# Run and time assembly
t = -timeit.default_timer()
A = assemble(dofmap, a, dtype=numpy.float64)
t += timeit.default_timer()
print('Assembly time a: {}'.format(t))
b = numpy.zeros(A.shape[0], dtype=A.dtype)
x = numpy.zeros_like(b)
# Set some BCs - fix bottom edge, and move top corner
bc_dofs = list(range(n * 2 + 2)) + [len(b) - 2, len(b) - 1]
bc_vals = numpy.zeros_like(bc_dofs, dtype=A.dtype)
bc_vals[-2] = 0.01
bc_apply(bc_dofs, bc_vals, A, b)
print('bnorm = ', numpy.linalg.norm(b))
print('Anorm = ', scipy.sparse.linalg.norm(A))
t = -timeit.default_timer()
x = scipy.sparse.linalg.spsolve(A, b)
t += timeit.default_timer()
print('Solve time: {}'.format(t))
res = b - A * x
print(len(res), len(b), len(x))
print("residual: ", numpy.linalg.norm(res), res.max(), res.min())
# Plotting...
for i, x in enumerate(mesh.vertices):
if (x[0] == -10.0):
idx = i * 3
dofs.append(idx)
vals.append(0.0)
dofs.append(idx + 1)
vals.append(0.0)
dofs.append(idx + 2)
vals.append(0.0)
if (x[0] == 0.0):
idx = i * 3 + 1
dofs.append(idx)
vals.append(0.1)
bc_apply(dofs, numpy.array(vals, dtype=A.dtype), A, b)
# Null space
B = numpy.zeros((A.shape[0], 6), dtype=A.dtype)
# Translation
B[0::3, 0] = 1
B[1::3, 1] = 1
B[2::3, 2] = 1
# Rotation
B[0::3, 3] = 1
B[1::3, 3] = -1
B[1::3, 4] = 1
B[2::3, 4] = -1
B[2::3, 5] = 1
B[0::3, 5] = -1
B = scipy.linalg.orth(B)