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squareScatteringHomog.py
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Sat, Nov 9, 07:08

squareScatteringHomog.py
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import numpy as np
from rrompy.hfengines.linear_problem import \
HelmholtzCavityScatteringProblemEngine as HCSPE
from rrompy.reduction_methods.distributed_greedy import \
RationalInterpolantGreedy as Pade
from rrompy.reduction_methods.distributed_greedy import \
RBDistributedGreedy as RB
from rrompy.utilities.fenics import L2NormMatrix
verb = 2
timed = False
algo = "Pade"
#algo = "RB"
polyBasis = "LEGENDRE"
polyBasis = "CHEBYSHEV"
#polyBasis = "MONOMIAL"
errorEstimatorKind = "BARE"
errorEstimatorKind = "BASIC"
#errorEstimatorKind = "EXACT"
k0s = np.linspace(10, 15, 100)
k0 = np.mean(k0s)
kl, kr = min(k0s), max(k0s)
params = {'muBounds':[kl, kr], 'nTestPoints':500, 'Delta':0,
'greedyTol':5e-3, 'S':2, 'polybasis':polyBasis,
'errorEstimatorKind':errorEstimatorKind}
if timed:
verb = 0
solver = HCSPE(kappa = 5, n = 20, verbosity = verb)
solver.omega = np.real(k0)
if algo == "Pade":
approx = Pade(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
else:
params.pop('Delta')
params.pop('polybasis')
params.pop('errorEstimatorKind')
approx = RB(solver, mu0 = k0, approxParameters = params, verbosity = verb)
approx.initEstimatorNormEngine(L2NormMatrix(solver.V))
if timed:
from time import clock
start_time = clock()
approx.greedy()
print("Time: ", clock() - start_time)
else:
approx.greedy(True)
approx.samplingEngine.verbosity = 0
approx.trainedModel.verbosity = 0
approx.verbosity = 0
from matplotlib import pyplot as plt
normApp = np.zeros(len(k0s))
norm = np.zeros_like(normApp)
res = np.zeros_like(normApp)
err = np.zeros_like(normApp)
for j in range(len(k0s)):
normApp[j] = approx.normApprox(k0s[j])
norm[j] = approx.normHF(k0s[j])
res[j] = (approx.estimatorNormEngine.norm(approx.getRes(k0s[j]))
/ approx.estimatorNormEngine.norm(approx.getRHS(k0s[j])))
err[j] = approx.normErr(k0s[j]) / approx.normHF(k0s[j])
resApp = approx.errorEstimator(k0s)
plt.figure()
plt.plot(k0s, norm)
plt.plot(k0s, normApp, '--')
plt.plot(np.real(approx.mus),
1.25*np.max(norm)*np.ones_like(approx.mus, dtype = float), 'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, res)
plt.semilogy(k0s, resApp, '--')
plt.semilogy(np.real(approx.mus),
4.*np.max(resApp)*np.ones_like(approx.mus, dtype = float), 'rx')
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, err)
plt.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
polesApp = approx.getPoles()
mask = (np.real(polesApp) < kl) | (np.real(polesApp) > kr)
print("Outliers:", polesApp[mask])
polesApp = polesApp[~mask]
plt.figure()
plt.plot(np.real(polesApp), np.imag(polesApp), 'kx')
plt.axis('equal')
plt.grid()
plt.show()
plt.close()

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