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 = gmsh.NodeData(phi, mesh=sphere3_msh)
dadt = .2 * sphere3_msh.nodes.node_coord
dadt = gmsh.NodeData(dadt, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E = [-1, -2, 3] - dadt.node_data2elm_data().value
E = gmsh.ElementData(E, mesh=sphere3_msh)
E.assign_triangle_values()
cond = sphere3_msh.elm.tag1
cond = gmsh.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(self, sphere3_msh):
dipole_pos = np.array([0., 0., 200])
dipole_moment = np.array([1., 0., 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), mesh=sphere3_msh)
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)
m.elmdata.append(gmsh.ElementData(E_analytical))
#gmsh.write_msh(m, '~/Tests/tms.msh')
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_flux_electrodes(self, cube_msh):
v = gmsh.NodeData(cube_msh.nodes.node_coord[:, 1], mesh=cube_msh)
cond = gmsh.ElementData(np.ones(cube_msh.elm.nr), mesh=cube_msh)
areas = cube_msh.elements_volumes_and_areas().value
area_el1 = np.sum(areas[cube_msh.elm.tag1 == 1100]) * 1e-3
flux = fem._calc_flux_electrodes(v, cond, 500, 1005)
assert np.isclose(np.abs(flux), area_el1)
def test_tms_getdp_write_first(self, sphere3_msh):
dipole_pos = np.array([0., 0., 200])
dipole_moment = np.array([1., 0., 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)
fn_dadt = tempfile.NamedTemporaryFile(suffix='.msh', delete=False).name
sphere3_msh.nodedata = [dAdt]
gmsh.write_msh(sphere3_msh, fn_dadt)
sphere3_msh.nodedata = []
cond = gmsh.ElementData(np.ones(sphere3_msh.elm.nr), mesh=sphere3_msh)
fn_cond = tempfile.NamedTemporaryFile(suffix='.msh', delete=False).name
sphere3_msh.elmdata = [cond]
gmsh.write_msh(sphere3_msh, fn_cond)
sphere3_msh.elmdata = []
fn_msh = tempfile.NamedTemporaryFile(suffix='.msh', delete=False).name
gmsh.write_msh(sphere3_msh, fn_msh)
fn_pro = tempfile.NamedTemporaryFile(suffix='.pro', delete=False).name
fem.tms_getdp(fn_msh, fn_cond, fn_dadt, fn_pro)
assert os.path.isfile(fn_dadt)
assert os.path.isfile(fn_cond)
assert os.path.isfile(fn_msh)
assert os.path.isfile(fn_pro)
os.remove(fn_dadt)
os.remove(fn_cond)
os.remove(fn_msh)
os.remove(fn_pro)
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 = gmsh.NodeData(phi, mesh=sphere3_msh)
E = np.zeros((sphere3_msh.elm.nr, 3))
E[:] = [-1., -2., 3.]
E = gmsh.ElementData(E, mesh=sphere3_msh)
cond = sphere3_msh.elm.tag1
cond = gmsh.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_visualization(self, tensor):
eig_val, eig_vec = np.linalg.eig(tensor)
max_eig = eig_val.argmax()
min_eig = eig_val.argmin()
t = np.tile(tensor, [10, 1, 1])
factor = np.arange(1, 11)
t *= factor[:, None, None]
t = gmsh.ElementData(t.reshape(-1, 9))
fields = cond.TensorVisualization(t, all_compoents=True)
assert np.allclose(fields[0].value / factor[:, None],
eig_val[max_eig] * eig_vec[:, max_eig])
assert np.allclose(fields[2].value / factor[:, None],
eig_val[min_eig] * eig_vec[:, min_eig])
assert np.allclose(fields[3].value / factor,
np.prod(eig_val)**(1.0 / 3.0))
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_sphere(self, sphere_el_msh):
surface_tags = [1100, 1101]
currents = [-1, 1]
cond = gmsh.ElementData(np.ones(sphere_el_msh.elm.nr), mesh=cube_msh)
cond.value[sphere_el_msh.elm.tag1 == 4] = .01
v = fem.tdcs_getdp(sphere_el_msh, cond, currents, surface_tags)
m = copy.deepcopy(sphere_el_msh)
m.nodedata = [v]
m = m.crop_mesh(3)
v_fem = m.nodedata[0].value - m.nodedata[0].value[0]
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[0]
rdm = np.linalg.norm(
v_fem/np.linalg.norm(v_fem) -
v_analytical/np.linalg.norm(v_analytical))
#m.nodedata.append(gmsh.NodeData(v_analytical))
#gmsh.write_msh(m, '~/Tests/tdcs.msh')
assert rdm < .2
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)