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RROMPy/examples/Python_FEniCS/HelmholtzPadeLagrangeApproximant.py
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HelmholtzPadeLagrangeApproximant.py
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#!/usr/bin/env python3
import numpy as np
from context import FenicsHelmholtzEngine as HFEngine
from context import FenicsHelmholtzScatteringEngine as HFSEngine
from context import FenicsHelmholtzScatteringAugmentedEngine as HFSAEngine
from context import FenicsHSEngine as HSEngine
from context import FenicsHSAugmentedEngine as HSAEngine
from context import ROMApproximantLagrangePade as Pade
testNo = 1
if testNo == 1:
params = {'N':4, 'M':3, 'S':5, 'POD':True}
z0s = [10 + 0.j, 14 + 0.j]
z0 = np.mean(z0s)
ztar = 11 + .5j
from FEniCS_snippets import SquareHomogeneousBubble
boundary, mesh, forcingTerm = SquareHomogeneousBubble(kappa = 12 ** .5,
theta = np.pi / 3,
n = 40)
solver = HFEngine(mesh = mesh, wavenumber = z0**.5,
forcingTerm = forcingTerm, FEDegree = 3,
DirichletBoundary = boundary, DirichletDatum = 0)
plotter = HSEngine(solver.V)
approx = Pade(solver, plotter, mus = z0s, w = np.real(z0**.5),
approxParameters = params)
approx.setNodesWeights(z0s, "CHEBYSHEV")
approx.plotApp(ztar, name = 'u_Pade''')
approx.plotHF(ztar, name = 'u_HF')
approx.plotErr(ztar, name = 'err')
appErr, solNorm = approx.approxError(ztar), approx.HFNorm(ztar)
print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
np.divide(appErr, solNorm)))
print('\nPoles Pade'':')
print(approx.getPoles())
############
elif testNo == 2:
params = {'N':9, 'M':8, 'S':10, 'POD':True}
z0s = np.power([3.85 + 0.j, 4.15 + 0.j], 2.)
z0 = np.mean(z0s)
ztar = (4 + .15j) ** 2.
from FEniCS_snippets import SquareTransmissionDirichlet
boundary, mesh, n, u0 = SquareTransmissionDirichlet(nT = 2, nB = 1,
theta = np.pi * 45 / 180,
kappa = 4., n = 50)
solver = HFEngine(mesh = mesh, wavenumber = z0**.5,
refractionIndex = n, FEDegree = 3,
DirichletBoundary = boundary, DirichletDatum = u0)
plotter = HSEngine(solver.V)
approx = Pade(solver, plotter, mus = z0s, w = np.real(z0**.5),
approxParameters = params, plotSnap = 'ALL')
approx.setNodesWeights(z0s, "CHEBYSHEV")
approx.ws = np.ones_like(approx.ws)
approx.plotApp(ztar, name = 'u_Pade''')
approx.plotHF(ztar, name = 'u_HF')
approx.plotErr(ztar, name = 'err')
appErr, solNorm = approx.approxError(ztar), approx.HFNorm(ztar)
print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
np.divide(appErr, solNorm)))
print('\nPoles Pade'':')
print(approx.getPoles())
############
elif testNo in [3, 4]:
params = {'N':15, 'M':14, 'S':20, 'POD':True}
k0s = np.array([5, 7])
k0 = np.mean(k0s)
ktar = 6.7 - .2j
from FEniCS_snippets import SquareScatteringTB
bdrD, bdrN, mesh, forcingTerm = SquareScatteringTB(kappa = 4,
theta = np.pi / 3,
n = 40)
if testNo == 3:
solver = HFSEngine(mesh = mesh, wavenumber = k0, FEDegree = 3,
forcingTerm = forcingTerm, DirichletBoundary = bdrD,
RobinBoundary = bdrN)
plotter = HSEngine(solver.V)
else:
solver = HFSAEngine(mesh = mesh, wavenumber = k0, FEDegree = 3,
forcingTerm = forcingTerm,
DirichletBoundary = bdrD, RobinBoundary = bdrN)
plotter = HSAEngine(solver.V, 2)
approx = Pade(solver, plotter, mus = k0s, approxParameters = params)
approx.setNodesWeights(k0s, "CHEBYSHEV")
approx.plotApp(ktar, name = 'u_RB')
approx.plotHF(ktar, name = 'u_HF')
approx.plotErr(ktar, name = 'err')
appErr, solNorm = approx.approxError(ktar), approx.HFNorm(ktar)
print(('SolNorm:\t{}\nErr:\t{}\nErrRel:\t{}').format(solNorm, appErr,
np.divide(appErr, solNorm)))
print('\nPoles Pade'':')
print(approx.getPoles())
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