def getError(self):
# Test function
phi = lambda x: np.sin(np.pi * x[:, 0]) * np.sin(
np.pi * x[:, 1]) * np.sin(np.pi * x[:, 2])
j_funX = lambda x: np.pi * np.cos(np.pi * x[:, 0]) * np.sin(
np.pi * x[:, 1]) * np.sin(np.pi * x[:, 2])
j_funY = lambda x: np.pi * np.sin(np.pi * x[:, 0]) * np.cos(
np.pi * x[:, 1]) * np.sin(np.pi * x[:, 2])
j_funZ = lambda x: np.pi * np.sin(np.pi * x[:, 0]) * np.sin(
np.pi * x[:, 1]) * np.cos(np.pi * x[:, 2])
q_fun = lambda x: -3 * (np.pi**2) * phi(x)
mesh = self.M
if self._meshType == "rotateCurv":
nodes_x, nodes_y, nodes_z = mesh.node_list
nodes_x -= 0.25
nodes_y -= 0.25
nodes_z -= 0.25
mesh = discretize.CurvilinearMesh([nodes_x, nodes_y, nodes_z])
else:
mesh.origin = np.r_[-0.25, -0.25, -0.25]
phi_ana = phi(mesh.nodes)
q_ana = q_fun(mesh.nodes)
j_ana = np.r_[j_funX(mesh.edges_x),
j_funY(mesh.edges_y),
j_funZ(mesh.edges_z)]
if self.boundary_type == "Nuemann":
# Nuemann with J defined at boundary nodes
jx_bc = j_funX(mesh.boundary_nodes)
jy_bc = j_funY(mesh.boundary_nodes)
jz_bc = j_funZ(mesh.boundary_nodes)
j_bc = np.c_[jx_bc, jy_bc, jz_bc]
M_bn = mesh.boundary_node_vector_integral
B_bc = sp.csr_matrix((mesh.n_nodes, mesh.n_nodes))
b_bc = M_bn @ (j_bc.reshape(-1, order='F'))
else:
phi_bc = phi(mesh.boundary_faces)
jx_bc = j_funX(mesh.boundary_faces)
jy_bc = j_funY(mesh.boundary_faces)
jz_bc = j_funZ(mesh.boundary_faces)
j_bc = np.c_[jx_bc, jy_bc, jz_bc]
j_bc_dot_n = np.sum(j_bc * mesh.boundary_face_outward_normals,
axis=-1)
# construct matrix with robin operator
if self.boundary_type == "Robin":
alpha = 1.0
else:
# get indices of x0, y0 and z0 boundaries
n_boundary_faces = len(j_bc_dot_n)
robin_locs = np.any(mesh.boundary_faces == -0.25, axis=1)
alpha = np.zeros(n_boundary_faces)
alpha[robin_locs] = 1.0
beta = 1.0
gamma = alpha * phi_bc + beta * j_bc_dot_n
B_bc, b_bc = mesh.edge_divergence_weak_form_robin(
alpha, beta, gamma)
Me = mesh.get_edge_inner_product()
Mn = sp.diags(mesh.average_node_to_cell.T @ mesh.cell_volumes)
G = mesh.nodal_gradient
A = -G.T @ Me @ G + B_bc
rhs = Mn @ q_ana - b_bc
if self.boundary_type == "Nuemann":
A[0, :] = 0.0
A[0, 0] = 1.0
rhs[0] = phi_ana[0]
phi_test = Pardiso(A) * rhs
if self.boundary_type == "Nuemann":
# set them both to have a 0 mean
phi_test -= phi_test.mean()
phi_ana -= phi_ana.mean()
err = np.linalg.norm(phi_test - phi_ana) / np.sqrt(mesh.n_nodes)
return err