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RROMPy/examples/Python_FreeFem++/HelmholtzTaylorPoleIdentification.py
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HelmholtzTaylorPoleIdentification.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
from __future__ import print_function
import numpy as np
from context import utilities
from context import FreeFemHelmholtzEngine as HFEngine
from context import FreeFemHSEngine as HSEngine
from context import ROMApproximantTaylorPade as Pade
from context import ROMApproximantTaylorRB as RB
PI = np.pi
V = ("int n = 25;\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))")
z0 = 12 + 1.j
Nmin, Nmax = 2, 10
Nvals = np.arange(Nmin, Nmax + 1, 2)
params = {'N':Nmin, 'M':0, 'Emax':Nmax, 'POD':True, 'sampleType':'Arnoldi'}
#, 'robustTol':1e-14}
#boolCon = lambda x : np.abs(np.imag(x)) < 1e-1 * np.abs(np.real(x) - np.real(z0))
#cleanupParameters = {'boolCondition':boolCon, 'residueCheck':True}
solver = HFEngine(V, z0 ** .5, forcingTerm = f, DirichletBoundary = "1,2,3,4")
plotter = HSEngine(solver.V)
approxP = Pade(solver, plotter, k0 = z0, w = np.real(z0**.5),
approxParameters = params)#, equilibration = True,
# cleanupParameters = cleanupParameters)
approxR = RB(solver, plotter, k0 = z0, w = np.real(z0**.5),
approxParameters = params)
rP, rE = [None] * len(Nvals), [None] * len(Nvals)
verbose = 1
for j, N in enumerate(Nvals):
if verbose > 0:
print('N = E = {}'.format(N))
approxP.approxParameters = {'N':N, 'E':N}
approxR.approxParameters = {'R':N, 'E':N}
if verbose > 1:
print(approxP.approxParameters)
print(approxR.approxParameters)
rP[j] = approxP.getPoles(True)
rE[j] = approxR.getPoles(True)
if verbose > 2:
print(rP)
print(rE)
from matplotlib import pyplot as plt
plotRows = int(np.ceil(len(Nvals) / 3))
fig, axes = plt.subplots(plotRows, 3, figsize = (15, 3.5 * plotRows))
for j, N in enumerate(Nvals):
i1, i2 = int(np.floor(j / 3)), j % 3
axes[i1, i2].set_title('N = E = {}'.format(N))
axes[i1, i2].plot(np.real(rP[j]), np.imag(rP[j]), 'Xb',
label="Pade'", markersize = 8)
axes[i1, i2].plot(np.real(rE[j]), np.imag(rE[j]), '*r',
label="RB", markersize = 10)
axes[i1, i2].axhline(linewidth=1, color='k')
xmin, xmax = axes[i1, i2].get_xlim()
res = utilities.squareResonances(xmin, xmax, False)
axes[i1, i2].plot(res, np.zeros_like(res), 'ok', markersize = 4)
axes[i1, i2].grid()
axes[i1, i2].set_xlim(xmin, xmax)
axes[i1, i2].axis('equal')
p = axes[i1, i2].legend()
plt.tight_layout()
for j in range((len(Nvals) - 1) % 3 + 1, 3):
axes[plotRows - 1, j].axis('off')
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