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RROMPy/examples/Python/HelmholtzTaylorPoleIdentification.py
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HelmholtzTaylorPoleIdentification.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
# Example homogeneous Dirichlet forcing wave
from __future__ import print_function
import fenics as fen
import numpy as np
import sympy as sp
from context import utilities
from context import FenicsHelmholtzEngine as HFEngine
from context import FenicsHSEngine as HSEngine
from context import ROMApproximantTaylorPade as Pade
from context import ROMApproximantTaylorRB as RB
PI = np.pi
nu = 12**.5
z0 = 12+1.j
theta = PI / 3
x, y = sp.symbols('x[0] x[1]', real=True)
wex = 16/PI**4 * x * y * (x - PI) * (y - PI)
phiex = nu * (x * np.cos(theta) + y * np.sin(theta))
uex = wex * sp.exp(-1.j * phiex)
fex = - uex.diff(x, 2) - uex.diff(y, 2) - nu**2 * uex
nx = ny = 25
mesh = fen.RectangleMesh(fen.Point(0,0), fen.Point(PI,PI), nx, ny)
forcingTerm = [sp.printing.ccode(sp.simplify(sp.re(fex))), sp.printing.ccode(sp.simplify(sp.im(fex)))]
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(mesh = mesh, wavenumber = z0**.5, forcingTerm = forcingTerm, FEDegree = 3,
DirichletBoundary = 'all', DirichletDatum = 0)
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
plt.set_cmap('jet')
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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