from laplace import poisson
resids, err = [], []
NGRID = [8, 16, 32, 64, 128, 256, 512, 1024]
for N in NGRID:
source = zeros([N,N], dtype=float)
x = zeros([N,N], dtype=float)
y = zeros([N,N], dtype=float)
x[:] = (arange(N) / float(N-1) - 0.5) * 8.0
y.transpose()[:] = (arange(N) / float(N-1) - 0.5) * 8.0
bcmask = logical_or(x**2 + y**2 >= 16.0, x**2 + y**2 <= 1.0)
bcvalue = zeros([N,N], dtype=float)
bcvalue[x**2 + y**2 <= 1.0] = 1.0
phi, relres = poisson(source, bcmask, bcvalue)
pylab.figure(); pylab.contour(x, y, phi)
pylab.axis('scaled'); pylab.savefig('soln%04d.png' % N)
resids.append(relres)
phi_exact = (log(16.0) - log(x**2 + y**2)) / log(16.0)
phi_exact[bcmask] = phi[bcmask]
err.append(absolute(phi - phi_exact).max())
pylab.figure()
legends = []
for relres, N in zip(resids, NGRID):
pylab.semilogy(range(0, len(relres)*2, 2), relres, '+-')
legends.append('%d by %d' % (N, N))
pylab.semilogy([0, 18], [1.0E-9, 1.0E-9], ':')
pylab.legend(legends)
import pylab import numpy from numpy import zeros, ones from laplace import poisson # n = 128 n = 1024 # n = 4096 source = ones([n, n], dtype=float) bcmask = zeros([n, n], dtype=bool) bcvalue = zeros([n, n], dtype=float) # bcmask[0,:] = True # bcmask[-1,:] = True # bcmask[:,0] = True # bcmask[:,-1] = True phi = poisson(source, bcmask, bcvalue) # pylab.contour(phi) # pylab.show()