def apply_boundary_condition(self, A, b, uh, timeline):
from fealpy.boundarycondition import RobinBC
from fealpy.boundarycondition import NeumannBC
from fealpy.boundarycondition import DirichletBC
t0 = timeline.current_time_level()
t1 = timeline.next_time_level()
i = timeline.current
# 对 robin 边界条件进行处理
bc = RobinBC(self.space,
lambda x, n: self.pde.robin(x, n, t0),
threshold=self.pde.is_robin_boundary)
A0, b = bc.apply(A, b)
# 对 neumann 边界条件进行处理
bc = NeumannBC(self.space,
lambda x, n: self.pde.neumann(x, n, t0),
threshold=self.pde.is_neumann_boundary)
b = bc.apply(b) # 混合边界条件不需要输入矩阵A
return b
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()
n = int(sys.argv[1])
p = int(sys.argv[2])
scale = float(sys.argv[3])
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)