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RROMPy/examples/Python/HelmholtzRBTaylorApproximant.py
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HelmholtzRBTaylorApproximant.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 FenicsHelmholtzEngine as HFEngine
from context import FenicsHSEngine as HSEngine
from context import ROMApproximantTaylorRB as RB
PI = np.pi
testNo = 3
if testNo == 1:
nu = 12**.5
theta = PI / 3
z0 = 12+.5j
ztar = 11
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
params = {'E':5, 'POD':True, 'sampleType':'ARNOLDI'}
nx = ny = 40
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)))]
solver = HFEngine.FenicsHelmholtzEngine(mesh = mesh, wavenumber = z0**.5, forcingTerm = forcingTerm, FEDegree = 3,
DirichletBoundary = 'all', DirichletDatum = 0)
plotter = HSEngine.FenicsHSEngine(solver.V)
approx = RB.ROMApproximantTaylorRB(solver, plotter, k0 = z0, w = np.real(z0**.5),
approxParameters = params)
approx.plotApp(ztar, name = 'u_RB')
approx.plotHF(ztar, name = 'u_HF')
approx.plotErr(ztar, name = 'err')
appErr, solNorm = approx.approxError(ztar), approx.HFNorm(ztar)
print(appErr, solNorm, appErr/solNorm)
print(approx.getPoles(True))
############
elif testNo == 2:
def Dboundary(x, on_boundary):
return on_boundary and (fen.near(x[0], 0) or fen.near(x[0], PI))
A = 10
kappa = 2
theta = PI * 30 / 180
x, y = sp.symbols('x[0] x[1]', real=True)
wex = 4/PI**2 * x * (PI - x)
phiex = kappa * (x * np.cos(theta) + y * np.sin(theta))
uex = wex * sp.exp(-1.j * phiex)
fex = - uex.diff(x, 2) - uex.diff(y, 2) - kappa**2 * uex
nx = ny = 20
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)))]
params = {'E':8, 'POD':True}
solver = HFEngine.FenicsHelmholtzScatteringEngine(mesh = mesh, wavenumber = kappa, forcingTerm = forcingTerm,
FEDegree = 3, DirichletBoundary = Dboundary,
RobinBoundary = 'rest', DirichletDatum = 0)
plotter = HSEngine.FenicsHSEngine(solver.V)
approx = RB.ROMApproximantTaylorRB(solver, plotter, k0 = kappa,
approxParameters = params,
plotDer = False)
ktar = 1.8 - .2j
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(appErr, solNorm, appErr/solNorm)
print(approx.getPoles(True))
############
elif testNo == 3:
def Dboundary(x, on_boundary):
return on_boundary and (fen.near(x[0], 0) or fen.near(x[0], PI))
A = 10
kappa = 2
theta = PI * 30 / 180
x, y = sp.symbols('x[0] x[1]', real=True)
wex = 4/PI**2 * x * (PI - x)
phiex = kappa * (x * np.cos(theta) + y * np.sin(theta))
uex = wex * sp.exp(-1.j * phiex)
fex = - uex.diff(x, 2) - uex.diff(y, 2) - kappa**2 * uex
nx = ny = 20
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)))]
params = {'E':8, 'POD':True}
solver = HFEngine.FenicsHelmholtzScatteringAugmentedEngine(mesh = mesh, wavenumber = kappa, forcingTerm = forcingTerm,
FEDegree = 3, DirichletBoundary = Dboundary,
RobinBoundary = 'rest', DirichletDatum = 0,
constraintType = 'MASS')
plotter = HSEngine.FenicsHSAugmentedEngine(solver.V, 2)
approx = RB.ROMApproximantTaylorRB(solver, plotter, k0 = kappa,
approxParameters = params,
plotDer = False)
ktar = 1.8 - .2j
approx.plotApp(ktar, name = 'u_RB')
approx.plotHF(ktar, name = 'u_HF')
approx.plotErr(ktar, name = 'err')
appErr, solNorm = approx.approxError(ktar, kappa), approx.HFNorm(ktar, kappa)
print(appErr, solNorm, np.divide(appErr, solNorm))
print(approx.getPoles(True))
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