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] cells = geometry.compute_colliding_cells(bb_tree, mesh, a, n=1) a_shift_x = np.array([a[0] - offset, a[1], a[2]]) cells_shift_x = geometry.compute_colliding_cells(bb_tree, mesh, a_shift_x, n=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) ]) cells_shift_xyz = geometry.compute_colliding_cells(bb_tree, mesh, a_shift_xyz, n=1) assert u0.eval(a, cells)[0] == pytest.approx( u0.eval(a_shift_xyz, cells_shift_xyz)[0])
def test_eval(V, W, Q, mesh): u1 = Function(V) u2 = Function(W) u3 = Function(Q) 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 u1.interpolate(lambda x: x[0] + x[1] + x[2]) u2.interpolate(e2) u3.interpolate(e3) x0 = (mesh.geometry.x[0] + mesh.geometry.x[1]) / 2.0 tree = BoundingBoxTree(mesh, mesh.geometry.dim) cell_candidates = compute_collisions(tree, x0) cell = compute_colliding_cells(mesh, cell_candidates, x0) first_cell = cell[0] assert np.allclose(u3.eval(x0, first_cell)[:3], u2.eval(x0, first_cell), rtol=1e-15, atol=1e-15)
def evaluate(points, mesh, u): tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim) num_local_cells = mesh.topology.index_map(mesh.topology.dim).size_local colliding_cells = -np.ones(points.shape[1], dtype=np.int32) for i, point in enumerate(points.T): # Find first colliding cell colliding_cell = geometry.compute_colliding_cells(tree, mesh, point, 1) # Only add cell to list if it is owned by the processor if len(colliding_cell) > 0 and colliding_cell[0] < num_local_cells: colliding_cells[i] = colliding_cell[0] local_cells = np.argwhere(colliding_cells != -1).T[0] on_proc = np.zeros(colliding_cells.shape[0]) on_proc[local_cells] = 1 # Workaround since the cell exists on multiple processors, not respecting # ghosting. num_proc = MPI.COMM_WORLD.allgather(on_proc) # from IPython import embed; embed() u_on_proc = u.eval(points.T, colliding_cells) u_g = MPI.COMM_WORLD.allgather(u_on_proc) u_gathered = sum(u_g).T[0] #/ sum(num_proc) return u_gathered
def test_collision_2nd_order_triangle(): points = np.array([[0, 0], [1, 0], [0, 1], [0.65, 0.65], [0, 0.5], [0.5, 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], [0.2, 0.5, 0], [0.6, 0.6, 0]]) # Create boundingboxtree tree = geometry.BoundingBoxTree(mesh, mesh.geometry.dim) for point in sample_points: colliding_cell = geometry.compute_colliding_cells(tree, mesh, 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_sub_entity(dim): """Compute distance from subset of cells in a mesh to a point inside the mesh""" ref_distance = 0.31 xc, yc, zc = 0.5, 0.5, 0.5 points = np.array([xc + ref_distance, yc, zc]) mesh = create_unit_cube(MPI.COMM_WORLD, 8, 8, 8) mesh.topology.create_entities(dim) left_entities = locate_entities(mesh, dim, lambda x: x[0] <= xc) tree = BoundingBoxTree(mesh, dim, left_entities) midpoint_tree = create_midpoint_tree(mesh, dim, left_entities) closest_entities = compute_closest_entity(tree, midpoint_tree, mesh, points) # Find which entity is colliding with known closest point on mesh p_c = np.array([xc, yc, zc]) colliding_entity_bboxes = compute_collisions(tree, p_c) # Refine search by checking for actual collision if the entities are # cells if dim == mesh.topology.dim: colliding_cells = compute_colliding_cells(mesh, colliding_entity_bboxes, p_c) if len(colliding_cells) > 0: assert np.isin(closest_entities[0], colliding_cells) else: if len(colliding_entity_bboxes.links(0)) > 0: assert np.isin(closest_entities[0], colliding_entity_bboxes.links(0))
def test_compute_closest_entity_3d(dim): points = np.array([0.9, 0, 1.135]) mesh = create_unit_cube(MPI.COMM_WORLD, 8, 8, 8) mesh.topology.create_entities(dim) tree = BoundingBoxTree(mesh, dim) num_entities_local = mesh.topology.index_map(dim).size_local + mesh.topology.index_map(dim).num_ghosts entities = np.arange(num_entities_local, dtype=np.int32) midpoint_tree = create_midpoint_tree(mesh, dim, entities) closest_entities = compute_closest_entity(tree, midpoint_tree, mesh, points) # Find which entity is colliding with known closest point on mesh p_c = np.array([0.9, 0, 1]) colliding_entity_bboxes = compute_collisions(tree, p_c) # Refine search by checking for actual collision if the entities are # cells if dim == mesh.topology.dim: colliding_cells = compute_colliding_cells(mesh, colliding_entity_bboxes, p_c) if len(colliding_cells) > 0: assert np.isin(closest_entities[0], colliding_cells) else: if len(colliding_entity_bboxes.links(0)) > 0: assert np.isin(closest_entities[0], colliding_entity_bboxes.links(0))
def test_compute_closest_entity_1d(dim): ref_distance = 0.75 N = 16 points = np.array([[-ref_distance, 0, 0], [2 / N, 2 * ref_distance, 0]]) mesh = create_unit_interval(MPI.COMM_WORLD, N) tree = BoundingBoxTree(mesh, dim) num_entities_local = mesh.topology.index_map(dim).size_local + mesh.topology.index_map(dim).num_ghosts entities = np.arange(num_entities_local, dtype=np.int32) midpoint_tree = create_midpoint_tree(mesh, dim, entities) closest_entities = compute_closest_entity(tree, midpoint_tree, mesh, points) # Find which entity is colliding with known closest point on mesh p_c = np.array([[0, 0, 0], [2 / N, 0, 0]]) colliding_entity_bboxes = compute_collisions(tree, p_c) # Refine search by checking for actual collision if the entities are # cells if dim == mesh.topology.dim: colliding_cells = compute_colliding_cells(mesh, colliding_entity_bboxes, p_c) for i in range(points.shape[0]): # If colliding entity is on process if colliding_cells.links(i).size > 0: assert np.isin(closest_entities[i], colliding_cells.links(i)) else: for i in range(points.shape[0]): # Only check closest entity if any bounding box on the # process intersects with the point if colliding_entity_bboxes.links(i).size > 0: assert np.isin(closest_entities[i], colliding_entity_bboxes.links(i))
def test_manifold_point_search(): # Simple two-triangle surface in 3d vertices = np.array([[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 = np.array([[0, 1, 2], [0, 1, 3]], dtype=np.int64) domain = ufl.Mesh(ufl.VectorElement("Lagrange", "triangle", 1)) mesh = create_mesh(MPI.COMM_WORLD, cells, vertices, domain) bb = BoundingBoxTree(mesh, mesh.topology.dim) # Find cell colliding with point points = np.array([[0.5, 0.25, 0.75], [0.25, 0.5, 0.75]]) cell_candidates = geometry.compute_collisions(bb, points) colliding_cells = geometry.compute_colliding_cells(mesh, cell_candidates, points) # Extract vertices of cell indices = _cpp.mesh.entities_to_geometry( mesh, mesh.topology.dim, [colliding_cells.links(0)[0], colliding_cells.links(1)[0]], False) cell_vertices = mesh.geometry.x[indices] # Compare vertices with input assert np.allclose(cell_vertices, vertices[cells])
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE) set_bc(b, [bc]) uc = Function(U) solver = PETSc.KSP().create(A_cond.getComm()) solver.setOperators(A_cond) solver.solve(b, uc.vector) # Pure displacement based formulation a = form(- ufl.inner(sigma_u(u), ufl.grad(v)) * ufl.dx) A = assemble_matrix(a, bcs=[bc]) A.assemble() # Create bounding box for function evaluation bb_tree = geometry.BoundingBoxTree(mesh, 2) # Check against standard table value p = np.array([48.0, 52.0, 0.0], dtype=np.float64) cell_candidates = geometry.compute_collisions(bb_tree, p) cells = geometry.compute_colliding_cells(mesh, cell_candidates, p) uc.x.scatter_forward() if len(cells) > 0: value = uc.eval(p, cells[0]) print(value[1]) assert np.isclose(value[1], 23.95, rtol=1.e-2) # Check the equality of displacement based and mixed condensed global # matrices, i.e. check that condensation is exact assert np.isclose((A - A_cond).norm(), 0.0)