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HelmholtzAirfoilTaylor.py
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Fri, May 17, 06:41
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9 KB
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text/x-python
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Sun, May 19, 06:41 (2 d)
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blob
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R6746 RationalROMPy
HelmholtzAirfoilTaylor.py
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#!/usr/bin/env python3
import
numpy
as
np
from
context
import
FreeFemHelmholtzScatteringEngine
as
HFS
from
context
import
FreeFemHelmholtzScatteringAugmentedEngine
as
HFSA
from
context
import
FreeFemHSEngine
as
HS
from
context
import
FreeFemHSAugmentedEngine
as
HSA
from
context
import
ROMApproximantTaylorPade
as
TP
from
context
import
ROMApproximantTaylorRB
as
TRB
from
context
import
ROMApproximantLagrangePade
as
LP
from
context
import
ROMApproximantLagrangeRB
as
LRB
from
context
import
ROMApproximantSweeper
as
Sweeper
from
matplotlib
import
pyplot
as
plt
from
operator
import
itemgetter
def
subdict
(
d
,
ks
):
return
dict
(
zip
(
ks
,
itemgetter
(
*
ks
)(
d
)))
####################
test
=
"solve"
test
=
"Taylor"
#test = "Lagrange"
test
=
"TaylorSweep"
#test = "LagrangeSweep"
ttype
=
"simple"
#ttype = "augmentedI"
#ttype = "augmentedM"
plotSamples
=
'ALL'
#plotSamples = []
k0
=
10
+
1.j
kLeft
,
kRight
=
8
+
1.j
,
12
+
1.j
ktar
=
11
ktars
=
np
.
linspace
(
8
,
12
,
33
)
-
.
5j
ktars
=
np
.
linspace
(
12.125
,
12.5
,
4
)
-
.
5j
####################
PI
=
np
.
pi
kappa
=
10
theta
=
PI
*
-
30
/
180.
mu
=
1.1
epsilon
=
.
1
V
=
(
"real epsilon = {}, mu = {};
\n
"
"macro sign(f) (f >= 0 ? 1. : -1.)//
\n
"
"macro mBase1() (x^2 - x + y^2)//
\n
"
"macro mBase2() (((x^2 + y^2) / ((x - 1)^2 + y^2))^.25)//
\n
"
"macro mBase3() (- y / mBase1)//
\n
"
"macro mPhi1() (atan(mBase3) / 2)//
\n
"
"macro mPhi2() (mPhi1 - pi/2 * sign(mBase3))//
\n
"
"macro mK1() ((((1 + cos(mPhi1) / mBase2 + (.5 / mBase2)^2.) / (1 - 2. * cos(mPhi1) / mBase2 + mBase2^-2.))^.5 - mu)/ epsilon)//
\n
"
"macro mK2() ((((1 + cos(mPhi2) / mBase2 + (.5 / mBase2)^2.) / (1 - 2. * cos(mPhi2) / mBase2 + mBase2^-2.))^.5 - mu)/ epsilon)//
\n
"
"macro mHep1() (.9 * .5 * (1. + mK1 + sin(mK1) / pi) + .1)//
\n
"
"macro mHep2() (.9 * .5 * (1. + mK2 + sin(mK2) / pi) + .1)//
\n
"
"int n = 100, R = 2;
\n
"
"border wing(t = 0, 2 * pi){{x = cos(t)/3 + 5./12 + (3*cos(t) - 3/4) / (17 - 8*cos(t)); y = sin(t)/3 - 3*sin(t) / (17 - 8*cos(t)); label = 1;}}
\n
"
"border Inf(t = 0, 2 * pi){{x = R * cos(t); y = R * sin(t); label = 2;}}
\n
"
"mesh Th = buildmesh(wing(-n) + Inf(n));
\n
"
"load
\"
Element_P3
\"
;
\n
"
"fespace V(Th, P3);"
)
.
format
(
epsilon
,
mu
)
u0
=
"- exp(1.i * {} * ({} * x + {} * y))"
.
format
(
kappa
,
np
.
cos
(
theta
),
np
.
sin
(
theta
))
a
=
(
"(mBase1 >= 0 ? (mK1>= -1. ? (mK1 <= 1. ? mHep1 : 1) : .1) : "
"(mK2 >= -1. ? (mK2 <= 1. ? mHep2 : 1) : .1))"
)
if
ttype
==
"simple"
:
solver
=
HFS
(
V
,
k0
,
diffusivity
=
a
,
DirichletBoundary
=
"1"
,
RobinBoundary
=
"2"
,
DirichletDatum
=
u0
)
plotter
=
HS
(
solver
.
V
)
else
:
if
ttype
[
-
1
]
==
"I"
:
constraintType
=
"IDENTITY"
else
:
constraintType
=
"MASS"
solver
=
HFSA
(
V
,
k0
,
diffusivity
=
a
,
DirichletBoundary
=
"1"
,
RobinBoundary
=
"2"
,
DirichletDatum
=
u0
,
constraintType
=
constraintType
)
plotter
=
HSA
(
solver
.
V
,
d
=
2
)
uinc
=
solver
.
liftDirichletData
()
if
ttype
[:
-
1
]
==
"augmented"
:
uinc
=
[
uinc
[:
int
(
len
(
uinc
)
/
2
)],
kappa
*
uinc
[:
int
(
len
(
uinc
)
/
2
)]]
if
test
==
"solve"
:
av
=
plotter
.
convExpression
(
a
)
uh
=
solver
.
solve
()
print
(
plotter
.
norm
(
uh
,
kappa
))
if
ttype
==
"simple"
:
uhtot
=
uh
-
uinc
else
:
uhtot
=
[
x
-
y
for
x
,
y
in
zip
(
uh
,
uinc
)]
print
(
plotter
.
norm
(
uhtot
,
kappa
))
plotter
.
plot
(
av
,
split
=
False
,
what
=
'Real'
,
name
=
'a'
)
plotter
.
plot
(
uhtot
-
uh
,
what
=
'Real'
,
name
=
'u_inc'
)
plotter
.
plot
(
uh
,
what
=
'ABS'
)
plotter
.
plot
(
uhtot
,
what
=
'ABS'
,
name
=
'u + u_inc'
)
elif
test
in
[
"Taylor"
,
"Lagrange"
]:
if
test
==
"Taylor"
:
params
=
{
'N'
:
8
,
'M'
:
7
,
'R'
:
8
,
'E'
:
8
,
'sampleType'
:
'Krylov'
,
'POD'
:
False
}
parPade
=
subdict
(
params
,
[
'N'
,
'M'
,
'E'
,
'sampleType'
,
'POD'
])
parRB
=
subdict
(
params
,
[
'R'
,
'E'
,
'sampleType'
,
'POD'
])
approxPade
=
TP
(
solver
,
plotter
,
k0
=
k0
,
plotDer
=
plotSamples
,
approxParameters
=
parPade
)
approxRB
=
TRB
(
solver
,
plotter
,
k0
=
k0
,
approxParameters
=
parRB
)
else
:
params
=
{
'N'
:
8
,
'M'
:
7
,
'R'
:
9
,
'S'
:
9
,
'polyBasis'
:
'CHEBYSHEV'
,
'nodesType'
:
'CHEBYSHEV'
,
'POD'
:
True
}
parPade
=
subdict
(
params
,
[
'N'
,
'M'
,
'S'
,
'polyBasis'
,
'POD'
])
parRB
=
subdict
(
params
,
[
'R'
,
'S'
,
'nodesType'
,
'POD'
])
approxPade
=
LP
(
solver
,
plotter
,
ks
=
[
kLeft
,
kRight
],
w
=
kappa
,
plotSnap
=
plotSamples
,
approxParameters
=
parPade
)
approxRB
=
LRB
(
solver
,
plotter
,
ks
=
[
kLeft
,
kRight
],
w
=
kappa
,
approxParameters
=
parRB
)
PadeErr
,
solNorm
=
approxPade
.
approxError
(
ktar
),
approxPade
.
HFNorm
(
ktar
)
RBErr
=
approxRB
.
approxError
(
ktar
)
print
((
'SolNorm:
\t
{}
\n
ErrPade:
\t
{}
\n
ErrRelPade:
\t
{}
\n
ErrRB:
\t\t
{}'
'
\n
ErrRelRB:
\t
{}'
)
.
format
(
solNorm
,
PadeErr
,
np
.
divide
(
PadeErr
,
solNorm
),
RBErr
,
np
.
divide
(
RBErr
,
solNorm
)))
print
(
'
\n
Poles Pade'':'
)
print
(
approxPade
.
getPoles
(
True
))
print
(
'
\n
Poles RB:'
)
print
(
approxRB
.
getPoles
(
True
))
uHF
=
approxPade
.
getHF
(
ktar
)
plotter
.
plot
(
uHF
,
name
=
'u_ex'
)
approxPade
.
plotApp
(
ktar
,
name
=
'u_Pade'''
)
approxPade
.
plotErr
(
ktar
,
name
=
'errPade'''
)
approxRB
.
plotApp
(
ktar
,
name
=
'u_RB'
)
approxRB
.
plotErr
(
ktar
,
name
=
'errRB'
)
elif
test
in
[
"TaylorSweep"
,
"LagrangeSweep"
]:
if
test
==
"TaylorSweep"
:
shift
=
2
nsets
=
4
stride
=
3
Emax
=
stride
*
(
nsets
-
1
)
+
shift
+
1
params
=
{
'Emax'
:
Emax
,
'sampleType'
:
'Krylov'
,
'POD'
:
False
}
paramsSetsPade
=
[
None
]
*
nsets
paramsSetsRB
=
[
None
]
*
nsets
for
i
in
range
(
nsets
):
paramsSetsPade
[
i
]
=
{
'N'
:
stride
*
i
+
shift
+
1
,
'M'
:
stride
*
i
+
shift
,
'E'
:
stride
*
i
+
shift
+
1
}
paramsSetsRB
[
i
]
=
{
'E'
:
stride
*
i
+
shift
,
'R'
:
stride
*
i
+
shift
+
1
}
approxPade
=
TP
(
solver
,
plotter
,
k0
=
kappa
,
approxParameters
=
params
)
approxRB
=
TRB
(
solver
,
plotter
,
k0
=
kappa
,
approxParameters
=
params
)
else
:
kLeft
,
kRight
=
8
,
12
shift
=
3
nsets
=
3
stride
=
3
Smax
=
stride
*
(
nsets
-
1
)
+
shift
+
2
paramsPade
=
{
'S'
:
Smax
,
'polyBasis'
:
'CHEBYSHEV'
,
'POD'
:
True
}
paramsRB
=
{
'S'
:
Smax
,
'nodesType'
:
'CHEBYSHEV'
,
'POD'
:
True
}
paramsSetsPade
=
[
None
]
*
nsets
paramsSetsRB
=
[
None
]
*
nsets
for
i
in
range
(
nsets
):
paramsSetsPade
[
i
]
=
{
'N'
:
stride
*
i
+
shift
+
1
,
'M'
:
stride
*
i
+
shift
,
'S'
:
stride
*
i
+
shift
+
2
}
paramsSetsRB
[
i
]
=
{
'R'
:
stride
*
i
+
shift
+
1
,
'S'
:
stride
*
i
+
shift
+
2
}
approxPade
=
LP
(
solver
,
plotter
,
ks
=
[
kLeft
,
kRight
],
w
=
kappa
,
approxParameters
=
paramsPade
)
approxRB
=
LRB
(
solver
,
plotter
,
ks
=
[
kLeft
,
kRight
],
w
=
kappa
,
approxParameters
=
paramsRB
)
sweeper
=
Sweeper
.
ROMApproximantSweeper
(
ktars
=
ktars
,
mostExpensive
=
'Approx'
)
sweeper
.
ROMEngine
=
approxPade
sweeper
.
params
=
paramsSetsPade
filenamePade
=
sweeper
.
sweep
(
'../Data/HelmholtzAirfoil'
+
test
[:
-
5
]
+
'PadeFF.dat'
)
sweeper
.
ROMEngine
=
approxRB
sweeper
.
params
=
paramsSetsRB
filenameRB
=
sweeper
.
sweep
(
'../Data/HelmholtzAirfoil'
+
test
[:
-
5
]
+
'RBFF.dat'
)
for
i
in
range
(
nsets
):
if
test
==
"TaylorSweep"
:
val
=
stride
*
i
+
shift
PadeOutput
=
sweeper
.
read
(
filenamePade
,
{
'M'
:
val
},
[
'kRe'
,
'HFNorm'
,
'AppNorm'
,
'ErrNorm'
])
RBOutput
=
sweeper
.
read
(
filenameRB
,
{
'E'
:
val
},
[
'kRe'
,
'AppNorm'
,
'ErrNorm'
])
let
=
'E'
else
:
val
=
stride
*
i
+
shift
+
2
PadeOutput
=
sweeper
.
read
(
filenamePade
,
{
'S'
:
val
},
[
'kRe'
,
'HFNorm'
,
'AppNorm'
,
'ErrNorm'
])
RBOutput
=
sweeper
.
read
(
filenameRB
,
{
'S'
:
val
},
[
'kRe'
,
'AppNorm'
,
'ErrNorm'
])
let
=
'S'
ktarsF
=
PadeOutput
[
'kRe'
]
solNormF
=
PadeOutput
[
'HFNorm'
]
PadektarsF
=
PadeOutput
[
'kRe'
]
PadeNormF
=
PadeOutput
[
'AppNorm'
]
PadeErrorF
=
PadeOutput
[
'ErrNorm'
]
RBktarsF
=
RBOutput
[
'kRe'
]
RBNormF
=
RBOutput
[
'AppNorm'
]
RBErrorF
=
RBOutput
[
'ErrNorm'
]
plt
.
figure
(
figsize
=
(
10
,
5
))
plt
.
plot
(
ktarsF
,
solNormF
,
'k-'
,
label
=
'Sol norm'
)
plt
.
plot
(
PadektarsF
,
PadeNormF
,
'b--'
,
label
=
'Pade'' norm, {1} = {0}'
.
format
(
val
,
let
))
plt
.
plot
(
RBktarsF
,
RBNormF
,
'g--'
,
label
=
'RB norm, {1} = {0}'
.
format
(
val
,
let
))
plt
.
legend
()
plt
.
grid
()
p
=
plt
.
legend
(
loc
=
'upper left'
)
plt
.
savefig
(
'./normA'
+
str
(
i
)
+
'.eps'
,
format
=
'eps'
,
dpi
=
1000
)
plt
.
figure
(
figsize
=
(
10
,
5
))
plt
.
semilogy
(
PadektarsF
,
PadeErrorF
,
'b'
,
label
=
'Pade'' error, {1} = {0}'
.
format
(
val
,
let
))
plt
.
semilogy
(
RBktarsF
,
RBErrorF
,
'g'
,
label
=
'RB error, {1} = {0}'
.
format
(
val
,
let
))
plt
.
legend
()
plt
.
grid
()
p
=
plt
.
legend
(
loc
=
'lower right'
)
plt
.
savefig
(
'./errorA'
+
str
(
i
)
+
'.eps'
,
format
=
'eps'
,
dpi
=
1000
)
plt
.
figure
(
figsize
=
(
10
,
5
))
plt
.
semilogy
(
ktarsF
,
np
.
divide
(
PadeErrorF
,
solNormF
),
'b'
,
label
=
'Pade'' relative error, {1} = {0}'
.
format
(
val
,
let
))
plt
.
semilogy
(
RBktarsF
,
np
.
divide
(
RBErrorF
,
solNormF
),
'g'
,
label
=
'RB relative error, {1} = {0}'
.
format
(
val
,
let
))
plt
.
legend
()
plt
.
grid
()
p
=
plt
.
legend
(
loc
=
'lower right'
)
plt
.
savefig
(
'./errorAR'
+
str
(
i
)
+
'.eps'
,
format
=
'eps'
,
dpi
=
1000
)
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