def test_assemble_fem_matrix(self, sphere3_msh):
msh = sphere3_msh
cond = np.ones(msh.elm.nr)
s = fem.FEMSystem(msh, cond)
assert np.allclose(s.A.dot(np.ones(s.A.shape[0])), 0)
assert np.allclose(s.A.dot(np.pi*np.ones(s.A.shape[0])), 0)
assert np.allclose(s.A.T.toarray(), s.A.toarray())
cond = np.tile(np.eye(3), (msh.elm.nr, 1, 1))
s = fem.FEMSystem(msh, cond)
assert np.allclose(s.A.dot(np.pi*np.ones(s.A.shape[0])), 0)
assert np.allclose(s.A.T.toarray(), s.A.toarray())
def test_dirichlet_problem_sphere(self, sphere3_msh):
m = sphere3_msh.crop_mesh(elm_type=4)
cond = np.ones(len(m.elm.tetrahedra))
cond[m.elm.tag1 == 4] = .01
anode = m.nodes.node_number[m.nodes.node_coord[:, 2].argmax()]
cathode = m.nodes.node_number[m.nodes.node_coord[:, 2].argmin()]
bcs = [fem.DirichletBC([anode], [1]),
fem.DirichletBC([cathode], [-1])]
S = fem.FEMSystem(m, cond)
A = S.A
b = np.zeros(m.nodes.nr)
dof_map = S.dof_map
for bc in bcs:
A, b, dof_map = bc.apply(A, b, dof_map)
x = spalg.spsolve(A, b)
for bc in bcs:
x, dof_map = bc.apply_to_solution(x, dof_map)
order = dof_map.inverse.argsort()
x = x[order].squeeze()
v_analytical = analytical_solutions.potential_3layers_surface_electrodes(
[85, 90, 95], [1., .01, 1.], [0, 0, -95], [0, 0, 95], m.nodes.node_coord)
v_analytical /= v_analytical[anode - 1]
v_analytical -= v_analytical[0]
x -= x[0]
m.nodedata = [mesh_io.NodeData(v_analytical, 'Analytical'),
mesh_io.NodeData(x, 'FEM')]
#mesh_io.write_msh(m, '~/Tests/fem.msh')
m = m.crop_mesh(3)
assert rdm(m.nodedata[0].value, m.nodedata[1].value) < .1
def test_dirichlet_problem_cube(self, cube_lr):
m = cube_lr.crop_mesh(5)
cond = np.ones(len(m.elm.tetrahedra))
top = m.nodes.node_number[m.nodes.node_coord[:, 2] > 49]
bottom = m.nodes.node_number[m.nodes.node_coord[:, 2] < -49]
bcs = [fem.DirichletBC(top, np.ones(len(top))),
fem.DirichletBC(bottom, -np.ones(len(bottom)))]
S = fem.FEMSystem(m, cond)
A = S.A
b = np.zeros(m.nodes.nr)
dof_map = S.dof_map
for bc in bcs:
A, b, dof_map = bc.apply(A, b, dof_map)
x = spalg.spsolve(A, b)
for bc in bcs:
x, dof_map = bc.apply_to_solution(x, dof_map)
order = dof_map.inverse.argsort()
x = x[order]
sol = m.nodes.node_coord[:, 2]/50.
assert np.allclose(sol, x.T)