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show-off.py
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show-off.py
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#!/usr/bin/env python
# coding: utf8
import numpy as np
import scipy.linalg as la
import matplotlib.pyplot as plt
from time import time
import bempp.api as bem
from assemb import MultiTrace, checker
from domains import *
lmbda = 0.5
kRef = 2 * np.pi / lmbda
print('KRef:', kRef)
#meshname = 'geo/mtf-logo.msh'
meshname = 'geo/rings.msh'
dd = [
{ 'name': 0,
'union': [-1, -2, -3],
'phys': 1.,
},
{ 'name': 'M',
'union': 1,
'phys': 4.,
},
{ 'name': 'T',
'union': 2,
'phys': 9.,
},
{ 'name': 'F',
'union': 3,
'phys': 16.,
},
]
doms = Domains(dd)
doms.write2dot()
mtf = MultiTrace(kRef, meshname, doms)
At, X, J, iJ = mtf.tolinop()
shape = mtf.shape
A = 2.0 * At
A2 = A * iJ * A
print('')
print(mtf.shape, flush=True)
print('')
Ce = 0.5 * J - At
Ci = 0.5 * J + At
Ce2 = Ce * iJ * Ce
Ci2 = Ci * iJ * Ci
x = np.random.rand(shape[0]) + 1j * np.random.rand(shape[0])
xr = np.random.rand(shape[0])
checker('A2 = J', A2, J, x)
checker('exterior Proj.', Ce2, Ce, x)
checker('interior Proj.', Ci2, Ci, x)
checker('error-Calderon with random [no-sense]', A, J, x)
#################################################
#################################################
def dir_data(x, normal, dom_ind, result):
result[0] = -np.exp( 1j * kRef * x[0])
def neu_data(x, normal, dom_ind, result):
result[0] = -1j * normal[0] * kRef * np.exp( 1j * kRef * x[0])
#################################################
#################################################
b = mtf.rhs(dir_data, neu_data)
M = A - X
#################################################
#################################################
#################################################
from krylov import gmres, bicgstab
#################################################
#################################################
tol = 1e-6
res = []
restart = None
if restart is None: scale = 1
else: scale = restart
maxiter = int((M.shape[0] / scale) * 0.05)
if maxiter < 50: maxiter = 50
if maxiter > 1000: maxiter = 1000
norm_b = la.norm(b)
#################################################
#################################################
#################################################
iA = iJ * A * iJ
#################################################
Pjac = iA
E = mtf.upper()
Pgs = iA + iA * E * iA
Prec = Pjac
#################################################
#################################################
#################################################
def rescaleRes(res, P, b):
scale = 1.0 / la.norm(P(b))
new_res = scale * res
return new_res
#################################################
print('\nPrec restart={0} maxiter={1}'.format(restart, maxiter), flush=True)
del res
res = []
tt = time()
xx, info = gmres(M, b,
M = Prec,
orthog='mgs',
tol=tol,
residuals=res,
restrt=restart,
maxiter=maxiter)
tt = time() - tt
print(info, len(res))
oRes = np.array(res)
Res = rescaleRes(oRes, Prec, b)
print('#time: {}'.format(tt))
checker('Calderon Prec', A, J, xx)
checker('Transmission Prec', J, X, xx, b)
#################################################
slices = mtf.getSlices()
s = slices['0']
sol = xx[s[0]:s[1]]
d = mtf.domains.getIndexDom('0')
(space, _) , (_, _) = mtf.spaces[d]
n, = sol.shape
n = int(n/2)
sold, soln = sol[:n], sol[n:]
gsold = bem.GridFunction(space, coefficients=sold)
gsoln = bem.GridFunction(space, coefficients=soln)
bem.export(grid_function=gsold,
file_name="soldR.msh",
transformation=np.real)
bem.export(grid_function=gsold,
file_name="soldI.msh",
transformation=np.imag)
print('solution saved.')
# Nx = 200
# Ny = 200
# xmin, xmax, ymin, ymax = [-0.5, 4.5, -0.5, 1.5]
# plot_grid = np.mgrid[xmin:xmax:Nx * 1j, ymin:ymax:Ny * 1j]
# points = np.vstack((plot_grid[0].ravel(),
# plot_grid[1].ravel(),
# np.zeros(plot_grid[0].size)))
# u = np.zeros(points.shape[1], dtype=np.complex)
# u[:] = np.nan
# slp = bem.operators.potential.helmholtz.single_layer(
# space, points, kRef)
# dlp = bem.operators.potential.helmholtz.double_layer(
# space, points, kRef)
# u = slp * gsoln - dlp * gsoln
# uu = u.reshape((Nx, Ny))
# plt.imshow(np.real(uu.T), extent=[xmin, xmax, ymin, ymax])
# plt.colorbar()
# plt.show()