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helmholtz_square_domain_problem_engine.py
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Sat, May 11, 14:55
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text/x-python
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Mon, May 13, 14:55 (2 d)
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R6746 RationalROMPy
helmholtz_square_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
import
scipy.sparse
as
scsp
import
fenics
as
fen
from
rrompy.utilities.base.types
import
(
ScOp
,
List
,
Tuple
,
paramVal
,
Np1D
,
FenExpr
)
from
rrompy.solver.fenics
import
fenZERO
,
fenONE
from
rrompy.hfengines.linear_problem.helmholtz_problem_engine
import
(
HelmholtzProblemEngine
)
from
rrompy.utilities.base
import
verbosityDepth
from
rrompy.utilities.poly_fitting.polynomial
import
(
hashDerivativeToIdx
as
hashD
,
hashIdxToDerivative
as
hashI
)
__all__
=
[
'HelmholtzSquareDomainProblemEngine'
]
class
HelmholtzSquareDomainProblemEngine
(
HelmholtzProblemEngine
):
"""
Solver for square Helmholtz problems with parametric laplacian.
- \dxx u - mu_2**2 \dyy u - mu_1**2 * u = f(mu_2) in \Omega = [0,\pi]^2
u = 0 on \partial\Omega
"""
def
__init__
(
self
,
kappa
:
float
,
theta
:
float
,
n
:
int
,
mu0
:
paramVal
=
[
12.
**
.
5
,
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
=
6
,
11
*
12
//
2
self
.
npar
=
2
self
.
rescalingExp
=
[
2.
,
1.
]
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
)[:]
self
.
forcingTerm
=
[
fen
.
cos
(
kappa
*
(
c
*
x
+
s
/
self
.
mu0
(
0
,
1
)
*
y
)),
fen
.
sin
(
kappa
*
(
c
*
x
+
s
/
self
.
mu0
(
0
,
1
)
*
y
))]
self
.
forcingTermDer
=
kappa
*
s
*
y
def
getExtraFactorB
(
self
,
mu
:
paramVal
=
[],
derI
:
int
=
0
)
->
Tuple
[
FenExpr
,
FenExpr
]:
"""Compute extra expression in RHS."""
mu
=
self
.
checkParameter
(
mu
)
def
getPowMinusj
(
x
,
power
):
powR
=
x
**
power
powI
=
fenZERO
if
power
%
2
==
1
:
powR
,
powI
=
powI
,
powR
if
power
%
4
>
1
:
powR
,
powI
=
-
powR
,
-
powI
return
powR
,
powI
if
self
.
verbosity
>=
25
:
verbosityDepth
(
"INIT"
,
(
"Assembling auxiliary expression for "
"forcing term derivative."
),
timestamp
=
self
.
timestamp
)
if
derI
==
0
:
return
fenONE
,
fenZERO
coeffs
=
np
.
zeros
(
derI
+
1
)
coeffs
[
1
]
=
-
2.
for
j
in
range
(
2
,
derI
+
1
):
coeffs
[
1
:]
=
(
-
2.
/
j
*
coeffs
[
1
:]
-
(
3
-
(
1
+
2
*
np
.
arange
(
derI
))
/
j
)
*
coeffs
[:
-
1
])
for
j
in
range
(
derI
):
powR
,
powI
=
getPowMinusj
(
self
.
forcingTermDer
,
derI
-
j
)
mupBase
=
coeffs
[
j
+
1
]
*
mu
(
0
,
1
)
**
(
-
3
*
derI
+
2
*
j
)
mupR
,
mupI
=
np
.
real
(
mupBase
),
np
.
imag
(
mupBase
)
if
j
==
0
:
exprR
=
mupR
*
powR
-
mupI
*
powI
exprI
=
mupI
*
powR
+
mupR
*
powI
else
:
exprR
+=
mupR
*
powR
-
mupI
*
powI
exprI
+=
mupI
*
powR
+
mupR
*
powI
if
self
.
verbosity
>=
25
:
verbosityDepth
(
"DEL"
,
"Done assembling auxiliary expression."
,
timestamp
=
self
.
timestamp
)
return
exprR
,
exprI
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
()
for
j
in
range
(
2
,
5
):
if
derI
<=
j
and
self
.
As
[
j
]
is
None
:
self
.
As
[
j
]
=
self
.
checkAInBounds
(
-
1
)
if
derI
<=
0
and
self
.
As
[
0
]
is
None
:
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"INIT"
,
"Assembling operator term A0."
,
timestamp
=
self
.
timestamp
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
a0Re
=
fen
.
dot
(
self
.
u
.
dx
(
0
),
self
.
v
.
dx
(
0
))
*
fen
.
dx
A0Re
=
fen
.
assemble
(
a0Re
)
DirichletBC0
.
apply
(
A0Re
)
A0ReMat
=
fen
.
as_backend_type
(
A0Re
)
.
mat
()
A0Rer
,
A0Rec
,
A0Rev
=
A0ReMat
.
getValuesCSR
()
self
.
As
[
0
]
=
scsp
.
csr_matrix
((
A0Rev
,
A0Rec
,
A0Rer
),
shape
=
A0ReMat
.
size
,
dtype
=
np
.
complex
)
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"DEL"
,
"Done assembling operator term."
,
timestamp
=
self
.
timestamp
)
if
derI
<=
1
and
self
.
As
[
1
]
is
None
:
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"INIT"
,
"Assembling operator term A1."
,
timestamp
=
self
.
timestamp
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
nRe
,
nIm
=
self
.
refractionIndex
n2Re
,
n2Im
=
nRe
*
nRe
-
nIm
*
nIm
,
2
*
nRe
*
nIm
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
n2Re
],
[
"refractionIndexSquaredReal"
]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
n2Im
],
[
"refractionIndexSquaredImag"
]))
a1Re
=
-
n2Re
*
fen
.
dot
(
self
.
u
,
self
.
v
)
*
fen
.
dx
a1Im
=
-
n2Im
*
fen
.
dot
(
self
.
u
,
self
.
v
)
*
fen
.
dx
A1Re
=
fen
.
assemble
(
a1Re
,
form_compiler_parameters
=
parsRe
)
A1Im
=
fen
.
assemble
(
a1Im
,
form_compiler_parameters
=
parsIm
)
DirichletBC0
.
zero
(
A1Re
)
DirichletBC0
.
zero
(
A1Im
)
A1ReMat
=
fen
.
as_backend_type
(
A1Re
)
.
mat
()
A1ImMat
=
fen
.
as_backend_type
(
A1Im
)
.
mat
()
A1Rer
,
A1Rec
,
A1Rev
=
A1ReMat
.
getValuesCSR
()
A1Imr
,
A1Imc
,
A1Imv
=
A1ImMat
.
getValuesCSR
()
self
.
As
[
1
]
=
(
scsp
.
csr_matrix
((
A1Rev
,
A1Rec
,
A1Rer
),
shape
=
A1ReMat
.
size
)
+
1.j
*
scsp
.
csr_matrix
((
A1Imv
,
A1Imc
,
A1Imr
),
shape
=
A1ImMat
.
size
))
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"DEL"
,
"Done assembling operator term."
,
timestamp
=
self
.
timestamp
)
if
derI
<=
5
and
self
.
As
[
5
]
is
None
:
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"INIT"
,
"Assembling operator term A5."
,
timestamp
=
self
.
timestamp
)
DirichletBC0
=
fen
.
DirichletBC
(
self
.
V
,
fenZERO
,
self
.
DirichletBoundary
)
a5Re
=
fen
.
dot
(
self
.
u
.
dx
(
1
),
self
.
v
.
dx
(
1
))
*
fen
.
dx
A5Re
=
fen
.
assemble
(
a5Re
)
DirichletBC0
.
zero
(
A5Re
)
A5ReMat
=
fen
.
as_backend_type
(
A5Re
)
.
mat
()
A5Rer
,
A5Rec
,
A5Rev
=
A5ReMat
.
getValuesCSR
()
self
.
As
[
5
]
=
scsp
.
csr_matrix
((
A5Rev
,
A5Rec
,
A5Rer
),
shape
=
A5ReMat
.
size
,
dtype
=
np
.
complex
)
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"DEL"
,
"Done assembling operator term."
,
timestamp
=
self
.
timestamp
)
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
)
for
j
in
range
(
derI
,
nbsTot
):
derH
=
hashI
(
j
,
self
.
npar
)
if
bs
[
j
]
is
None
:
if
np
.
sum
(
derH
)
!=
derH
[
-
1
]:
if
homogeneized
:
self
.
bsH
[
j
]
=
self
.
checkbInBounds
(
-
1
)
else
:
self
.
bs
[
j
]
=
self
.
checkbInBounds
(
-
1
)
continue
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"INIT"
,
(
"Assembling forcing term "
"b{}."
)
.
format
(
j
),
timestamp
=
self
.
timestamp
)
if
j
==
0
:
u0Re
,
u0Im
=
self
.
DirichletDatum
else
:
u0Re
,
u0Im
=
fenZERO
,
fenZERO
if
j
<
self
.
nbs
:
fRe
,
fIm
=
self
.
forcingTerm
cRe
,
cIm
=
self
.
getExtraFactorB
(
self
.
mu0
,
derH
[
-
1
])
cfRe
,
cfIm
=
cRe
*
fRe
-
cIm
*
fIm
,
cRe
*
fIm
+
cIm
*
fRe
else
:
cfRe
,
cfIm
=
fenZERO
,
fenZERO
parsRe
=
self
.
iterReduceQuadratureDegree
(
zip
([
cfRe
],
[
"forcingTermDer{}Real"
.
format
(
j
)]))
parsIm
=
self
.
iterReduceQuadratureDegree
(
zip
([
cfIm
],
[
"forcingTermDer{}Imag"
.
format
(
j
)]))
L0Re
=
fen
.
dot
(
cfRe
,
self
.
v
)
*
fen
.
dx
L0Im
=
fen
.
dot
(
cfIm
,
self
.
v
)
*
fen
.
dx
b0Re
=
fen
.
assemble
(
L0Re
,
form_compiler_parameters
=
parsRe
)
b0Im
=
fen
.
assemble
(
L0Im
,
form_compiler_parameters
=
parsIm
)
DBCR
=
fen
.
DirichletBC
(
self
.
V
,
u0Re
,
self
.
DirichletBoundary
)
DBCI
=
fen
.
DirichletBC
(
self
.
V
,
u0Im
,
self
.
DirichletBoundary
)
DBCR
.
apply
(
b0Re
)
DBCI
.
apply
(
b0Im
)
b
=
np
.
array
(
b0Re
[:]
+
1.j
*
b0Im
[:],
dtype
=
np
.
complex
)
if
homogeneized
:
Ader
=
self
.
A
(
self
.
mu0
,
derH
)
b
-=
Ader
.
dot
(
self
.
liftedDirichletDatum
)
if
homogeneized
:
self
.
bsH
[
j
]
=
b
else
:
self
.
bs
[
j
]
=
b
if
self
.
verbosity
>=
20
:
verbosityDepth
(
"DEL"
,
"Done assembling forcing term."
,
timestamp
=
self
.
timestamp
)
return
self
.
_assembleb
(
mu
,
der
,
derI
,
homogeneized
,
self
.
mu0
)
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