def test_calc_dadt(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
dadt = .2 * sphere3_msh.nodes.node_coord
dadt = mesh_io.NodeData(dadt, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E = [-1, -2, 3] - dadt.node_data2elm_data().value
E = mesh_io.ElementData(E, mesh=sphere3_msh)
E.assign_triangle_values()
cond = sphere3_msh.elm.tag1
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vDJEgsej', cond, dadt=dadt,
units='m')
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['D'].value, dadt.value)
assert np.allclose(m.field['g'].value, [1, 2, -3])
assert np.allclose(m.field['E'].value, E.value)
assert np.allclose(m.field['J'].value, cond.value[:, None] * E.value)
assert np.allclose(m.field['conductivity'].value, cond.value)
assert np.allclose(m.field['normE'].value, np.linalg.norm(E.value, axis=1))
assert np.allclose(m.field['normJ'].value,
np.linalg.norm(cond.value[:, None] * E.value, axis=1))
def test_tms_getdp_aniso(self, sphere3_msh):
dipole_pos = np.array([0., 0., 200])
dipole_moment = np.array([0., 1., 0.])
didt = 1e6
r = (sphere3_msh.nodes.node_coord - dipole_pos) * 1e-3
dAdt = 1e-7 * didt * np.cross(dipole_moment, r) / (np.linalg.norm(r, axis=1)[:, None] ** 3)
dAdt = gmsh.NodeData(dAdt, mesh=sphere3_msh)
cond = gmsh.ElementData(np.ones((sphere3_msh.elm.nr, 9)), mesh=sphere3_msh)
cond.value[:] = [1, 0, 0, 0, 1, 0, 0, 0, 1]
phi_sim = fem.tms_getdp(sphere3_msh, cond, dAdt)
m = fem.calc_fields(phi_sim, 'vE', dadt=dAdt)
m = m.crop_mesh(elm_type=4)
E_fem = m.field['E'].value
pos = m.elements_baricenters().value
E_analytical = analytical_solutions.tms_E_field(dipole_pos * 1e-3,
dipole_moment, didt,
pos * 1e-3)
rdm = np.linalg.norm(
E_fem.reshape(-1)/np.linalg.norm(E_fem) -
E_analytical.reshape(-1)/np.linalg.norm(E_analytical))
mag = np.log(np.linalg.norm(E_fem)/np.linalg.norm(E_analytical))
assert rdm < .2
assert np.abs(mag) < np.log(1.1)
def test_calc_vEJgs(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E[:] = [-1., -2., 3.]
E = mesh_io.ElementData(E, mesh=sphere3_msh)
cond = sphere3_msh.elm.tag1
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vJEgsej', cond)
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['E'].value, E.value * 1e3)
assert np.allclose(m.field['J'].value,
cond.value[:, None] * E.value * 1e3)
assert np.allclose(m.field['g'].value, -E.value * 1e3)
assert np.allclose(m.field['conductivity'].value, cond.value)
assert np.allclose(m.field['normE'].value,
np.linalg.norm(E.value, axis=1) * 1e3)
assert np.allclose(
m.field['normJ'].value,
np.linalg.norm(cond.value[:, None] * E.value, axis=1) * 1e3)
def test_calc_tensor(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = mesh_io.NodeData(phi, mesh=sphere3_msh)
o = np.ones(sphere3_msh.elm.nr)
z = np.zeros(sphere3_msh.elm.nr)
cond = np.reshape(np.eye(3) * np.array([1, 2, 3]), -1)
cond = np.tile(cond, [sphere3_msh.elm.nr, 1])
cond = mesh_io.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vJEgsej', cond, units='m')
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['g'].value, [1, 2, -3])
assert np.allclose(m.field['E'].value, [-1, -2, 3])
assert np.allclose(m.field['J'].value, [-1, -4, 9])
def test_calc_tensor(self, sphere3_msh):
phi = sphere3_msh.nodes.node_coord[:, 0] + \
2 * sphere3_msh.nodes.node_coord[:, 1] + \
-3 * sphere3_msh.nodes.node_coord[:, 2]
potential = gmsh.NodeData(phi, mesh=sphere3_msh)
o = np.ones(sphere3_msh.elm.nr)
z = np.zeros(sphere3_msh.elm.nr)
cond = np.vstack([z, o, z, o, z, z, z, z, o]).T
cond = gmsh.ElementData(cond, mesh=sphere3_msh)
m = fem.calc_fields(potential, 'vJEgsej', cond, units='m')
assert np.allclose(m.field['v'].value, potential.value)
assert np.allclose(m.field['g'].value, [1, 2, -3])
assert np.allclose(m.field['E'].value, [-1, -2, 3])
assert np.allclose(m.field['J'].value, [-2, -1, 3])
assert np.allclose(m.field['normE'].value, np.sqrt(4+1+9))
assert np.allclose(m.field['normJ'].value, np.sqrt(4+1+9))
def test_tdcs_getdp_cube(self, cube_msh):
surface_tags = [1100, 1101]
currents = [-1, 1]
cond = gmsh.ElementData(np.ones(cube_msh.elm.nr), mesh=cube_msh)
cond.value[cube_msh.elm.tag1 != 5] = 1e6
v = fem.tdcs_getdp(cube_msh, cond, currents, surface_tags)
m = fem.calc_fields(v, 'vE')
# Take a section in the middle of the cube
bar = m.elements_baricenters()
elements_in_mid = m.elm.elm_number[np.abs(bar.value[:, 1]) < 20]
m = m.crop_mesh(elements=elements_in_mid)
E_fem = m.field['E'].value
#gmsh.write_msh(m, '~/Tests/tdcs.msh')
E_analytical = np.zeros_like(E_fem)
E_analytical[:, 1] = 100
rdm = np.linalg.norm(
E_fem.reshape(-1)/np.linalg.norm(E_fem) -
E_analytical.reshape(-1)/np.linalg.norm(E_analytical))
mag = np.log(np.linalg.norm(E_fem)/np.linalg.norm(E_analytical))
assert rdm < .2
assert np.abs(mag) < np.log(1.1)