def test_constructor_linear(self):
t = Hexahedron()
self.assertTrue((t.nodes() == np.array([[-1, -1, -1], [+1, -1, -1],
[+1, +1, -1], [-1, +1, -1],
[-1, -1, +1], [+1, -1, +1],
[+1, +1, +1], [-1, +1,
+1]])).all())
# 3D
t = Hexahedron([-1, -1, -1], [+1, -1, -1], [+1, +1, -1], [-1, +1, -1],
[-1, -1, +1], [+1, -1, +1], [+1, +1, +1], [-1, +1, +1])
self.assertTrue((t.nodes() == np.array([[-1, -1, -1], [+1, -1, -1],
[+1, +1, -1], [-1, +1, -1],
[-1, -1, +1], [+1, -1, +1],
[+1, +1, +1], [-1, +1,
+1]])).all())
t = Hexahedron([[-1, -1, -1], [+1, -1, -1], [+1, +1, -1], [-1, +1, -1],
[-1, -1, +1], [+1, -1, +1], [+1, +1, +1], [-1, +1,
+1]])
self.assertTrue((t.nodes() == np.array([[-1, -1, -1], [+1, -1, -1],
[+1, +1, -1], [-1, +1, -1],
[-1, -1, +1], [+1, -1, +1],
[+1, +1, +1], [-1, +1,
+1]])).all())
def test_deformed_liver_hexa(self):
m = meshio.read(
os.path.join(os.path.dirname(__file__), '..', 'meshes',
'deformed_liver_volume_hexahedrons.vtu'))
mesh = Mesh(m.points)
if type(m.cells) == dict:
cells = m.cells['hexahedron']
else:
cells = m.cells_dict['hexahedron']
domain = mesh.add_domain("hexa", Hexahedron(Caribou.Linear), cells)
undeformed_markers = np.array([[265.83, -155.11, -1539.04],
[260.11, -126.47, -1540.98],
[274.25, -176.07, -1505.73],
[285.61, -211.77, -1503.08],
[260.49, -124.21, -1514.15],
[264.56, -143.91, -1478.4],
[231.42, -167.12, -1478.51],
[204.36, -193.61, -1501.44],
[210.5, -149.3, -1519.34],
[232.38, -248.64, -1507.46],
[271.51, -192.76, -1462.05],
[294.9, -162.29, -1478.03],
[312.83, -191.94, -1482.31],
[302.98, -269.28, -1493.],
[315.78, -226.09, -1504.54]])
deformed_markers = np.array(
[[270.9119593, -157.71215294, -1555.40946454],
[262.14820601, -128.06090875, -1552.47007965],
[277.19378591, -177.43088076, -1516.55486109],
[293.97624055, -213.41924186, -1522.43362963],
[265.88433766, -126.62070365, -1524.0396069],
[266.88009204, -147.60863833, -1490.24440459],
[262.09361709, -173.36263398, -1499.35976378],
[243.77807901, -199.20167085, -1529.01202647],
[246.71909105, -156.88296646, -1546.59187345],
[252.34989369, -255.47322977, -1531.41912502],
[275.70481717, -198.33630816, -1478.29025749],
[296.66730156, -168.05975732, -1487.89185992],
[316.39825186, -196.90427925, -1493.97027093],
[302.8963988, -274.06481598, -1510.41305086],
[319.35443171, -231.06013115, -1521.27203137]])
interpolated_displacements = domain.embed(
undeformed_markers).interpolate(m.point_data['u'])
self.assertMatrixAlmostEqual(interpolated_displacements,
(deformed_markers - undeformed_markers))
def test_quadratic_3D(self):
t = Hexahedron(Caribou.Quadratic)
self.assertEqual(t.number_of_boundary_elements(), 6)
self.assertEqual(t.number_of_nodes(), 20)
# Center
self.assertMatrixAlmostEqual(t.center(), [0, 0, 0])
# Inverse transformation
for gauss_node in t.gauss_nodes():
self.assertMatrixAlmostEqual(
gauss_node.position,
t.local_coordinates(t.world_coordinates(gauss_node.position)))
for node in t.nodes():
self.assertMatrixAlmostEqual(
node, t.world_coordinates(t.local_coordinates(node)))
# Contains point
self.assertTrue(t.contains_local(t.local_coordinates(t.center())))
# Integration
numerical_solution = 0.
for gauss_node in t.gauss_nodes():
x = gauss_node.position
w = gauss_node.weight
J = t.jacobian(x)
detJ = np.linalg.det(J)
numerical_solution += p2(t.world_coordinates(x)) * w * detJ
analytic_solution = 50.666666666666664
self.assertAlmostEqual(numerical_solution,
analytic_solution,
delta=1e-10)