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RROMPy/examples/Python_FreeFem++/HelmholtzTaylorApproximantsSweep.py
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HelmholtzTaylorApproximantsSweep.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Example homogeneous Dirichlet forcing wave SWEEP
from __future__ import print_function
import numpy as np
from context import FreeFemHelmholtzEngine as HFEngine
from context import FreeFemHSEngine as HSEngine
from context import ROMApproximantTaylorPade as Pade
from context import ROMApproximantTaylorRB as RB
from context import ROMApproximantSweeper as Sweeper
PI = np.pi
nu = 12**.5
theta = PI / 3
z0 = 12 + .5j
npoints = 31
ktars = np.linspace(7, 16, npoints)
V = ("int n = 10;\n"
"real nu = 12^.5, theta = pi / 3;\n"
"mesh Th = square(n, n, [pi * x, pi * y]);\n"
"load \"Element_P3\";\n"
"fespace V(Th, P3);")
f = ("16 / pi^4 * exp(-1i * nu*(cos(theta) * x + sin(theta) * y)) * ( 2i *"
" nu *cos(theta) * (2 * x * y^2 - 2 * pi * x * y - pi * y^2 + pi^2 * "
"y) + 2i * nu * sin(theta) * (2 *x^2 * y - pi * x^2 - 2 * pi * x * y "
"+ pi^2 * x) - (2 * y^2 - 2 * pi * y + 2 * x^2 - 2 * pi * x))")
solver = HFEngine(V, nu, forcingTerm = f, DirichletBoundary = "1,2,3,4")
plotter = HSEngine(solver.V)
shift = 5
nsets = 3
stride = 2
Emax = stride * (nsets - 1) + shift + 2
params = {'Emax':Emax, 'sampleType':'ARNOLDI', 'POD':True}
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+1,'R':stride*i+shift+2}
appPade = Pade(solver, plotter, k0 = z0, w = np.real(z0**.5),
approxParameters = params)
appRB = RB(solver, plotter, k0 = z0, w = np.real(z0**.5),
approxParameters = params)
sweeper = Sweeper.ROMApproximantSweeper(ktars = ktars, mostExpensive = 'Approx')
sweeper.ROMEngine = appPade
sweeper.params = paramsSetsPade
filenamePade = sweeper.sweep('../Data/HelmholtzBubbleTaylorPadeFF.dat',
outputs = 'ALL')
sweeper.ROMEngine = appRB
sweeper.params = paramsSetsRB
filenameRB = sweeper.sweep('../Data/HelmholtzBubbleTaylorRBFF.dat',
outputs = 'ALL')
####################
from matplotlib import pyplot as plt
for i in range(nsets):
nDerivatives = stride*i+shift+1
PadeOutput = sweeper.read(filenamePade, {'E':nDerivatives},
['kRe', 'HFNorm', 'AppNorm', 'ErrNorm'])
RBOutput = sweeper.read(filenameRB, {'E':nDerivatives},
['kRe', 'AppNorm', 'ErrNorm'])
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()
plt.semilogy(ktarsF, solNormF, 'k-', label='Sol norm')
plt.semilogy(PadektarsF, PadeNormF, 'b.--',
label='Pade'' norm, E = {}'.format(nDerivatives))
plt.semilogy(RBktarsF, RBNormF, 'g.--',
label='RB norm, E = {}'.format(nDerivatives))
plt.legend()
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(PadektarsF, PadeErrorF, 'b',
label='Pade'' error, E = {}'.format(nDerivatives))
plt.semilogy(RBktarsF, RBErrorF, 'g',
label='RB error, E = {}'.format(nDerivatives))
plt.legend()
plt.grid()
plt.show()
plt.close()
plt.figure()
plt.semilogy(ktarsF, PadeErrorF / solNormF, 'b',
label='Pade'' relative error, E = {}'.format(nDerivatives))
plt.semilogy(RBktarsF, RBErrorF / solNormF, 'g',
label='RB relative error, E = {}'.format(nDerivatives))
plt.legend()
plt.grid()
plt.show()
plt.close()
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