# Try the quad mesh with Q1 elements:
if True:
import poisson_optimized as poisson
# import poisson
pts, quads, tri = create_mesh.quad_rectangle(0, 1, 0, 1, 21, 21)
bc_nodes = set_bc_nodes_square(pts)
# forcing term at mesh nodes
f_pts = f(pts)
# Dirichlet boundary conditions at *all* mesh nodes (most of these values are not used)
u_bc_pts = u_bc(pts)
# Set up the system and solve:
tic = time.clock()
A, b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts,
FEM.Q1Aligned, FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
if pts.shape[0] < 50:
print "cond(A) = %3.3f" % np.linalg.cond(A.todense())
tic = time.clock()
x = spsolve(A.tocsr(), b)
toc = time.clock()
print "Sparse solve took %f s" % (toc - tic)
# Plot:
plt.figure()
plot_mesh.plot_mesh(pts, quads)
plt.figure()
for n in Ns:
print "Running with N = %d" % n
tic = time.clock()
pts, quads, tri = create_mesh.quad_rectangle(-1, 1, -1, 1, n, n)
bc_nodes = set_bc_nodes_square(pts)
toc = time.clock()
print "Mesh generation took %f s" % (toc - tic)
f_pts = f(pts)
u_bc_pts = u_exact(pts)
# Set up the system and solve:
tic = time.clock()
A, b = poisson.poisson(pts, quads, bc_nodes, f_pts, u_bc_pts, FEM.Q1,
FEM.GaussQuad2x2())
toc = time.clock()
print "Matrix assembly took %f s" % (toc - tic)
tic = time.clock()
x = spsolve(A.tocsr(), b)
toc = time.clock()
print "Sparse solve took %f s\n" % (toc - tic)
x_exact = u_exact(pts)
errors.append(np.max(np.fabs(x - x_exact)))
dxs = 2.0 / np.array(Ns - 1)
p = np.polyfit(np.log10(dxs), np.log10(errors), 1)