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F85450626
HelmholtzRBLagrangeApproximant.py
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Sun, Sep 29, 08:00
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4 KB
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text/x-python
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Tue, Oct 1, 08:00 (1 d, 21 h)
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blob
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21184023
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R6746 RationalROMPy
HelmholtzRBLagrangeApproximant.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from
__future__
import
print_function
import
fenics
as
fen
import
numpy
as
np
import
sympy
as
sp
from
context
import
FenicsHelmholtzEngine
as
HFEngine
from
context
import
FenicsHelmholtzScatteringEngine
as
HFSEngine
from
context
import
FenicsHelmholtzScatteringAugmentedEngine
as
HFSAEngine
from
context
import
FenicsHSEngine
as
HSEngine
from
context
import
FenicsHSAugmentedEngine
as
HSAEngine
from
context
import
ROMApproximantLagrangeRB
as
RB
PI
=
np
.
pi
testNo
=
3
if
testNo
==
1
:
params
=
{
'S'
:
5
,
'nodesType'
:
'CHEBYSHEV'
,
'POD'
:
True
}
nu
=
12
**.
5
theta
=
PI
/
3
ztar
=
11
x
,
y
=
sp
.
symbols
(
'x[0] x[1]'
,
real
=
True
)
wex
=
16
/
PI
**
4
*
x
*
y
*
(
x
-
PI
)
*
(
y
-
PI
)
phiex
=
nu
*
(
x
*
np
.
cos
(
theta
)
+
y
*
np
.
sin
(
theta
))
uex
=
wex
*
sp
.
exp
(
-
1.j
*
phiex
)
fex
=
-
uex
.
diff
(
x
,
2
)
-
uex
.
diff
(
y
,
2
)
-
nu
**
2
*
uex
nx
=
ny
=
40
mesh
=
fen
.
RectangleMesh
(
fen
.
Point
(
0
,
0
),
fen
.
Point
(
PI
,
PI
),
nx
,
ny
)
forcingTerm
=
[
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
re
(
fex
))),
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
im
(
fex
)))]
solver
=
HFEngine
(
mesh
=
mesh
,
wavenumber
=
nu
,
forcingTerm
=
forcingTerm
,
FEDegree
=
3
,
DirichletBoundary
=
'all'
,
DirichletDatum
=
0
)
plotter
=
HSEngine
(
solver
.
V
)
approx
=
RB
(
solver
,
plotter
,
ks
=
[
10
+
.
5j
,
14
+
.
5j
],
w
=
np
.
real
(
nu
),
approxParameters
=
params
)
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
==
2
:
def
Dboundary
(
x
,
on_boundary
):
return
on_boundary
and
(
fen
.
near
(
x
[
0
],
0
)
or
fen
.
near
(
x
[
0
],
PI
))
A
=
10
kappa
=
4
theta
=
PI
*
90
/
180
x
,
y
=
sp
.
symbols
(
'x[0] x[1]'
,
real
=
True
)
phiex
=
kappa
*
(
x
*
np
.
cos
(
theta
)
+
y
*
np
.
sin
(
theta
))
u0ex
=
-
A
*
sp
.
exp
(
1.j
*
phiex
)
nx
=
ny
=
40
mesh
=
fen
.
RectangleMesh
(
fen
.
Point
(
0
,
0
),
fen
.
Point
(
PI
,
PI
),
nx
,
ny
)
DirichletTerm
=
[
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
re
(
u0ex
))),
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
im
(
u0ex
)))]
params
=
{
'S'
:
30
,
'nodesType'
:
'CHEBYSHEV'
,
'POD'
:
True
}
solver
=
HFSEngine
(
mesh
=
mesh
,
wavenumber
=
kappa
,
forcingTerm
=
0
,
FEDegree
=
3
,
DirichletBoundary
=
Dboundary
,
RobinBoundary
=
'rest'
,
DirichletDatum
=
DirichletTerm
)
plotter
=
HSEngine
(
solver
.
V
)
approx
=
RB
(
solver
,
plotter
,
ks
=
[
0
,
8
],
approxParameters
=
params
,
plotSnapshots
=
False
)
ktar
=
4.5
approx
.
plotApp
(
ktar
,
name
=
'u_RB'
)
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
==
3
:
def
Dboundary
(
x
,
on_boundary
):
return
on_boundary
and
(
fen
.
near
(
x
[
0
],
0
)
or
fen
.
near
(
x
[
0
],
PI
))
A
=
10
kappa
=
4
theta
=
PI
*
90
/
180
x
,
y
=
sp
.
symbols
(
'x[0] x[1]'
,
real
=
True
)
phiex
=
kappa
*
(
x
*
np
.
cos
(
theta
)
+
y
*
np
.
sin
(
theta
))
u0ex
=
-
A
*
sp
.
exp
(
1.j
*
phiex
)
nx
=
ny
=
40
mesh
=
fen
.
RectangleMesh
(
fen
.
Point
(
0
,
0
),
fen
.
Point
(
PI
,
PI
),
nx
,
ny
)
DirichletTerm
=
[
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
re
(
u0ex
))),
sp
.
printing
.
ccode
(
sp
.
simplify
(
sp
.
im
(
u0ex
)))]
params
=
{
'S'
:
30
,
'nodesType'
:
'CHEBYSHEV'
,
'POD'
:
True
}
solver
=
HFSAEngine
(
mesh
=
mesh
,
wavenumber
=
kappa
,
forcingTerm
=
0
,
FEDegree
=
3
,
DirichletBoundary
=
Dboundary
,
RobinBoundary
=
'rest'
,
DirichletDatum
=
DirichletTerm
,
constraintType
=
'IDENTITY'
)
plotter
=
HSAEngine
(
solver
.
V
,
2
)
approx
=
RB
(
solver
,
plotter
,
ks
=
[
0
,
8
],
approxParameters
=
params
,
plotSnapshots
=
False
)
ktar
=
4.5
approx
.
plotApp
(
ktar
,
name
=
'u_RB'
)
approx
.
plotHF
(
ktar
,
name
=
'u_HF'
)
approx
.
plotErr
(
ktar
,
name
=
'err'
)
appErr
,
solNorm
=
approx
.
approxError
(
ktar
,
kappa
),
approx
.
HFNorm
(
ktar
,
kappa
)
print
(
appErr
,
solNorm
,
np
.
divide
(
appErr
,
solNorm
))
print
(
approx
.
getPoles
(
True
))
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