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RROMPy/examples/fenics/HelmholtzLagrangeApproximantsSweep.py
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HelmholtzLagrangeApproximantsSweep.py
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from copy import copy
import numpy as np
from rrompy.hfengines.fenics import HelmholtzSquareBubbleProblemEngine as HSBPE
from rrompy.hfengines.fenics import HelmholtzBoxScatteringProblemEngine as HBSPE
from rrompy.hsengines.fenics import HSEngine as HS
from rrompy.reduction_methods.lagrange import ApproximantLagrangePade as Pade
from rrompy.reduction_methods.lagrange import ApproximantLagrangeRB as RB
from rrompy.reduction_methods.base import ParameterSweeper as Sweeper
from rrompy.sampling import QuadratureSampler as QS
testNo = 2
npoints = 31
if testNo == 1:
ks = [4 + .5j, 14 + .5j]
solver = HSBPE(kappa = 12 ** .5, theta = np.pi / 3, n = 10)
mutars = np.linspace(0, 21, npoints)
filenamebase = '../data/output/HelmholtzBubbleLagrange'
elif testNo == 2:
ks = [10 + .25j, 14 + .25j]
solver = HBSPE(R = 5, kappa = 3, theta = - np.pi * 75 / 180, n = 10)
mutars = np.linspace(9, 14, npoints)
filenamebase = '../data/output/HelmholtzBoxLagrange'
plotter = HS(solver.V)
k0 = np.mean(ks)
shift = 12
nsets = 5
stride = 3
Smax = stride * (nsets - 1) + shift + 2
paramsPade = {'S':Smax, 'POD':True, 'sampler':QS(ks, "CHEBYSHEV")}
paramsRB = copy(paramsPade)
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}
appPade = Pade(solver, plotter, mu0 = k0, approxParameters = paramsPade)
appRB = RB(solver, plotter, mu0 = k0, approxParameters = paramsRB)
sweeper = Sweeper(mutars = mutars, mostExpensive = 'Approx')
sweeper.ROMEngine = appPade
sweeper.params = paramsSetsPade
filenamePade = sweeper.sweep(filenamebase + 'PadeFE.dat', outputs = 'ALL')
sweeper.ROMEngine = appRB
sweeper.params = paramsSetsRB
filenameRB = sweeper.sweep(filenamebase + 'RBFE.dat', outputs = 'ALL')
####################
from matplotlib import pyplot as plt
for i in range(nsets):
nSamples = stride * i + shift + 2
PadeOutput = sweeper.read(filenamePade, {'S':nSamples},
['muRe', 'HFNorm', 'AppNorm', 'ErrNorm'])
RBOutput = sweeper.read(filenameRB, {'S':nSamples},
['muRe', 'AppNorm', 'ErrNorm'])
ztarsF = PadeOutput['muRe']
solNormF = PadeOutput['HFNorm']
PadeztarsF = PadeOutput['muRe']
PadeNormF = PadeOutput['AppNorm']
PadeErrorF = PadeOutput['ErrNorm']
RBztarsF = RBOutput['muRe']
RBNormF = RBOutput['AppNorm']
RBErrorF = RBOutput['ErrNorm']
plt.figure()
plt.semilogy(ztarsF, solNormF, 'k-', label='Sol norm')
plt.semilogy(PadeztarsF, PadeNormF, 'b.--',
label='Pade'' norm, S = {}'.format(nSamples))
plt.semilogy(RBztarsF, RBNormF, 'g.--',
label='RB norm, S = {}'.format(nSamples))
plt.legend()
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(ztarsF, PadeErrorF / solNormF, 'b',
label='Pade'' relative error, S = {}'.format(nSamples))
plt.semilogy(RBztarsF, RBErrorF / solNormF, 'g',
label='RB relative error, S = {}'.format(nSamples))
plt.legend()
plt.grid()
plt.show()
plt.close()
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