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_appy_to_vector(self):
bc = fem.DirichletBC([1, 3, 5], [2, 4, 6])
dof_map = fem.dofMap(np.arange(0, 6))
b = np.arange(6)
b, dof_map = bc.apply_to_vector(b, dof_map)
assert np.all(dof_map.inverse == [0, 2, 4])
assert np.allclose(b, [0, 2, 4])
def test_add_to_solution(self):
bc = fem.DirichletBC([1, 3, 5], [1, 3, 5])
dof_map = fem.dofMap([2, 6, 4])
x = -np.arange(3)
x, dof_map = bc.apply_to_solution(x, dof_map)
assert np.all(dof_map.inverse == [2, 6, 4, 1, 3, 5])
assert np.allclose(x.T, [0, -1, -2, 1, 3, 5])
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)
def test_dirichlet_apply(self):
bc = fem.DirichletBC([1, 3, 5], [2, 4, 6])
dof_map = fem.dofMap(np.arange(1, 7))
A = sparse.diags(1 + np.arange(6)).tocsc()
b = -np.arange(6)
A, b, dof_map = bc.apply(A, b, dof_map)
A = A.toarray()
assert A.shape == (3, 3)
assert b.shape == (3, 1)
assert A[0, 0] == 2
assert A[1, 1] == 4
assert A[2, 2] == 6
assert np.all(dof_map.inverse == [2, 4, 6])
assert dof_map[2] == 0
def test_join(self):
bc1 = fem.DirichletBC([1], [2])
bc2 = fem.DirichletBC([3, 5], [4, 6])
bc = fem.DirichletBC.join([bc1, bc2])
assert np.all(bc.nodes == [1, 3, 5])
assert np.all(bc.values == [2, 4, 6])
