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HelmholtzRBTaylorApproximant.py
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Created
Sun, Sep 29, 14:22
Size
5 KB
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text/x-python
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Tue, Oct 1, 14:22 (1 d, 23 h)
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blob
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21174308
Attached To
R6746 RationalROMPy
HelmholtzRBTaylorApproximant.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Example homogeneous Dirichlet forcing wave
from
__future__
import
print_function
import
numpy
as
np
from
context
import
FreeFemHelmholtzEngine
as
HFEngine
from
context
import
FreeFemHelmholtzScatteringEngine
as
HFSEngine
from
context
import
FreeFemHelmholtzScatteringAugmentedEngine
as
HFSAEngine
from
context
import
FreeFemHSEngine
as
HSEngine
from
context
import
FreeFemHSAugmentedEngine
as
HSAEngine
from
context
import
ROMApproximantTaylorRB
as
RB
PI
=
np
.
pi
testNo
=
4
if
testNo
==
1
:
params
=
{
'E'
:
3
,
'POD'
:
True
,
'sampleType'
:
'Arnoldi'
}
z0
=
12
+.
5j
ztar
=
11
V
=
(
"int n = 40;
\n
"
"real nu = 12^.5, theta = pi / 3;
\n
"
"mesh Th = square(n, n, [pi * x, pi * y]);
\n
"
"load
\"
Element_P3
\"
;
\n
"
"fespace V(Th, P3);"
)
f
=
(
"16 / pi^4 * exp(-1i * nu*(cos(theta) * x + sin(theta) * y)) * ( 2i *"
" nu *cos(theta) * (2 * x * y^2 - 2 * pi * x * y - pi * y^2 + pi^2 * "
"y) + 2i * nu * sin(theta) * (2 *x^2 * y - pi * x^2 - 2 * pi * x * y "
"+ pi^2 * x) - (2 * y^2 - 2 * pi * y + 2 * x^2 - 2 * pi * x))"
)
f
=
'1.'
solver
=
HFEngine
(
V
,
z0
**.
5
,
forcingTerm
=
f
,
DirichletBoundary
=
'1,2,3,4'
)
plotter
=
HSEngine
(
solver
.
V
)
approx
=
RB
(
solver
,
plotter
,
k0
=
z0
,
w
=
np
.
real
(
z0
**.
5
),
approxParameters
=
params
)
approx
.
plotApp
(
ztar
,
name
=
'u_Pade'''
)
approx
.
plotHF
(
ztar
,
name
=
'u_HF'
)
approx
.
plotErr
(
ztar
,
name
=
'err'
)
appErr
,
solNorm
=
approx
.
approxError
(
ztar
),
approx
.
HFNorm
(
ztar
)
print
(
appErr
,
solNorm
,
appErr
/
solNorm
)
print
(
approx
.
getPoles
(
True
))
############
elif
testNo
==
2
:
params
=
{
'E'
:
7
,
'sampleType'
:
'Arnoldi'
,
'POD'
:
True
}
ztar
=
3.95
**
2
kappa
=
4
theta
=
np
.
pi
*
45
/
180
k1
=
kappa
*
1
*
np
.
cos
(
theta
)
if
2
*
kappa
>
k1
:
k2
=
(
4.
*
kappa
**
2.
-
k1
**
2.
)
**.
5
else
:
k2
=
1.j
*
(
k1
**
2.
-
4.
*
kappa
**
2.
)
**.
5
R
=
(
kappa
*
1
*
np
.
sin
(
theta
)
-
k2
)
/
(
kappa
*
1
*
np
.
sin
(
theta
)
+
k2
)
T
=
R
+
1
V
=
(
"int n = 50;
\n
"
"real kappa = {}, theta = {};
\n
"
"mesh Th = square(n, n, [pi * (x - .5), pi * (y - .5)]);
\n
"
"load
\"
Element_P3
\"
;
\n
"
"fespace V(Th, P3);"
)
.
format
(
kappa
,
theta
)
n
=
"(y >= 0 ? 2. : 1.)"
u0
=
(
"(y >= 0 ? {0}*exp(1.i*({1}*x+{2}*y)) : exp(1.i*{3}*({4}*x+{5}*y)) "
"+ {6}*exp(1.i*{3}*({4}*x-{5}*y)))"
)
.
format
(
T
,
k1
,
k2
,
kappa
,
np
.
cos
(
theta
),
np
.
sin
(
theta
),
R
)
solver
=
HFEngine
(
V
,
kappa
,
refractionIndex
=
n
,
DirichletBoundary
=
"1,2,3,4"
,
DirichletDatum
=
u0
)
plotter
=
HSEngine
(
solver
.
V
)
approx
=
RB
(
solver
,
plotter
,
k0
=
kappa
**
2
,
w
=
kappa
,
approxParameters
=
params
,
plotDer
=
'ALL'
)
approx
.
plotApp
(
ztar
,
name
=
'u_RB'
)
approx
.
plotHF
(
ztar
,
name
=
'u_HF'
)
approx
.
plotErr
(
ztar
,
name
=
'err'
)
appErr
,
solNorm
=
approx
.
approxError
(
ztar
),
approx
.
HFNorm
(
ztar
)
print
(
appErr
,
solNorm
,
appErr
/
solNorm
)
print
(
approx
.
getPoles
(
True
))
############
elif
testNo
==
3
:
V
=
(
"int n = 50;
\n
"
"real nu = 2, theta = pi / 6;
\n
"
"mesh Th = square(n, n, [pi * x, pi * y]);
\n
"
"load
\"
Element_P3
\"
;
\n
"
"fespace V(Th, P3);"
)
f
=
(
"4 / pi^2 * exp(-1i * nu * (cos(theta) * x + sin(theta) * y)) * "
"(2i * nu * cos(theta) * (pi - 2 * x) + 2)"
)
params
=
{
'E'
:
7
,
'sampleType'
:
'Krylov'
,
'POD'
:
False
}
kappa
=
2.
solver
=
HFSEngine
(
V
,
kappa
,
forcingTerm
=
f
,
DirichletBoundary
=
"2,4"
,
RobinBoundary
=
"1,3"
)
plotter
=
HSEngine
(
solver
.
V
)
approx
=
RB
(
solver
,
plotter
,
k0
=
kappa
,
approxParameters
=
params
,
plotDer
=
'ALL'
)
approx
.
setupApprox
()
ktar
=
1.8
-
.
3j
approx
.
plotApp
(
ktar
,
name
=
'u_Pade'''
)
approx
.
plotHF
(
ktar
,
name
=
'u_HF'
)
approx
.
plotErr
(
ktar
,
name
=
'err'
)
appErr
,
solNorm
=
approx
.
approxError
(
ktar
),
approx
.
HFNorm
(
ktar
)
print
(
appErr
,
solNorm
,
appErr
/
solNorm
)
print
(
approx
.
getPoles
(
True
))
############
elif
testNo
==
4
:
V
=
(
"int n = 50;
\n
"
"real nu = 2, theta = pi / 6;
\n
"
"mesh Th = square(n, n, [pi * x, pi * y]);
\n
"
"load
\"
Element_P3
\"
;
\n
"
"fespace V(Th, P3);"
)
f
=
(
"4 / pi^2 * exp(-1i * nu * (cos(theta) * x + sin(theta) * y)) * "
"(2i * nu * cos(theta) * (pi - 2 * x) + 2)"
)
params
=
{
'E'
:
8
,
'sampleType'
:
'Arnoldi'
,
'POD'
:
True
}
kappa
=
2.
solver
=
HFSAEngine
(
V
,
kappa
,
forcingTerm
=
f
,
DirichletBoundary
=
"2,4"
,
RobinBoundary
=
"1,3"
,
constraintType
=
"IDENTITY"
)
plotter
=
HSAEngine
(
solver
.
V
,
2
)
approx
=
RB
(
solver
,
plotter
,
k0
=
kappa
,
approxParameters
=
params
,
plotDer
=
'ALL'
)
approx
.
setupApprox
()
ktar
=
1.8
-
.
3j
approx
.
plotApp
(
ktar
,
name
=
'u_Pade'''
)
approx
.
plotHF
(
ktar
,
name
=
'u_HF'
)
approx
.
plotErr
(
ktar
,
name
=
'err'
)
appErr
=
approx
.
approxError
(
ktar
,
kappa
)
solNorm
=
approx
.
HFNorm
(
ktar
,
kappa
)
print
(
appErr
,
solNorm
,
np
.
divide
(
appErr
,
solNorm
))
print
(
approx
.
getPoles
(
True
))
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