def coarsening_example1(**kwargs):
#######################
# Simple 2d coarsening based on tpfa for simplex grids
# isotropic permeability
#######################
Nx = Ny = 7
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
part = create_partition(tpfa_matrix(g))
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
part = create_partition(tpfa_matrix(g), cdepth=3)
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
def coarsening_example3(**kwargs):
#######################
# Simple 2d coarsening based on tpfa for simplex grids
# anisotropic permeability
#######################
Nx = Ny = 7
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
kxx = 3 * np.ones(g.num_cells)
kyy = np.ones(g.num_cells)
perm = tensor.SecondOrderTensor(g.dim, kxx=kxx, kyy=kyy)
part = create_partition(tpfa_matrix(g, perm=perm))
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
part = create_partition(tpfa_matrix(g, perm=perm), cdepth=3)
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
part = create_partition(tpfa_matrix(g, perm=perm), cdepth=2, epsilon=1e-2)
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
part = create_partition(tpfa_matrix(g, perm=perm), cdepth=2, epsilon=1)
g = generate_coarse_grid(g, part)
g.compute_geometry(is_starshaped=True)
if kwargs["visualize"]:
plot_grid(g, info="all", alpha=0)
def test_upwind_2d_simplex_surf_discharge_positive(self):
g = simplex.StructuredTriangleGrid([2, 1], [1, 1])
R = cg.rot(np.pi / 2., [1, 1, 0])
g.nodes = np.dot(R, g.nodes)
g.compute_geometry()
solver = upwind.Upwind()
param = Parameters(g)
dis = solver.discharge(g, np.dot(R, [1, 0, 0]))
bf = g.tags["domain_boundary_faces"].nonzero()[0]
bc = BoundaryCondition(g, bf, bf.size * ["neu"])
param.set_bc(solver, bc)
data = {"param": param, "discharge": dis}
M = solver.matrix_rhs(g, data)[0].todense()
deltaT = solver.cfl(g, data)
M_known = np.array([[1, -1, 0, 0], [0, 1, 0, 0], [0, 0, 0, -1],
[-1, 0, 0, 1]])
deltaT_known = 1 / 6
rtol = 1e-15
atol = rtol
self.assertTrue(np.allclose(M, M_known, rtol, atol))
self.assertTrue(np.allclose(deltaT, deltaT_known, rtol, atol))
def main(N):
Nx = Ny = N
#g = structured.CartGrid([Nx, Ny], [2, 2])
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
#co.coarsen(g, 'by_volume')
# Assign parameters
data = add_data(g)
# Choose and define the solvers
solver_flow = vem_dual.DualVEM('flow')
A_flow, b_flow = solver_flow.matrix_rhs(g, data)
solver_source = vem_source.DualSource('flow')
A_source, b_source = solver_source.matrix_rhs(g, data)
up = sps.linalg.spsolve(A_flow + A_source, b_flow + b_source)
u = solver_flow.extract_u(g, up)
p = solver_flow.extract_p(g, up)
P0u = solver_flow.project_u(g, u, data)
diam = np.amax(g.cell_diameters())
return diam, error_p(g, p)
def test_upwind_2d_simplex_discharge_negative(self):
g = simplex.StructuredTriangleGrid([2, 1], [1, 1])
g.compute_geometry()
solver = upwind.Upwind()
param = Parameters(g)
dis = solver.discharge(g, [-1, 0, 0])
bf = g.get_boundary_faces()
bc = BoundaryCondition(g, bf, bf.size * ['neu'])
param.set_bc(solver, bc)
data = {'param': param, 'discharge': dis}
M = solver.matrix_rhs(g, data)[0].todense()
deltaT = solver.cfl(g, data)
M_known = np.array([[ 1, 0, 0,-1],
[-1, 0, 0, 0],
[ 0, 0, 1, 0],
[ 0, 0,-1, 1]])
deltaT_known = 1/6
rtol = 1e-15
atol = rtol
assert np.allclose(M, M_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
def test_create_partition_2d_tri(self):
g = simplex.StructuredTriangleGrid([3, 2])
g.compute_geometry()
part = co.create_partition(co.tpfa_matrix(g))
known = np.array([1, 1, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2])
known_map = np.array([4, 3, 7, 5, 11, 8, 1, 2, 10, 6, 12, 9]) - 1
assert np.array_equal(part, known[known_map])
def test_upwind_2d_simplex_surf_discharge_negative(self):
g = simplex.StructuredTriangleGrid([2, 1], [1, 1])
R = cg.rot(-np.pi / 5., [1, 1, -1])
g.nodes = np.dot(R, g.nodes)
g.compute_geometry(is_embedded=True)
solver = upwind.Upwind()
param = Parameters(g)
dis = solver.discharge(g, np.dot(R, [-1, 0, 0]))
bf = g.tags['domain_boundary_faces'].nonzero()[0]
bc = BoundaryCondition(g, bf, bf.size * ['neu'])
param.set_bc(solver, bc)
data = {'param': param, 'discharge': dis}
M = solver.matrix_rhs(g, data)[0].todense()
deltaT = solver.cfl(g, data)
M_known = np.array([[1, 0, 0, -1],
[-1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, -1, 1]])
deltaT_known = 1 / 6
rtol = 1e-15
atol = rtol
assert np.allclose(M, M_known, rtol, atol)
assert np.allclose(deltaT, deltaT_known, rtol, atol)
def make_grid(grid, grid_dims, domain, dim):
if grid.lower() == "cart" or grid.lower() == "cartesian":
return structured.CartGrid(grid_dims, domain)
elif (grid.lower() == "simplex" and dim == 2) or grid.lower() == "triangular":
return simplex.StructuredTriangleGrid(grid_dims, domain)
elif grid.lower() == "tetrahedral":
g = simplex.StructuredTetrahedralGrid(grid_dims, domain)
return g
def make_grid(grid, grid_dims, domain, dim):
if grid.lower() == 'cart' or grid.lower() == 'cartesian':
return structured.CartGrid(grid_dims, domain)
elif (grid.lower() == 'simplex' and dim == 2) \
or grid.lower() == 'triangular':
return simplex.StructuredTriangleGrid(grid_dims, domain)
elif grid.lower() == 'tetrahedral':
g =simplex.StructuredTetrahedralGrid(grid_dims, domain)
return g
def test_simplex_2d(self):
g = simplex.StructuredTriangleGrid(np.array([3, 2]))
g.compute_geometry()
c = np.array([0, 1, 3])
true_nodes = np.array([0, 1, 4, 5, 6])
true_faces = np.array([0, 1, 2, 4, 5, 10, 13])
h, sub_f, sub_n = partition.extract_subgrid(g, c)
assert np.array_equal(true_nodes, sub_n)
assert np.array_equal(true_faces, sub_f)
self.compare_grid_geometries(g, h, c, true_faces, true_nodes)
def darcy_dualVEM_example2(**kwargs):
#######################
# Simple 2d Darcy problem on a surface with known exact solution
#######################
Nx = Ny = 25
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
R = cg.rot(np.pi / 6., [0, 1, 1])
g.nodes = np.dot(R, g.nodes)
g.compute_geometry()
T = cg.tangent_matrix(g.nodes)
kxx = np.ones(g.num_cells)
perm = tensor.SecondOrderTensor(g.dim, kxx)
def funP_ex(pt):
return np.pi * pt[0] - 6 * pt[1] + np.exp(1) * pt[2] - 4
def funU_ex(pt):
return np.dot(T, [-np.pi, 6, -np.exp(1)])
def fun(pt):
return 0
f = np.array([fun(pt) for pt in g.cell_centers.T])
b_faces = g.get_all_boundary_faces()
bnd = bc.BoundaryCondition(g, b_faces, ["dir"] * b_faces.size)
bnd_val = np.zeros(g.num_faces)
bnd_val[b_faces] = funP_ex(g.face_centers[:, b_faces])
solver = dual.DualVEM()
data = {"perm": perm, "source": f, "bc": bnd, "bc_val": bnd_val}
D, rhs = solver.matrix_rhs(g, data)
up = sps.linalg.spsolve(D, rhs)
u, p = solver.extract_u(g, up), solver.extract_p(g, up)
P0u = solver.project_u(g, u)
if kwargs["visualize"]:
plot_grid(g, p, P0u)
p_ex = error.interpolate(g, funP_ex)
u_ex = error.interpolate(g, funU_ex)
errors = np.array(
[error.error_L2(g, p, p_ex),
error.error_L2(g, P0u, u_ex)])
errors_known = np.array([0, 0])
assert np.allclose(errors, errors_known)
def main(N):
Nx = Ny = N
#g = structured.CartGrid([Nx, Ny], [1, 1])
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
g.compute_geometry()
# Assign parameters
data = add_data(g)
# Choose and define the solvers
solver = mpfa.Mpfa('flow')
A, b_flux = solver.matrix_rhs(g, data)
_, b_source = source.Integral('flow').matrix_rhs(g, data)
p = sps.linalg.spsolve(A, b_flux + b_source)
diam = np.amax(g.cell_diameters())
return diam, error_p(g, p)
# ------------------------------------------------------------------------------#
def error_p(g, p):
sol = np.array([solution(*pt) for pt in g.cell_centers.T])
return np.sqrt(np.sum(np.power(np.abs(p - sol), 2) * g.cell_volumes))
# ------------------------------------------------------------------------------#
Nx = Ny = 20
# g = structured.CartGrid([Nx, Ny], [1, 1])
g = simplex.StructuredTriangleGrid([Nx, Ny], [1, 1])
R = cg.rot(np.pi / 4.0, [1, 0, 0])
g.nodes = np.dot(R, g.nodes)
g.compute_geometry()
# co.coarsen(g, 'by_volume')
# Assign parameters
data = add_data(g)
# Choose and define the solvers
solver = dual.DualVEM("flow")
A, b = solver.matrix_rhs(g, data)
up = sps.linalg.spsolve(A, b)
u = solver.extract_u(g, up)
p = solver.extract_p(g, up)
def test_coverage_triangles(self):
domain = np.array([2, 3])
grid_size = np.array([3, 5])
g = simplex.StructuredTriangleGrid(grid_size, domain)
g.compute_geometry()
self.assertTrue(np.abs(domain.prod() - np.sum(g.cell_volumes)) < 1e-10)
def setUp(self):
g = simplex.StructuredTriangleGrid([1, 1])
g.compute_geometry()
self.g = g
def test_tag_2d_simplex(self):
g = simplex.StructuredTriangleGrid([3] * 2, [1] * 2)
self.assertTrue(
np.array_equal(g.tags["fracture_faces"], [False] * g.num_faces))
self.assertTrue(
np.array_equal(g.tags["fracture_nodes"], [False] * g.num_nodes))
self.assertTrue(
np.array_equal(g.tags["tip_faces"], [False] * g.num_faces))
self.assertTrue(
np.array_equal(g.tags["tip_nodes"], [False] * g.num_nodes))
known = np.array(
[
True,
True,
False,
True,
False,
False,
True,
False,
False,
True,
False,
True,
False,
False,
False,
False,
False,
False,
False,
True,
False,
True,
False,
False,
False,
False,
False,
False,
False,
True,
True,
True,
True,
],
dtype=bool,
)
self.assertTrue(np.array_equal(g.tags["domain_boundary_faces"], known))
known = np.array(
[
True,
True,
True,
True,
True,
False,
False,
True,
True,
False,
False,
True,
True,
True,
True,
True,
],
dtype=bool,
)
self.assertTrue(np.array_equal(g.tags["domain_boundary_nodes"], known))
def test_determine_eta():
g = simplex.StructuredTriangleGrid([1, 1])
assert fvutils.determine_eta(g) == 1 / 3
g = structured.CartGrid([1, 1])
assert fvutils.determine_eta(g) == 0
def test_determine_eta(self):
g = simplex.StructuredTriangleGrid([1, 1])
self.assertTrue(fvutils.determine_eta(g) == 1 / 3)
g = structured.CartGrid([1, 1])
self.assertTrue(fvutils.determine_eta(g) == 0)