phi_1 = lambda x, y: y - 0.2 * (x - 0.5) - 0.475
phi_2 = lambda x, y: phi_1(x, y) - 0.05
omega_1, omega_2, omega_3 = [], [], []
volumes = mesh_gen.mb.get_entities_by_dimension(0, 3)
centroids = mesh_gen.mb.tag_get_data(mesh_gen.centroid_tag, volumes)
for vol, c in zip(volumes, centroids):
if phi_1(c[0], c[1]) < 0:
omega_1.append(vol)
elif phi_1(c[0], c[1]) > 0 and phi_2(c[0], c[1]) < 0:
omega_2.append(vol)
elif phi_1(c[0], c[1]) > 0:
omega_3.append(vol)
mesh_gen.set_homogeneous_permeability(K1, vols=omega_2)
mesh_gen.set_homogeneous_permeability(K2, vols=(omega_1 + omega_3))
mesh_gen.set_source_term(q_func)
dirichlet_faces = []
neumann_faces = []
all_faces = mesh_gen.mb.get_entities_by_dimension(0, 2)
for face in all_faces:
adj_vols = mesh_gen.mtu.get_bridge_adjacencies(face, 2, 3)
I, J, K = mesh_gen.mtu.get_bridge_adjacencies(face, 2, 0)
JI = mesh_gen.mb.get_coords([I]) - mesh_gen.mb.get_coords([J])
JK = mesh_gen.mb.get_coords([K]) - mesh_gen.mb.get_coords([J])
normal_area_vec = np.cross(JI, JK)
if len(adj_vols) < 2:
if np.dot(normal_area_vec, np.array([0.0, 0.0, 1.0])) != 0.0:
neumann_faces.append(face)
else:
dirichlet_faces.append(face)
K_sym = Matrix(
([C.y**2 + C.z**2 + 1, -C.x * C.y,
-C.x * C.z], [-C.x * C.y, C.x**2 + C.z**2 + 1,
-C.y * C.z], [-C.x * C.z, -C.y * C.z,
C.x**2 + C.y**2 + 1]))
K_func = lambda x, y, z: np.array([y**2 + z**2 + 1, -x*y, -x*z, \
-x*y, x**2 + z**2 + 1, -y*z, \
-x*z, -y*z, x**2 + y**2 + 1])
print("Generating mesh...")
mesh_gen = MeshGenerator('61052_vols.h5m')
vertices = mesh_gen.mb.get_entities_by_dimension(0, 0)
mesh_gen.mtu.construct_aentities(vertices)
mesh_gen.set_centroids()
mesh_gen.set_heterogeneous_permeability(K_func)
grad_u_matrix = Matrix(
[grad_u.coeff(C.i),
grad_u.coeff(C.j),
grad_u.coeff(C.k)])
F = K_sym * grad_u_matrix
div_F = F.diff(C.x)[0] + F.diff(C.y)[1] + F.diff(C.z)[2]
div_F_func = lambdify([C.x, C.y, C.z], div_F)
mesh_gen.set_source_term(div_F_func)
mesh_gen.set_dirichlet_boundary_conditions(u_func)
print("Done")
mesh_gen.mb.write_file('test_case_2_eymard.h5m')
omega_2.append(vol)
elif phi_1(c[0], c[1]) > 0:
omega_3.append(vol)
mesh_gen.set_homogeneous_permeability(K1.reshape(9), vols=omega_2)
mesh_gen.set_homogeneous_permeability(K2.reshape(9), vols=omega_1)
mesh_gen.set_homogeneous_permeability(K2.reshape(9), vols=omega_3)
grad_u_matrix = Matrix(
[grad_u.coeff(C.i),
grad_u.coeff(C.j),
grad_u.coeff(C.k)])
F1 = Matrix(K1) * grad_u_matrix
div_F1 = F1.diff(C.x)[0] + F1.diff(C.y)[1] + F1.diff(C.z)[2]
div_F1_func = lambdify([C.x, C.y, C.z], div_F1)
mesh_gen.set_source_term(div_F1_func, vols=omega_2)
F2 = Matrix(K2) * grad_u_matrix
div_F2 = F2.diff(C.x)[0] + F2.diff(C.y)[1] + F2.diff(C.z)[2]
div_F2_func = lambdify([C.x, C.y, C.z], div_F2)
mesh_gen.set_source_term(div_F2_func, vols=(omega_1 + omega_3))
dirichlet_faces = []
neumann_faces = []
all_faces = mesh_gen.mb.get_entities_by_dimension(0, 2)
for face in all_faces:
adj_vols = mesh_gen.mtu.get_bridge_adjacencies(face, 2, 3)
I, J, K = mesh_gen.mtu.get_bridge_adjacencies(face, 2, 0)
JI = mesh_gen.mb.get_coords([I]) - mesh_gen.mb.get_coords([J])
JK = mesh_gen.mb.get_coords([K]) - mesh_gen.mb.get_coords([J])
normal_area_vec = np.cross(JI, JK)