def test_uniform_displacement_neumann(self):
physdims = [1, 1]
g_size = [4, 8]
g_list = [structured.CartGrid([n, n], physdims=physdims) for n in g_size]
[g.compute_geometry() for g in g_list]
error = []
for g in g_list:
bot = np.ravel(np.argwhere(g.face_centers[1, :] < 1e-10))
left = np.ravel(np.argwhere(g.face_centers[0, :] < 1e-10))
dir_faces = np.hstack((left, bot))
bound = bc.BoundaryCondition(
g, dir_faces.ravel("F"), ["dir"] * dir_faces.size
)
constit = setup_stiffness(g)
# Python inverter is most efficient for small problems
stress, bound_stress = mpsa.mpsa(g, constit, bound, inverter="python")
div = fvutils.vector_divergence(g)
a = div * stress
d_x = np.random.rand(1)
d_y = np.random.rand(1)
d_bound = np.zeros((g.dim, g.num_faces))
d_bound[0, bound.is_dir] = d_x
d_bound[1, bound.is_dir] = d_y
rhs = div * bound_stress * d_bound.ravel("F")
d = np.linalg.solve(a.todense(), -rhs)
traction = stress * d + bound_stress * d_bound.ravel("F")
self.assertTrue(np.max(np.abs(d[::2] - d_x)) < 1e-8)
self.assertTrue(np.max(np.abs(d[1::2] - d_y)) < 1e-8)
self.assertTrue(np.max(np.abs(traction)) < 1e-8)
def test_uniform_displacement(self):
g_list = setup_grids.setup_2d()
for g in g_list:
bound_faces = np.argwhere(
np.abs(g.cell_faces).sum(axis=1).A.ravel("F") == 1
)
bound = bc.BoundaryCondition(
g, bound_faces.ravel("F"), ["dir"] * bound_faces.size
)
constit = setup_stiffness(g)
# Python inverter is most efficient for small problems
stress, bound_stress = mpsa.mpsa(g, constit, bound, inverter="python")
div = fvutils.vector_divergence(g)
a = div * stress
d_x = np.random.rand(1)
d_y = np.random.rand(1)
d_bound = np.zeros((g.dim, g.num_faces))
d_bound[0, bound.is_dir] = d_x
d_bound[1, bound.is_dir] = d_y
rhs = div * bound_stress * d_bound.ravel("F")
d = np.linalg.solve(a.todense(), -rhs)
traction = stress * d + bound_stress * d_bound.ravel("F")
self.assertTrue(np.max(np.abs(d[::2] - d_x)) < 1e-8)
self.assertTrue(np.max(np.abs(d[1::2] - d_y)) < 1e-8)
self.assertTrue(np.max(np.abs(traction)) < 1e-8)
def setup(self):
g = CartGrid([5, 5])
g.compute_geometry()
stiffness = StiffnessTensor(g.dim, np.ones(g.num_cells),
np.ones(g.num_cells))
bnd = bc.BoundaryCondition(g)
stress, bound_stress = mpsa.mpsa(g, stiffness, bnd, inverter="python")
return g, stiffness, bnd, stress, bound_stress
def setup(self):
g = pp.CartGrid([5, 5])
g.compute_geometry()
stiffness = pp.FourthOrderTensor(np.ones(g.num_cells), np.ones(g.num_cells))
bnd = pp.BoundaryConditionVectorial(g)
stress, bound_stress, _, _ = mpsa.mpsa(g, stiffness, bnd, inverter="python")
return g, stiffness, bnd, stress, bound_stress
def test_uniform_strain(self):
g_list = setup_grids.setup_2d()
for g in g_list:
bound_faces = np.argwhere(
np.abs(g.cell_faces).sum(axis=1).A.ravel("F") == 1)
bound = pp.BoundaryConditionVectorial(g, bound_faces.ravel("F"),
["dir"] * bound_faces.size)
mu = 1
l = 1
constit = setup_stiffness(g, mu, l)
# Python inverter is most efficient for small problems
stress, bound_stress, _, _ = mpsa.mpsa(g,
constit,
bound,
inverter="python")
div = fvutils.vector_divergence(g)
a = div * stress
xc = g.cell_centers
xf = g.face_centers
gx = np.random.rand(1)
gy = np.random.rand(1)
dc_x = np.sum(xc * gx, axis=0)
dc_y = np.sum(xc * gy, axis=0)
df_x = np.sum(xf * gx, axis=0)
df_y = np.sum(xf * gy, axis=0)
d_bound = np.zeros((g.dim, g.num_faces))
d_bound[0, bound.is_dir[0]] = df_x[bound.is_dir[0]]
d_bound[1, bound.is_dir[1]] = df_y[bound.is_dir[1]]
rhs = div * bound_stress * d_bound.ravel("F")
d = np.linalg.solve(a.todense(), -rhs)
traction = stress * d + bound_stress * d_bound.ravel("F")
s_xx = (2 * mu + l) * gx + l * gy
s_xy = mu * (gx + gy)
s_yx = mu * (gx + gy)
s_yy = (2 * mu + l) * gy + l * gx
n = g.face_normals
traction_ex_x = s_xx * n[0] + s_xy * n[1]
traction_ex_y = s_yx * n[0] + s_yy * n[1]
self.assertTrue(np.max(np.abs(d[::2] - dc_x)) < 1e-8)
self.assertTrue(np.max(np.abs(d[1::2] - dc_y)) < 1e-8)
self.assertTrue(
np.max(np.abs(traction[::2] - traction_ex_x)) < 1e-8)
self.assertTrue(
np.max(np.abs(traction[1::2] - traction_ex_y)) < 1e-8)
def test_conservation_of_momentum(self):
pts = np.random.rand(3, 9)
corners = [
[0, 0, 0, 0, 1, 1, 1, 1],
[0, 0, 1, 1, 0, 0, 1, 1],
[0, 1, 0, 1, 0, 1, 0, 1],
]
pts = np.hstack((corners, pts))
gt = pp.TetrahedralGrid(pts)
gc = pp.CartGrid([3, 3, 3], physdims=[1, 1, 1])
g_list = [gt, gc]
[g.compute_geometry() for g in g_list]
for g in g_list:
g.compute_geometry()
bot = np.ravel(np.argwhere(g.face_centers[1, :] < 1e-10))
left = np.ravel(np.argwhere(g.face_centers[0, :] < 1e-10))
dir_faces = np.hstack((left, bot))
bound = pp.BoundaryConditionVectorial(g, dir_faces.ravel("F"),
["dir"] * dir_faces.size)
constit = setup_stiffness(g)
# Python inverter is most efficient for small problems
stress, bound_stress, _, _ = mpsa.mpsa(g,
constit,
bound,
inverter="python")
div = fvutils.vector_divergence(g)
a = div * stress
bndr = g.get_all_boundary_faces()
d_x = np.random.rand(bndr.size)
d_y = np.random.rand(bndr.size)
d_bound = np.zeros((g.dim, g.num_faces))
d_bound[0, bndr] = d_x
d_bound[1, bndr] = d_y
rhs = div * bound_stress * d_bound.ravel("F")
d = np.linalg.solve(a.todense(), -rhs)
traction = stress * d + bound_stress * d_bound.ravel("F")
traction_2d = traction.reshape((g.dim, -1), order="F")
for cell in range(g.num_cells):
fid, _, sgn = sps.find(g.cell_faces[:, cell])
self.assertTrue(
np.all(np.sum(traction_2d[:, fid] * sgn, axis=1) < 1e-10))
def test_one_cell_a_time_node_keyword(self):
# Update one and one cell, and verify that the result is the same as
# with a single computation. The test is similar to what will happen
# with a memory-constrained splitting.
g = CartGrid([3, 3])
g.compute_geometry()
# Assign random permeabilities, for good measure
np.random.seed(42)
mu = np.random.random(g.num_cells)
lmbda = np.random.random(g.num_cells)
stiffness = StiffnessTensor(2, mu=mu, lmbda=lmbda)
stress = sps.csr_matrix((g.num_faces * g.dim, g.num_cells * g.dim))
bound_stress = sps.csr_matrix(
(g.num_faces * g.dim, g.num_faces * g.dim))
faces_covered = np.zeros(g.num_faces, np.bool)
bnd = bc.BoundaryCondition(g)
stress_full, bound_stress_full = mpsa.mpsa(g,
stiffness,
bnd,
inverter='python')
cn = g.cell_nodes()
for ci in range(g.num_cells):
ind = np.zeros(g.num_cells)
ind[ci] = 1
nodes = np.squeeze(np.where(cn * ind > 0))
partial_stress, partial_bound, active_faces = \
mpsa.mpsa_partial(g, stiffness, bnd, nodes=nodes,
inverter='python')
if np.any(faces_covered):
del_faces = self.expand_indices_nd(
np.where(faces_covered)[0], g.dim)
partial_stress[del_faces, :] *= 0
partial_bound[del_faces, :] *= 0
faces_covered[active_faces] = True
stress += partial_stress
bound_stress += partial_bound
assert (stress_full - stress).max() < 1e-8
assert (stress_full - stress).min() > -1e-8
assert (bound_stress - bound_stress_full).max() < 1e-8
assert (bound_stress - bound_stress_full).min() > -1e-8
