errorType = [
'$|| u - u_h||_{\Omega,0}$', '$||\\nabla u - \\nabla u_h||_{\Omega, 0}$'
]
errorMatrix = np.zeros((2, maxit), dtype=np.float)
NDof = np.zeros(maxit, dtype=np.float)
for i in range(maxit):
space = LagrangeFiniteElementSpace(mesh, p=p)
NDof[i] = space.number_of_global_dofs()
uh = space.function()
A = space.stiff_matrix()
F = space.source_vector(pde.source)
bc = NeumannBC(space, pde.neumann)
A, F = bc.apply(
F, A=A) # Here is the case for pure Neumann bc, we also need modify A
# bc.apply(F) # Not pure Neumann bc case
uh[:] = spsolve(A, F)[:-1] # we add a addtional dof
# Here can not work
#ml = pyamg.ruge_stuben_solver(A)
#x = ml.solve(F, tol=1e-12, accel='cg').reshape(-1)
#uh[:] = x[-1]
errorMatrix[0, i] = space.integralalg.L2_error(pde.solution, uh)
errorMatrix[1, i] = space.integralalg.L2_error(pde.gradient, uh.grad_value)
if i < maxit - 1:
mesh.uniform_refine()
if d == 2:
mu = pde.mu
lam = pde.lam
mesh = pde.init_mesh(n=n)
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
plt.show()
space = LagrangeFiniteElementSpace(mesh, p=p)
bc0 = DirichletBC(space, pde.dirichlet, threshold=pde.is_dirichlet_boundary)
bc1 = NeumannBC(space, pde.neumann, threshold=pde.is_neumann_boundary)
uh = space.function(dim=2)
A = space.linear_elasticity_matrix(mu, lam)
F = space.source_vector(pde.source, dim=2)
bc1.apply(F)
A, F = bc0.apply(A, F, uh)
uh.T.flat[:] = spsolve(A, F)
scale = np.arange(1.0, scale, 0.1)
node = mesh.entity('node')
fname = 'test'
for val in scale:
mesh.node = node + val * uh
fig = plt.figure()
axes = fig.gca()
mesh.add_plot(axes)
plt.savefig(fname + str(val) + '.png')
plt.close()
pde = BoxDomain2DData()
mesh = pde.init_mesh(n=n)
area = mesh.entity_measure('cell')
space = LagrangeFiniteElementSpace(mesh, p=p)
bc0 = DirichletBC(space, pde.dirichlet, threshold=pde.is_dirichlet_boundary)
bc1 = NeumannBC(space, pde.neumann, threshold=pde.is_neumann_boundary)
uh = space.function(dim=2) # (gdof, 2) and vector fem function uh[i, j]
P = space.stiff_matrix(c=2 * pde.mu)
A = space.linear_elasticity_matrix(pde.mu, pde.lam) # (2*gdof, 2*gdof)
F = space.source_vector(pde.source, dim=2)
F = bc1.apply(F)
A, F = bc0.apply(A, F, uh)
print(A.shape)
if False:
uh.T.flat[:] = spsolve(A, F) # (2, gdof ).flat
elif False:
N = len(F)
print(N)
ilu = spilu(A.tocsc(), drop_tol=1e-6, fill_factor=40)
M = LinearOperator((N, N), lambda x: ilu.solve(x))
start = timer()
uh.T.flat[:], info = cg(A, F, tol=1e-8, M=M) # solve with CG
print(info)
end = timer()
p = int(sys.argv[2])
pde = BeamData2d(E=2 * 10**6, nu=0.3)
mu = pde.mu
lam = pde.lam
mesh = pde.init_mesh(n=n)
space = LagrangeFiniteElementSpace(mesh, p=p, q=4)
uh = space.function(dim=2)
A = space.linear_elasticity_matrix(lam, mu)
#A = space.recovery_linear_elasticity_matrix(lam, mu)
F = space.source_vector(pde.source, dim=2)
bc = NeumannBC(space, pde.neumann, threshold=pde.is_neumann_boundary)
F = bc.apply(F)
bc = DirichletBC(space, pde.dirichlet, threshold=pde.is_dirichlet_boundary)
A, F = bc.apply(A, F, uh)
ctx = DMumpsContext()
ctx.set_silent()
if ctx.myid == 0:
ctx.set_centralized_sparse(A)
x = F.copy()
ctx.set_rhs(x) # Modified in place
ctx.run(job=6) # Analysis + Factorization + Solve
ctx.destroy() # Cleanup
uh.T.flat[:] = x
# uh.T.flat[:] = spsolve(A, F) # (2, gdof ).flat