def test_manifold_point_search():
# Simple two-triangle surface in 3d
vertices = [(0.0, 0.0, 1.0), (1.0, 1.0, 1.0), (1.0, 0.0, 0.0),
(0.0, 1.0, 0.0)]
cells = [(0, 1, 2), (0, 1, 3)]
mesh = Mesh(MPI.COMM_WORLD, CellType.triangle,
numpy.array(vertices, dtype=numpy.float64),
numpy.array(cells, dtype=numpy.int32), [])
bb = BoundingBoxTree(mesh, mesh.topology.dim)
p = numpy.array([0.5, 0.25, 0.75])
assert geometry.compute_first_entity_collision(bb, mesh, p) == 0
p = numpy.array([0.25, 0.5, 0.75])
assert geometry.compute_first_entity_collision(bb, mesh, p) == 1
def test_compute_first_entity_collision_3d():
reference = [876, 877, 878, 879, 880, 881]
p = numpy.array([0.3, 0.3, 0.3])
mesh = UnitCubeMesh(MPI.comm_world, 8, 8, 8)
tree = BoundingBoxTree(mesh, mesh.topology.dim)
first = geometry.compute_first_entity_collision(tree, mesh, p)
assert first in reference
def test_compute_first_entity_collision_2d():
reference = [136, 137]
p = numpy.array([0.3, 0.3, 0.0])
mesh = UnitSquareMesh(MPI.comm_world, 16, 16)
tree = BoundingBoxTree(mesh, mesh.topology.dim)
first = geometry.compute_first_entity_collision(tree, mesh, p)
assert first in reference
def test_compute_first_entity_collision_1d():
reference = [4]
p = numpy.array([0.3, 0, 0])
mesh = UnitIntervalMesh(MPI.comm_world, 16)
tree = BoundingBoxTree(mesh, mesh.topology.dim)
first = geometry.compute_first_entity_collision(tree, mesh, p)
assert first in reference
def test_eval_multiple(W):
u = Function(W)
u.vector.set(1.0)
mesh = W.mesh
x0 = (mesh.geometry.x[0] + mesh.geometry.x[1]) / 2.0
x = np.array([x0, x0 + 1.0e8])
tree = geometry.BoundingBoxTree(mesh, W.mesh.geometry.dim)
cells = geometry.compute_first_entity_collision(tree, mesh, x)
u.eval(x[0], cells[0])
def test_manufactured_vector2(family, degree, filename, datadir):
"""Projection into H(div/curl) spaces"""
# Skip slowest tests
if "tetra" in filename and degree > 2:
return
with XDMFFile(MPI.comm_world, os.path.join(datadir, filename)) as xdmf:
mesh = xdmf.read_mesh(GhostMode.none)
# FIXME: these test are currently failing on unordered meshes
if "tetra" in filename:
if family == "N1curl":
Ordering.order_simplex(mesh)
V = FunctionSpace(mesh, (family, degree + 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
a = inner(u, v) * dx
xp = np.array([0.33, 0.33, 0.0])
tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim)
cells = geometry.compute_first_entity_collision(tree, mesh, xp)
# Source term
x = SpatialCoordinate(mesh)
u_ref = x[0]**degree
L = inner(u_ref, v[0]) * dx
b = assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
A = assemble_matrix(a)
A.assemble()
# Create LU linear solver (Note: need to use a solver that
# re-orders to handle pivots, e.g. not the PETSc built-in LU
# solver)
solver = PETSc.KSP().create(MPI.comm_world)
solver.setType("preonly")
solver.getPC().setType('lu')
solver.setOperators(A)
# Solve
uh = Function(V)
solver.solve(b, uh.vector)
uh.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
up = uh.eval(xp, cells[0])
print("test0:", up)
print("test1:", xp[0]**degree)
u_exact = np.zeros(mesh.geometry.dim)
u_exact[0] = xp[0]**degree
assert np.allclose(up, u_exact)
def test_manufactured_vector1(family, degree, filename, datadir):
"""Projection into H(div/curl) spaces"""
with XDMFFile(MPI.COMM_WORLD,
os.path.join(datadir, filename),
"r",
encoding=XDMFFile.Encoding.ASCII) as xdmf:
mesh = xdmf.read_mesh(name="Grid")
V = FunctionSpace(mesh, (family, degree))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
a = inner(u, v) * dx
# Source term
x = SpatialCoordinate(mesh)
u_ref = x[0]**degree
L = inner(u_ref, v[0]) * dx
b = assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
A = assemble_matrix(a)
A.assemble()
# Create LU linear solver (Note: need to use a solver that
# re-orders to handle pivots, e.g. not the PETSc built-in LU
# solver)
solver = PETSc.KSP().create(MPI.COMM_WORLD)
solver.setType("preonly")
solver.getPC().setType('lu')
solver.setOperators(A)
# Solve
uh = Function(V)
solver.solve(b, uh.vector)
uh.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
xp = np.array([0.33, 0.33, 0.0])
tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim)
cells = geometry.compute_first_entity_collision(tree, mesh, xp)
up = uh.eval(xp, cells[0])
print("test0:", up)
print("test1:", xp[0]**degree)
u_exact = np.zeros(mesh.geometry.dim)
u_exact[0] = xp[0]**degree
assert np.allclose(up, u_exact)
def test_eval(R, V, W, Q, mesh):
u0 = Function(R)
u1 = Function(V)
u2 = Function(W)
u3 = Function(Q)
def e1(x):
return x[0] + x[1] + x[2]
def e2(x):
values = np.empty((3, x.shape[1]))
values[0] = x[0] + x[1] + x[2]
values[1] = x[0] - x[1] - x[2]
values[2] = x[0] + x[1] + x[2]
return values
def e3(x):
values = np.empty((9, x.shape[1]))
values[0] = x[0] + x[1] + x[2]
values[1] = x[0] - x[1] - x[2]
values[2] = x[0] + x[1] + x[2]
values[3] = x[0]
values[4] = x[1]
values[5] = x[2]
values[6] = -x[0]
values[7] = -x[1]
values[8] = -x[2]
return values
u0.vector.set(1.0)
u1.interpolate(e1)
u2.interpolate(e2)
u3.interpolate(e3)
x0 = (mesh.geometry.x(0) + mesh.geometry.x(1)) / 2.0
tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim)
cells = geometry.compute_first_entity_collision(tree, mesh, x0)
assert np.allclose(u3.eval(x0, cells)[:3],
u2.eval(x0, cells),
rtol=1e-15,
atol=1e-15)
with pytest.raises(ValueError):
u0.eval([0, 0, 0, 0], 0)
with pytest.raises(ValueError):
u0.eval([0, 0], 0)
