot
(
self
.
liftedDirichletDatum
)
if
homogeneized
:
self
.
bsH
[
j
]
=
b
else
:
self
.
bs
[
j
]
=
b
vbMng
(
self
,
"DEL"
,
"Done assembling forcing term."
,
20
)
return
self
.
_assembleb
(
mu
,
der
,
derI
,
homogeneized
)
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