def test_near_evaluations(R, mesh):
# Test that we allow point evaluation that are slightly outside
u0 = Function(R)
u0.vector.set(1.0)
offset = 0.99 * np.finfo(float).eps
bb_tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim)
a = mesh.geometry.x[0]
cell_candidates = geometry.compute_collisions_point(bb_tree, a)
cells = geometry.select_colliding_cells(mesh, cell_candidates, a, 1)
a_shift_x = np.array([a[0] - offset, a[1], a[2]])
cell_candidates = geometry.compute_collisions_point(bb_tree, a_shift_x)
cells_shift_x = geometry.select_colliding_cells(mesh, cell_candidates,
a_shift_x, 1)
assert u0.eval(a, cells)[0] == pytest.approx(
u0.eval(a_shift_x, cells_shift_x)[0])
a_shift_xyz = np.array([
a[0] - offset / math.sqrt(3), a[1] - offset / math.sqrt(3),
a[2] - offset / math.sqrt(3)
])
cell_candidates = geometry.compute_collisions_point(bb_tree, a)
cells_shift_xyz = geometry.select_colliding_cells(mesh, cell_candidates,
a_shift_xyz, 1)
assert u0.eval(a, cells)[0] == pytest.approx(
u0.eval(a_shift_xyz, cells_shift_xyz)[0])
def test_midpoint_tree(N):
"""
Test that midpoint tree speed up compute_closest_entity
"""
mesh = UnitCubeMesh(MPI.COMM_WORLD, N, N, N)
mesh.topology.create_entities(mesh.topology.dim)
left_cells = locate_entities(mesh, mesh.topology.dim,
lambda x: x[0] <= 0.4)
tree = BoundingBoxTree(mesh, mesh.topology.dim, left_cells)
midpoint_tree = create_midpoint_tree(mesh, mesh.topology.dim, left_cells)
p = numpy.array([1 / 3, 2 / 3, 2])
# Find entity closest to point in two steps
# 1. Find closest midpoint using midpoint tree
entity_m, distance_m = compute_closest_entity(midpoint_tree, p, mesh)
# 2. Refine search by using exact distance query
entity, distance = compute_closest_entity(tree, p, mesh, R=distance_m)
# Find entity closest to point in one step
e_r, d_r = compute_closest_entity(tree, p, mesh)
assert entity == e_r
assert distance == d_r
if len(left_cells) > 0:
assert distance < distance_m
else:
assert distance == -1
p_c = numpy.array([1 / 3, 2 / 3, 1])
entities = compute_collisions_point(tree, p_c)
entities = select_colliding_cells(mesh, entities, p_c, len(entities))
if len(entities) > 0:
assert numpy.isin(e_r, entities)
def test_compute_closest_sub_entity(dim):
"""
Compute distance from subset of cells in a mesh to a point inside the mesh
"""
ref_distance = 0.31
p = numpy.array([0.5 + ref_distance, 0.5, 0.5])
mesh = UnitCubeMesh(MPI.COMM_WORLD, 8, 8, 8)
mesh.topology.create_entities(dim)
left_entities = locate_entities(mesh, dim, lambda x: x[0] <= 0.5)
tree = BoundingBoxTree(mesh, dim, left_entities)
entity, distance = compute_closest_entity(tree, p, mesh)
min_distance = MPI.COMM_WORLD.allreduce(distance, op=MPI.MIN)
assert min_distance == pytest.approx(ref_distance, 1.0e-12)
# Find which entity is colliding with known closest point on mesh
p_c = numpy.array([0.5, 0.5, 0.5])
entities = compute_collisions_point(tree, p_c)
# Refine search by checking for actual collision if the entities are
# cells
if dim == mesh.topology.dim:
entities = select_colliding_cells(mesh, entities, p_c, len(entities))
if len(entities) > 0:
assert numpy.isin(entity, entities)
def test_collision_2nd_order_triangle():
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [0.65, 0.65],
[0.0, 0.5], [0.5, 0.0]])
cells = np.array([[0, 1, 2, 3, 4, 5]])
cell = ufl.Cell("triangle", geometric_dimension=2)
domain = ufl.Mesh(ufl.VectorElement("Lagrange", cell, 2))
mesh = create_mesh(MPI.COMM_WORLD, cells, points, domain)
# Sample points along an interior line of the domain. The last point
# is outside the simplex made by the vertices.
sample_points = np.array([[0.1, 0.3, 0.0], [0.2, 0.5, 0.0],
[0.6, 0.6, 0.0]])
# Create boundingboxtree
tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim)
for point in sample_points:
cell_candidates = geometry.compute_collisions_point(tree, point)
colliding_cell = geometry.select_colliding_cells(
mesh, cell_candidates, point, 1)
assert len(colliding_cell) == 1
# Check if there is a point on the linear approximation of the
# curved facet
def line_through_points(p0, p1):
return lambda x: (p1[1] - p0[1]) / (p1[0] - p0[0]) * (x - p0[0]) + p0[1
]
line_func = line_through_points(points[2], points[3])
point = np.array([0.2, line_func(0.2), 0])
# Point inside 2nd order geometry, outside linear approximation
# Usefull for debugging on a later stage
# point = np.array([0.25, 0.89320760, 0])
distance = cpp.geometry.squared_distance(mesh, mesh.topology.dim - 1, 2,
point)
assert np.isclose(distance, 0)
def test_compute_closest_entity_2d(dim):
p = numpy.array([-1.0, -0.01, 0.0])
mesh = UnitSquareMesh(MPI.COMM_WORLD, 15, 15)
tree = BoundingBoxTree(mesh, dim)
entity, distance = compute_closest_entity(tree, p, mesh)
min_distance = MPI.COMM_WORLD.allreduce(distance, op=MPI.MIN)
ref_distance = numpy.sqrt(p[0]**2 + p[1]**2)
assert min_distance == pytest.approx(ref_distance, 1.0e-12)
# Find which entity is colliding with known closest point on mesh
p_c = numpy.array([0, 0, 0])
entities = compute_collisions_point(tree, p_c)
# Refine search by checking for actual collision if the entities are
# cells
# NOTE: Could be done for all entities if we generalize
# select_colliding_cells to select_colliding_entities
if dim == mesh.topology.dim:
entities = select_colliding_cells(mesh, entities, p_c, len(entities))
if len(entities) > 0:
assert numpy.isin(entity, entities)
def test_compute_closest_entity_3d(dim):
ref_distance = 0.135
p = numpy.array([0.9, 0, 1 + ref_distance])
mesh = UnitCubeMesh(MPI.COMM_WORLD, 8, 8, 8)
mesh.topology.create_entities(dim)
tree = BoundingBoxTree(mesh, dim)
entity, distance = compute_closest_entity(tree, p, mesh)
min_distance = MPI.COMM_WORLD.allreduce(distance, op=MPI.MIN)
assert min_distance == pytest.approx(ref_distance, 1.0e-12)
# Find which entity is colliding with known closest point on mesh
p_c = numpy.array([0.9, 0, 1])
entities = compute_collisions_point(tree, p_c)
# Refine search by checking for actual collision if the entities are
# cells
# NOTE: Could be done for all entities if we generalize
# select_colliding_cells to select_colliding_entities
if dim == mesh.topology.dim:
entities = select_colliding_cells(mesh, entities, p_c, len(entities))
if len(entities) > 0:
assert numpy.isin(entity, entities)
else:
df.value = 0.0
fecoda.main.solve_displ_system(J[0], F[0], intern_var0, intern_var1,
expr_compiled, w0, w1, bcs_displ, df, dt, t,
k)
fecoda.main.post_update(expr_compiled, intern_var0, intern_var1, w0, w1)
fecoda.main.copyout_state(w0, w1, intern_var0, intern_var1)
force.value += df.value
bb_tree = BoundingBoxTree(mesh, 3)
p = numpy.array([0.0, 0.0, 0.3], dtype=numpy.float64)
cell_candidates = compute_collisions_point(bb_tree, p)
cell = select_colliding_cells(mesh, cell_candidates, p, 1)
interpolate(ufl.sym(ufl.grad(w1["displ"])), strain)
if len(cell) > 0:
value = strain.eval(p, cell)
value = value[-1]
else:
value = None
values = comm.gather(value, root=0)
if rank == 0:
value = [x for x in values if x is not None][0]
compl = value * -1.0e+6 / args.sigma
log["compl"].append(compl)
log["times"].append(float(t.value) - tp - fecoda.mps.t_begin)