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pod.py
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Tue, Apr 30, 14:09

pod.py
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import numpy as np
from diapason_engine import DiapasonEngine, DiapasonEngineDamped
from rrompy.reduction_methods.standard import RationalInterpolant as Pade
from rrompy.reduction_methods.standard import ReducedBasis as RB
from rrompy.parameter.parameter_sampling import QuadratureSampler as QS
verb = 100
sol = "single"
sol = "sweep"
algo = "Pade"
#algo = "RB"
polyBasis = "LEGENDRE"
polyBasis = "CHEBYSHEV"
#polyBasis = "MONOMIAL"
dampingEta = 0. * 1e4 / 2. / np.pi
ktar = 1.e4 # [Hz]
k0s = [2.5e2, 1.0e4]
#k0s = np.array([2.5e3, 1.5e4])
#k0s = np.array([5.0e4, 1.0e5])
k0s = [2.0e5, 3.0e5]
k0 = np.mean(np.power(k0s, 2.)) ** .5
theta = 20. * np.pi / 180.
phi = 10. * np.pi / 180.
c = 3.e2
rho = 8e3 * (2. * np.pi) ** 2.
E = 1.93e11
nu = .3
T = 1e6
###
if np.isclose(dampingEta, 0.):
rescalingExp = 2.
solver = DiapasonEngine(kappa = k0, c = c, rho = rho, E = E, nu = nu,
T = T, theta = theta, phi = phi, meshNo = 1,
degree_threshold = 8, verbosity = 0)
else:
rescalingExp = 1.
solver = DiapasonEngineDamped(kappa = k0, c = c, rho = rho, E = E, nu = nu,
T = T, theta = theta, phi = phi,
dampingEta = dampingEta, meshNo = 1,
degree_threshold = 8, verbosity = 0)
params = {'N':39, 'M':39, 'S':40, 'POD':True, 'polybasis':polyBasis,
'sampler':QS(k0s, "CHEBYSHEV", rescalingExp)}#,
# 'robustTol':1e-16}
if algo == "Pade":
approx = Pade(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
else:
params.pop("N")
params.pop("M")
params.pop("polybasis")
# params.pop("robustTol")
approx = RB(solver, mu0 = k0, approxParameters = params,
verbosity = verb)
approx.setupApprox()
if sol == "single":
approx.outParaviewTimeDomainSamples(
filename = "out/outSamples{}".format(dampingEta),
forceNewFile = False, folders = True)
nameBase = "{}_{}".format(ktar, dampingEta)
approx.outParaviewTimeDomainApprox(ktar, omega = 2. * np.pi * ktar,
filename = "out/outTApp{}".format(nameBase),
forceNewFile = False, folder = True)
approx.outParaviewTimeDomainHF(ktar, omega = 2. * np.pi * ktar,
filename = "out/outTHF{}".format(nameBase),
forceNewFile = False, folder = True)
approx.outParaviewTimeDomainErr(ktar, omega = 2. * np.pi * ktar,
filename = "out/outTErr{}".format(nameBase),
forceNewFile = False, folder = True)
approx.outParaviewTimeDomainRes(ktar, omega = 2. * np.pi * ktar,
filename = "out/outTRes{}".format(nameBase),
forceNewFile = False, folder = True)
appErr, solNorm = approx.normErr(ktar), approx.normHF(ktar)
resNorm, RHSNorm = approx.normRes(ktar), approx.normRHS(ktar)
print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
np.divide(appErr, solNorm)))
print(('RHSNorm:\t{}\nRes:\t{}\nResRel:\t{}').format(RHSNorm, resNorm,
np.divide(resNorm, RHSNorm)))
poles = approx.getPoles()
print('Poles:', poles)
if sol == "sweep":
k0s = np.linspace(k0s[0], k0s[1], 100)
kl, kr = min(k0s), max(k0s)
approx.samplingEngine.verbosity = 0
approx.trainedModel.verbosity = 0
approx.verbosity = 0
kl, kr = np.real(kl), np.real(kr)
from matplotlib import pyplot as plt
normApp = np.zeros(len(k0s))
norm = np.zeros_like(normApp)
err = np.zeros_like(normApp)
res = np.zeros_like(normApp)
# errApp = np.zeros_like(normApp)
fNorm = approx.normRHS(k0s[0])
for j in range(len(k0s)):
normApp[j] = approx.normApprox(k0s[j])
norm[j] = approx.normHF(k0s[j])
err[j] = approx.normErr(k0s[j]) / norm[j]
res[j] = approx.normRes(k0s[j]) / fNorm
# errApp[j] = res[j] / np.min(np.abs(k0s[j] - poles))
# errApp *= np.mean(err) / np.mean(errApp)
plt.figure()
plt.semilogy(k0s, norm)
plt.semilogy(k0s, normApp, '--')
plt.semilogy(np.real(approx.mus),
1.05*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.xlim([kl, kr])
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(k0s, err)
# plt.semilogy(k0s, errApp)
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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