def test_gmsh_input_quad(order):
pygmsh = pytest.importorskip("pygmsh")
# Parameterize test if gmsh gets wider support
R = 1
res = 0.2 if order == 2 else 0.2
algorithm = 2 if order == 2 else 5
element = "quad{0:d}".format(int((order + 1)**2))
geo = pygmsh.opencascade.Geometry()
geo.add_raw_code("Mesh.ElementOrder={0:d};".format(order))
geo.add_ball([0, 0, 0], R, char_length=res)
geo.add_raw_code("Recombine Surface {1};")
geo.add_raw_code("Mesh.Algorithm = {0:d};".format(algorithm))
msh = pygmsh.generate_mesh(geo, verbose=True, dim=2)
if order > 2:
# Quads order > 3 have a gmsh specific ordering, and has to be permuted.
msh_to_dolfin = np.array([0, 3, 11, 10, 1, 2, 6, 7, 4, 9, 12, 15, 5, 8, 13, 14])
cells = np.zeros(msh.cells_dict[element].shape)
for i in range(len(cells)):
for j in range(len(msh_to_dolfin)):
cells[i, j] = msh.cells_dict[element][i, msh_to_dolfin[j]]
else:
# XDMF does not support higher order quads
cells = permute_cell_ordering(msh.cells_dict[element], permutation_vtk_to_dolfin(
CellType.quadrilateral, msh.cells_dict[element].shape[1]))
mesh = Mesh(MPI.comm_world, CellType.quadrilateral, msh.points, cells,
[], GhostMode.none)
surface = assemble_scalar(1 * dx(mesh))
assert MPI.sum(mesh.mpi_comm(), surface) == pytest.approx(4 * np.pi * R * R, rel=1e-5)
def test_volume_quadrilateralR3(coordinates):
mesh = Mesh(MPI.comm_world, CellType.quadrilateral,
numpy.array(coordinates, dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.create_connectivity_all()
assert cpp.mesh.volume_entities(mesh, [0], mesh.topology.dim) == 1.0
def test_higher_order_coordinate_map(points, celltype, order):
"""Computes physical coordinates of a cell, based on the coordinate map."""
cells = np.array([range(len(points))])
mesh = Mesh(MPI.COMM_WORLD, celltype, points, cells, [], degree=order)
V = FunctionSpace(mesh, ("Lagrange", 2))
X = V.element.dof_reference_coordinates()
coord_dofs = mesh.geometry.dofmap
x_g = mesh.geometry.x
cmap = fem.create_coordinate_map(mesh.ufl_domain())
x_coord_new = np.zeros([len(points), mesh.geometry.dim])
i = 0
for node in range(len(points)):
x_coord_new[i] = x_g[coord_dofs.links(0)[node], :mesh.geometry.dim]
i += 1
x = np.zeros(X.shape)
cmap.push_forward(x, X, x_coord_new)
assert(np.allclose(x[:, 0], X[:, 0]))
assert(np.allclose(x[:, 1], 2 * X[:, 1]))
if mesh.geometry.dim == 3:
assert(np.allclose(x[:, 2], 3 * X[:, 2]))
def xtest_mesh_order_unchanged_hexahedron():
points = [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0], [0, 0, 1], [1, 0, 1],
[0, 1, 1], [1, 1, 1]]
cells = [[0, 1, 2, 3, 4, 5, 6, 7]]
mesh = Mesh(MPI.COMM_WORLD, CellType.hexahedron, points, cells, [],
cpp.mesh.GhostMode.none)
assert (mesh.cells()[0] == cells[0]).all()
def test_higher_order_coordinate_map(points, celltype):
"""
Computes physical coordinates of a cell, based on the coordinate map.
"""
cells = np.array([range(len(points))])
mesh = Mesh(MPI.comm_world, celltype, points, cells, [], GhostMode.none)
V = FunctionSpace(mesh, ("Lagrange", mesh.degree()))
X = V.element.dof_reference_coordinates()
coord_dofs = mesh.coordinate_dofs().entity_points()
x_g = mesh.geometry.points
cmap = fem.create_coordinate_map(mesh.ufl_domain())
x_coord_new = np.zeros([len(points), mesh.geometry.dim])
i = 0
for node in range(len(points)):
x_coord_new[i] = x_g[coord_dofs[0, node], :mesh.geometry.dim]
i += 1
x = np.zeros(X.shape)
cmap.push_forward(x, X, x_coord_new)
assert (np.allclose(x[:, 0], X[:, 0]))
assert (np.allclose(x[:, 1], 2 * X[:, 1]))
if mesh.geometry.dim == 3:
assert (np.allclose(x[:, 2], 3 * X[:, 2]))
def test_quadrilateral_dof_ordering(space_type):
"""Checks that dofs on shared quadrilateral edges match up"""
if MPI.COMM_WORLD.rank == 0:
# Create a quadrilateral mesh
N = 10
temp_points = np.array([[x / 2, y / 2] for x in range(N)
for y in range(N)])
order = [i for i, j in enumerate(temp_points)]
shuffle(order)
points = np.zeros(temp_points.shape)
for i, j in enumerate(order):
points[j] = temp_points[i]
cells = []
for x in range(N - 1):
for y in range(N - 1):
a = N * y + x
cell = [order[i] for i in [a, a + 1, a + N, a + N + 1]]
cells.append(cell)
# On process 0, input mesh data and distribute to other
# processes
mesh = Mesh(MPI.COMM_WORLD, CellType.quadrilateral, points,
np.array(cells), [])
else:
# On other processes, accept distributed data
mesh = Mesh(MPI.COMM_WORLD, CellType.quadrilateral, np.ndarray((0, 2)),
np.ndarray((0, 4)), [])
V = FunctionSpace(mesh, space_type)
dofmap = V.dofmap
edges = {}
# Get coordinates of dofs and edges and check that they are the same
# for each global dof number
X = V.element.dof_reference_coordinates()
coord_dofs = mesh.geometry.dofmap
x_g = mesh.geometry.x
cmap = fem.create_coordinate_map(mesh.ufl_domain())
for cell_n in range(coord_dofs.num_nodes):
dofs = dofmap.cell_dofs(cell_n)
x_coord_new = np.zeros([4, 2])
for v in range(4):
x_coord_new[v] = x_g[coord_dofs.links(cell_n)[v], :2]
x = X.copy()
cmap.push_forward(x, X, x_coord_new)
edge_dofs_local = []
for i in range(4):
edge_dofs_local += list(dofmap.dof_layout.entity_dofs(1, i))
edge_dofs = [dofs[i] for i in edge_dofs_local]
for i, j in zip(edge_dofs, x[edge_dofs_local]):
if i in edges:
assert np.allclose(j, edges[i])
else:
edges[i] = j
def test_triangle_mesh():
mesh = Mesh(
MPI.comm_world, CellType.triangle,
numpy.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]], dtype=numpy.float64),
numpy.array([[0, 1, 2]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
assert mesh.num_entities_global(0) == 3
assert mesh.num_entities_global(2) == 1
def test_third_order_tri():
# *---*---*---* 3--11--10--2
# | \ | | \ |
# * * * * 8 7 15 13
# | \ | | \ |
# * * * * 9 14 6 12
# | \ | | \ |
# *---*---*---* 0--4---5---1
for H in (1.0, 2.0):
for Z in (0.0, 0.5):
L = 1
points = np.array([
[0, 0, 0],
[L, 0, 0],
[L, H, Z],
[0, H, Z], # 0, 1, 2, 3
[L / 3, 0, 0],
[2 * L / 3, 0, 0], # 4, 5
[2 * L / 3, H / 3, 0],
[L / 3, 2 * H / 3, 0], # 6, 7
[0, 2 * H / 3, 0],
[0, H / 3, 0], # 8, 9
[2 * L / 3, H, Z],
[L / 3, H, Z], # 10, 11
[L, H / 3, 0],
[L, 2 * H / 3, 0], # 12, 13
[L / 3, H / 3, 0], # 14
[2 * L / 3, 2 * H / 3, 0]
]) # 15
cells = np.array([[0, 1, 3, 4, 5, 6, 7, 8, 9, 14],
[1, 2, 3, 12, 13, 10, 11, 7, 6, 15]])
cells = permute_cell_ordering(
cells,
permutation_vtk_to_dolfin(CellType.triangle, cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.triangle, points, cells, [],
GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
degree = mesh.degree()
# Interpolate function
V = FunctionSpace(mesh, ("CG", degree))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(u * dx(metadata={"quadrature_degree": 40}))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 9, 8, 3]
ref = sympy_scipy(points, nodes, L, H)
assert ref == pytest.approx(intu, rel=1e-6)
def test_third_order_quad(L, H, Z):
"""Test by comparing integration of z+x*y against sympy/scipy integration
of a quad element. Z>0 implies curved element.
*---------* 3--8--9--2-22-23-17
| | | | |
| | 11 14 15 7 26 27 21
| | | | |
| | 10 12 13 6 24 25 20
| | | | |
*---------* 0--4--5--1-18-19-16
"""
points = np.array([[0, 0, 0], [L, 0, 0], [L, H, Z], [0, H, Z], # 0 1 2 3
[L / 3, 0, 0], [2 * L / 3, 0, 0], # 4 5
[L, H / 3, 0], [L, 2 * H / 3, 0], # 6 7
[L / 3, H, Z], [2 * L / 3, H, Z], # 8 9
[0, H / 3, 0], [0, 2 * H / 3, 0], # 10 11
[L / 3, H / 3, 0], [2 * L / 3, H / 3, 0], # 12 13
[L / 3, 2 * H / 3, 0], [2 * L / 3, 2 * H / 3, 0], # 14 15
[2 * L, 0, 0], [2 * L, H, Z], # 16 17
[4 * L / 3, 0, 0], [5 * L / 3, 0, 0], # 18 19
[2 * L, H / 3, 0], [2 * L, 2 * H / 3, 0], # 20 21
[4 * L / 3, H, Z], [5 * L / 3, H, Z], # 22 23
[4 * L / 3, H / 3, 0], [5 * L / 3, H / 3, 0], # 24 25
[4 * L / 3, 2 * H / 3, 0], [5 * L / 3, 2 * H / 3, 0]]) # 26 27
# Change to multiple cells when matthews dof-maps work for quads
cells = np.array([[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],
[1, 16, 17, 2, 18, 19, 20, 21, 22, 23, 6, 7, 24, 25, 26, 27]])
cells = permute_cell_ordering(cells, permutation_vtk_to_dolfin(CellType.quadrilateral, cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.quadrilateral, points, cells,
[], GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
# Interpolate function
V = FunctionSpace(mesh, ("CG", 3))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(u * dx(mesh))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 3, 10, 11]
ref = sympy_scipy(points, nodes, 2 * L, H)
assert ref == pytest.approx(intu, rel=1e-6)
def test_volume_quadrilateral_coplanarity_check_2(scaling):
with pytest.raises(RuntimeError) as error:
# Unit square cell scaled down by 'scaling' and the first vertex
# is distorted so that the vertices are clearly non coplanar
mesh = Mesh(
MPI.comm_world, CellType.quadrilateral,
numpy.array([[1.0, 0.5, 0.6], [0.0, scaling, 0.0],
[0.0, 0.0, scaling], [0.0, 1.0, 1.0]],
dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.create_connectivity_all()
cpp.mesh.volume_entities(mesh, [0], mesh.topology.dim)
assert "Not coplanar" in str(error.value)
def test_fourth_order_tri():
L = 1
# *--*--*--*--* 3-21-20-19--2
# | \ | | \ |
# * * * * * 10 9 24 23 18
# | \ | | \ |
# * * * * * 11 15 8 22 17
# | \ | | \ |
# * * * * * 12 13 14 7 16
# | \ | | \ |
# *--*--*--*--* 0--4--5--6--1
for H in (1.0, 2.0):
for Z in (0.0, 0.5):
points = np.array(
[[0, 0, 0], [L, 0, 0], [L, H, Z], [0, H, Z], # 0, 1, 2, 3
[L / 4, 0, 0], [L / 2, 0, 0], [3 * L / 4, 0, 0], # 4, 5, 6
[3 / 4 * L, H / 4, Z / 2], [L / 2, H / 2, 0], # 7, 8
[L / 4, 3 * H / 4, 0], [0, 3 * H / 4, 0], # 9, 10
[0, H / 2, 0], [0, H / 4, Z / 2], # 11, 12
[L / 4, H / 4, Z / 2], [L / 2, H / 4, Z / 2], [L / 4, H / 2, 0], # 13, 14, 15
[L, H / 4, Z / 2], [L, H / 2, 0], [L, 3 * H / 4, 0], # 16, 17, 18
[3 * L / 4, H, Z], [L / 2, H, Z], [L / 4, H, Z], # 19, 20, 21
[3 * L / 4, H / 2, 0], [3 * L / 4, 3 * H / 4, 0], # 22, 23
[L / 2, 3 * H / 4, 0]] # 24
)
cells = np.array([[0, 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15],
[1, 2, 3, 16, 17, 18, 19, 20, 21, 9, 8, 7, 22, 23, 24]])
cells = permute_cell_ordering(cells, permutation_vtk_to_dolfin(CellType.triangle, cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.triangle, points, cells,
[], GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
degree = mesh.degree()
# Interpolate function
V = FunctionSpace(mesh, ("CG", degree))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(u * dx(metadata={"quadrature_degree": 50}))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 3, 10, 11, 12]
ref = sympy_scipy(points, nodes, L, H)
assert ref == pytest.approx(intu, rel=1e-4)
def unit_cell(cell_type, random_order=True):
if cell_type == CellType.interval:
points = np.array([[0.], [1.]])
if cell_type == CellType.triangle:
# Define equilateral triangle with area 1
root = 3**0.25 # 4th root of 3
points = np.array([[0., 0.], [2 / root, 0.], [1 / root, root]])
elif cell_type == CellType.tetrahedron:
# Define regular tetrahedron with volume 1
s = 2**0.5 * 3**(1 / 3) # side length
points = np.array([[0., 0., 0.], [s, 0., 0.],
[s / 2, s * np.sqrt(3) / 2, 0.],
[s / 2, s / 2 / np.sqrt(3), s * np.sqrt(2 / 3)]])
elif cell_type == CellType.quadrilateral:
# Define unit quadrilateral (area 1)
points = np.array([[0., 0.], [1., 0.], [0., 1.], [1., 1.]])
elif cell_type == CellType.hexahedron:
# Define unit hexahedron (volume 1)
points = np.array([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.],
[1., 1., 0.], [0., 0., 1.], [1., 0., 1.],
[0., 1., 1.], [1., 1., 1.]])
num_points = len(points)
# Randomly number the points and create the mesh
order = list(range(num_points))
if random_order:
shuffle(order)
ordered_points = np.zeros(points.shape)
for i, j in enumerate(order):
ordered_points[j] = points[i]
cells = np.array([order])
mesh = Mesh(MPI.COMM_WORLD, cell_type, ordered_points, cells, [])
mesh.topology.create_connectivity_all()
return mesh
def two_unit_cells(cell_type, agree=False, random_order=True, return_order=False):
if cell_type == CellType.interval:
points = np.array([[0.], [1.], [-1.]])
if agree:
cells = [[0, 1], [2, 0]]
else:
cells = [[0, 1], [0, 2]]
if cell_type == CellType.triangle:
# Define equilateral triangles with area 1
root = 3 ** 0.25 # 4th root of 3
points = np.array([[0., 0.], [2 / root, 0.],
[1 / root, root], [1 / root, -root]])
if agree:
cells = [[0, 1, 2], [0, 3, 1]]
else:
cells = [[0, 1, 2], [1, 0, 3]]
elif cell_type == CellType.tetrahedron:
# Define regular tetrahedra with volume 1
s = 2 ** 0.5 * 3 ** (1 / 3) # side length
points = np.array([[0., 0., 0.], [s, 0., 0.],
[s / 2, s * np.sqrt(3) / 2, 0.],
[s / 2, s / 2 / np.sqrt(3), s * np.sqrt(2 / 3)],
[s / 2, s / 2 / np.sqrt(3), -s * np.sqrt(2 / 3)]])
if agree:
cells = [[0, 1, 2, 3], [0, 1, 4, 2]]
else:
cells = [[0, 1, 2, 3], [0, 2, 1, 4]]
elif cell_type == CellType.quadrilateral:
# Define unit quadrilaterals (area 1)
points = np.array([[0., 0.], [1., 0.], [0., 1.], [1., 1.], [0., -1.], [1., -1.]])
if agree:
cells = [[0, 1, 2, 3], [4, 5, 0, 1]]
else:
cells = [[0, 1, 2, 3], [5, 1, 4, 0]]
elif cell_type == CellType.hexahedron:
# Define unit hexahedra (volume 1)
points = np.array([[0., 0., 0.], [1., 0., 0.], [0., 1., 0.],
[1., 1., 0.], [0., 0., 1.], [1., 0., 1.],
[0., 1., 1.], [1., 1., 1.], [0., 0., -1.],
[1., 0., -1.], [0., 1., -1.], [1., 1., -1.]])
if agree:
cells = [[0, 1, 2, 3, 4, 5, 6, 7], [8, 9, 10, 11, 0, 1, 2, 3]]
else:
cells = [[0, 1, 2, 3, 4, 5, 6, 7], [9, 11, 8, 10, 1, 3, 0, 2]]
num_points = len(points)
# Randomly number the points and create the mesh
order = list(range(num_points))
if random_order:
shuffle(order)
ordered_points = np.zeros(points.shape)
for i, j in enumerate(order):
ordered_points[j] = points[i]
ordered_cells = np.array([[order[i] for i in c] for c in cells])
mesh = Mesh(MPI.COMM_WORLD, cell_type, ordered_points, ordered_cells, [])
mesh.topology.create_connectivity_all()
if return_order:
return mesh, order
return mesh
def test_read_mesh_data(tempdir, tdim, n):
filename = os.path.join(tempdir, "mesh.xdmf")
mesh = mesh_factory(tdim, n)
encoding = XDMFFile.Encoding.HDF5
ghost_mode = cpp.mesh.GhostMode.none
with XDMFFile(mesh.mpi_comm(), filename, encoding) as file:
file.write(mesh)
with XDMFFile(MPI.comm_world, filename) as file:
cell_type, points, cells, indices = file.read_mesh_data(MPI.comm_world)
mesh2 = Mesh(MPI.comm_world, cell_type, points, cells, indices, ghost_mode)
assert (mesh.topology.cell_type == mesh2.topology.cell_type)
assert mesh.num_entities_global(0) == mesh2.num_entities_global(0)
dim = mesh.topology.dim
assert mesh.num_entities_global(dim) == mesh2.num_entities_global(dim)
def test_second_order_quad(L, H, Z):
""" Test by comparing integration of z+x*y against sympy/scipy
integration of a quad element. Z>0 implies curved element.
*-----* 3--6--2
| | | |
| | 7 8 5
| | | |
*-----* 0--4--1
"""
points = np.array([[0, 0, 0], [L, 0, 0], [L, H, Z], [0, H, Z],
[L / 2, 0, 0], [L, H / 2, 0], [L / 2, H, Z],
[0, H / 2, 0], [L / 2, H / 2, 0], [2 * L, 0, 0],
[2 * L, H, Z]])
cells = np.array([[0, 1, 2, 3, 4, 5, 6, 7, 8]])
cells = permute_cell_ordering(
cells, permutation_vtk_to_dolfin(CellType.quadrilateral,
cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.quadrilateral, points, cells, [],
GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
# Interpolate function
V = FunctionSpace(mesh, ("CG", 2))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(u * dx(mesh))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 3, 7]
ref = sympy_scipy(points, nodes, L, H)
assert ref == pytest.approx(intu, rel=1e-6)
def test_second_order_tri():
# Test second order mesh by computing volume of two cells
# *-----*-----* 3----6-----2
# | \ | | \ |
# | \ | | \ |
# * * * 7 8 5
# | \ | | \ |
# | \ | | \ |
# *-----*-----* 0----4-----1
for H in (1.0, 2.0):
for Z in (0.0, 0.5):
L = 1
points = np.array([[0, 0, 0], [L, 0, 0], [L, H, Z], [0, H, Z],
[L / 2, 0, 0], [L, H / 2, 0], [L / 2, H, Z],
[0, H / 2, 0], [L / 2, H / 2, 0]])
cells = np.array([[0, 1, 3, 4, 8, 7], [1, 2, 3, 5, 6, 8]])
cells = permute_cell_ordering(
cells,
permutation_vtk_to_dolfin(CellType.triangle, cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.triangle, points, cells, [],
GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
degree = mesh.degree()
# Interpolate function
V = FunctionSpace(mesh, ("CG", degree))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(
u * dx(mesh, metadata={"quadrature_degree": 20}))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 3, 7]
ref = sympy_scipy(points, nodes, L, H)
assert ref == pytest.approx(intu, rel=1e-6)
def test_higher_order_tetra_coordinate_map(order):
"""
Computes physical coordinates of a cell, based on the coordinate map.
"""
celltype = CellType.tetrahedron
points = np.array([[0, 0, 0], [1, 0, 0], [0, 2, 0], [0, 0, 3],
[0, 4 / 3, 1], [0, 2 / 3, 2],
[2 / 3, 0, 1], [1 / 3, 0, 2],
[2 / 3, 2 / 3, 0], [1 / 3, 4 / 3, 0],
[0, 0, 1], [0, 0, 2],
[0, 2 / 3, 0], [0, 4 / 3, 0],
[1 / 3, 0, 0], [2 / 3, 0, 0],
[1 / 3, 2 / 3, 1], [0, 2 / 3, 1],
[1 / 3, 0, 1], [1 / 3, 2 / 3, 0]])
if order == 1:
points = np.array([points[0, :], points[1, :], points[2, :], points[3, :]])
elif order == 2:
points = np.array([points[0, :], points[1, :], points[2, :], points[3, :],
[0, 1, 3 / 2], [1 / 2, 0, 3 / 2], [1 / 2, 1, 0], [0, 0, 3 / 2],
[0, 1, 0], [1 / 2, 0, 0]])
cells = np.array([range(len(points))])
mesh = Mesh(MPI.COMM_WORLD, celltype, points, cells, [], degree=order)
V = FunctionSpace(mesh, ("Lagrange", order))
X = V.element.dof_reference_coordinates()
coord_dofs = mesh.geometry.dofmap
x_g = mesh.geometry.x
cmap = fem.create_coordinate_map(mesh.ufl_domain())
x_coord_new = np.zeros([len(points), mesh.geometry.dim])
i = 0
for node in range(len(points)):
x_coord_new[i] = x_g[coord_dofs.links(0)[node], :mesh.geometry.dim]
i += 1
x = np.zeros(X.shape)
cmap.push_forward(x, X, x_coord_new)
assert(np.allclose(x[:, 0], X[:, 0]))
assert(np.allclose(x[:, 1], 2 * X[:, 1]))
assert(np.allclose(x[:, 2], 3 * X[:, 2]))
def test_eval_manifold():
# 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, cpp.mesh.CellType.triangle,
np.array(vertices, dtype=np.float64),
np.array(cells, dtype=np.int32), [])
Q = FunctionSpace(mesh, ("CG", 1))
u = Function(Q)
u.interpolate(lambda x: x[0] + x[1])
assert np.isclose(u.eval([0.75, 0.25, 0.5], 0)[0], 1.0)
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_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])
cell_candidates = geometry.compute_collisions_point(bb, p)
cell = cpp.geometry.select_colliding_cells(mesh, cell_candidates, p, 1)
assert cell[0] == 0
p = numpy.array([0.25, 0.5, 0.75])
cell_candidates = geometry.compute_collisions_point(bb, p)
cell = cpp.geometry.select_colliding_cells(mesh, cell_candidates, p, 1)
assert cell[0] == 1
def test_triangle_dof_ordering(space_type):
"""Checks that dofs on shared triangle edges match up"""
# Create a triangle mesh
if MPI.COMM_WORLD.rank == 0:
N = 6
# Create a grid of points [0, 0.5, ..., 9.5]**2, then order them
# in a random order
temp_points = np.array([[x / 2, y / 2] for x in range(N)
for y in range(N)])
order = [i for i, j in enumerate(temp_points)]
shuffle(order)
points = np.zeros(temp_points.shape)
for i, j in enumerate(order):
points[j] = temp_points[i]
# Make triangle cells using the randomly ordered points
cells = []
for x in range(N - 1):
for y in range(N - 1):
a = N * y + x
# Adds two triangle cells:
# a+N -- a+N+1
# | / |
# | / |
# | / |
# a --- a+1
for cell in [[a, a + 1, a + N + 1], [a, a + N + 1, a + N]]:
cells.append([order[i] for i in cell])
# On process 0, input mesh data and distribute to other
# processes
mesh = Mesh(MPI.COMM_WORLD, CellType.triangle, points, np.array(cells),
[])
else:
# On other processes, accept distributed data
mesh = Mesh(MPI.COMM_WORLD, CellType.triangle, np.ndarray((0, 2)),
np.ndarray((0, 3)), [])
V = FunctionSpace(mesh, space_type)
dofmap = V.dofmap
edges = {}
# Get coordinates of dofs and edges and check that they are the same
# for each global dof number
X = V.element.dof_reference_coordinates()
coord_dofs = mesh.geometry.dofmap
x_g = mesh.geometry.x
cmap = fem.create_coordinate_map(mesh.ufl_domain())
for cell_n in range(coord_dofs.num_nodes):
dofs = dofmap.cell_dofs(cell_n)
x_coord_new = np.zeros([3, 2])
for v in range(3):
x_coord_new[v] = x_g[coord_dofs.links(cell_n)[v], :2]
x = X.copy()
cmap.push_forward(x, X, x_coord_new)
edge_dofs_local = []
for i in range(3):
edge_dofs_local += list(dofmap.dof_layout.entity_dofs(1, i))
edge_dofs = [dofs[i] for i in edge_dofs_local]
for i, j in zip(edge_dofs, x[edge_dofs_local]):
if i in edges:
assert np.allclose(j, edges[i])
else:
edges[i] = j
def xtest_mesh_order_unchanged_quadrilateral():
points = [[0, 0], [1, 0], [0, 1], [1, 1]]
cells = [[0, 1, 2, 3]]
mesh = Mesh(MPI.COMM_WORLD, CellType.quadrilateral, points, cells, [],
cpp.mesh.GhostMode.none)
assert (mesh.cells()[0] == cells[0]).all()
def xtest_mesh_order_unchanged_triangle():
points = [[0, 0], [1, 0], [1, 1]]
cells = [[0, 1, 2]]
mesh = Mesh(MPI.COMM_WORLD, CellType.triangle, points, cells, [],
cpp.mesh.GhostMode.none)
assert (mesh.cells()[0] == cells[0]).all()
def test_mesh_construction_pygmsh():
pygmsh = pytest.importorskip("pygmsh")
if MPI.COMM_WORLD.rank == 0:
geom = pygmsh.opencascade.Geometry()
geom.add_ball([0.0, 0.0, 0.0], 1.0, char_length=0.2)
pygmsh_mesh = pygmsh.generate_mesh(geom)
points, cells = pygmsh_mesh.points, pygmsh_mesh.cells
else:
points = np.zeros([0, 3])
cells = {
"tetra": np.zeros([0, 4], dtype=np.int64),
"triangle": np.zeros([0, 3], dtype=np.int64),
"line": np.zeros([0, 2], dtype=np.int64)
}
mesh = Mesh(MPI.COMM_WORLD, dolfinx.cpp.mesh.CellType.tetrahedron, points,
cells['tetra'], [], cpp.mesh.GhostMode.none)
assert mesh.geometry.degree() == 1
assert mesh.geometry.dim == 3
assert mesh.topology.dim == 3
mesh = Mesh(MPI.COMM_WORLD, dolfinx.cpp.mesh.CellType.triangle, points,
cells['triangle'], [], cpp.mesh.GhostMode.none)
assert mesh.geometry.degree() == 1
assert mesh.geometry.dim == 3
assert mesh.topology.dim == 2
mesh = Mesh(MPI.COMM_WORLD, dolfinx.cpp.mesh.CellType.interval, points,
cells['line'], [], cpp.mesh.GhostMode.none)
assert mesh.geometry.degree() == 1
assert mesh.geometry.dim == 3
assert mesh.topology.dim == 1
if MPI.COMM_WORLD.rank == 0:
print("Generate mesh")
geom = pygmsh.opencascade.Geometry()
geom.add_ball([0.0, 0.0, 0.0], 1.0, char_length=0.2)
pygmsh_mesh = pygmsh.generate_mesh(
geom, extra_gmsh_arguments=['-order', '2'])
points, cells = pygmsh_mesh.points, pygmsh_mesh.cells
print("End Generate mesh", cells.keys())
else:
points = np.zeros([0, 3])
cells = {
"tetra10": np.zeros([0, 10], dtype=np.int64),
"triangle6": np.zeros([0, 6], dtype=np.int64),
"line3": np.zeros([0, 3], dtype=np.int64)
}
mesh = Mesh(MPI.COMM_WORLD, dolfinx.cpp.mesh.CellType.tetrahedron, points,
cells['tetra10'], [], cpp.mesh.GhostMode.none)
assert mesh.geometry.degree() == 2
assert mesh.geometry.dim == 3
assert mesh.topology.dim == 3
mesh = Mesh(MPI.COMM_WORLD, dolfinx.cpp.mesh.CellType.triangle, points,
cells['triangle6'], [], cpp.mesh.GhostMode.none)
assert mesh.geometry.degree() == 2
assert mesh.geometry.dim == 3
assert mesh.topology.dim == 2
def test_nth_order_triangle(order):
num_nodes = (order + 1) * (order + 2) / 2
cells = np.array([range(int(num_nodes))])
cells = permute_cell_ordering(
cells, permutation_vtk_to_dolfin(CellType.triangle, cells.shape[1]))
if order == 1:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000]])
elif order == 2:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.50000, 0.00000, 0.00000],
[0.50000, 0.50000, -0.25000],
[0.00000, 0.50000, -0.25000]])
elif order == 3:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.33333, 0.00000, 0.00000],
[0.66667, 0.00000, 0.00000],
[0.66667, 0.33333, -0.11111],
[0.33333, 0.66667, 0.11111],
[0.00000, 0.66667, 0.11111],
[0.00000, 0.33333, -0.11111],
[0.33333, 0.33333, -0.11111]])
elif order == 4:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.25000, 0.00000, 0.00000],
[0.50000, 0.00000, 0.00000],
[0.75000, 0.00000, 0.00000],
[0.75000, 0.25000, -0.06250],
[0.50000, 0.50000, 0.06250],
[0.25000, 0.75000, -0.06250],
[0.00000, 0.75000, -0.06250],
[0.00000, 0.50000, 0.06250],
[0.00000, 0.25000, -0.06250],
[0.25000, 0.25000, -0.06250],
[0.50000, 0.25000, -0.06250],
[0.25000, 0.50000, 0.06250]])
elif order == 5:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.20000, 0.00000, 0.00000],
[0.40000, 0.00000, 0.00000],
[0.60000, 0.00000, 0.00000],
[0.80000, 0.00000, 0.00000],
[0.80000, 0.20000, -0.04000],
[0.60000, 0.40000, 0.04000],
[0.40000, 0.60000, -0.04000],
[0.20000, 0.80000, 0.04000],
[0.00000, 0.80000, 0.04000],
[0.00000, 0.60000, -0.04000],
[0.00000, 0.40000, 0.04000],
[0.00000, 0.20000, -0.04000],
[0.20000, 0.20000, -0.04000],
[0.60000, 0.20000, -0.04000],
[0.20000, 0.60000, -0.04000],
[0.40000, 0.20000, -0.04000],
[0.40000, 0.40000, 0.04000],
[0.20000, 0.40000, 0.04000]])
elif order == 6:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.16667, 0.00000, 0.00000],
[0.33333, 0.00000, 0.00000],
[0.50000, 0.00000, 0.00000],
[0.66667, 0.00000, 0.00000],
[0.83333, 0.00000, 0.00000],
[0.83333, 0.16667, -0.00463],
[0.66667, 0.33333, 0.00463],
[0.50000, 0.50000, -0.00463],
[0.33333, 0.66667, 0.00463],
[0.16667, 0.83333, -0.00463],
[0.00000, 0.83333, -0.00463],
[0.00000, 0.66667, 0.00463],
[0.00000, 0.50000, -0.00463],
[0.00000, 0.33333, 0.00463],
[0.00000, 0.16667, -0.00463],
[0.16667, 0.16667, -0.00463],
[0.66667, 0.16667, -0.00463],
[0.16667, 0.66667, 0.00463],
[0.33333, 0.16667, -0.00463],
[0.50000, 0.16667, -0.00463],
[0.50000, 0.33333, 0.00463],
[0.33333, 0.50000, -0.00463],
[0.16667, 0.50000, -0.00463],
[0.16667, 0.33333, 0.00463],
[0.33333, 0.33333, 0.00463]])
elif order == 7:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.14286, 0.00000, 0.00000],
[0.28571, 0.00000, 0.00000],
[0.42857, 0.00000, 0.00000],
[0.57143, 0.00000, 0.00000],
[0.71429, 0.00000, 0.00000],
[0.85714, 0.00000, 0.00000],
[0.85714, 0.14286, -0.02041],
[0.71429, 0.28571, 0.02041],
[0.57143, 0.42857, -0.02041],
[0.42857, 0.57143, 0.02041],
[0.28571, 0.71429, -0.02041],
[0.14286, 0.85714, 0.02041],
[0.00000, 0.85714, 0.02041],
[0.00000, 0.71429, -0.02041],
[0.00000, 0.57143, 0.02041],
[0.00000, 0.42857, -0.02041],
[0.00000, 0.28571, 0.02041],
[0.00000, 0.14286, -0.02041],
[0.14286, 0.14286, -0.02041],
[0.71429, 0.14286, -0.02041],
[0.14286, 0.71429, -0.02041],
[0.28571, 0.14286, -0.02041],
[0.42857, 0.14286, -0.02041],
[0.57143, 0.14286, -0.02041],
[0.57143, 0.28571, 0.02041],
[0.42857, 0.42857, -0.02041],
[0.28571, 0.57143, 0.02041],
[0.14286, 0.57143, 0.02041],
[0.14286, 0.42857, -0.02041],
[0.14286, 0.28571, 0.02041],
[0.28571, 0.28571, 0.02041],
[0.42857, 0.28571, 0.02041],
[0.28571, 0.42857, -0.02041]])
# Higher order tests are too slow
elif order == 8:
points = np.array([[0.00000, 0.00000, 0.00000],
[1.00000, 0.00000, 0.00000],
[0.00000, 1.00000, 0.00000],
[0.12500, 0.00000, 0.00000],
[0.25000, 0.00000, 0.00000],
[0.37500, 0.00000, 0.00000],
[0.50000, 0.00000, 0.00000],
[0.62500, 0.00000, 0.00000],
[0.75000, 0.00000, 0.00000],
[0.87500, 0.00000, 0.00000],
[0.87500, 0.12500, -0.00195],
[0.75000, 0.25000, 0.00195],
[0.62500, 0.37500, -0.00195],
[0.50000, 0.50000, 0.00195],
[0.37500, 0.62500, -0.00195],
[0.25000, 0.75000, 0.00195],
[0.12500, 0.87500, -0.00195],
[0.00000, 0.87500, -0.00195],
[0.00000, 0.75000, 0.00195],
[0.00000, 0.62500, -0.00195],
[0.00000, 0.50000, 0.00195],
[0.00000, 0.37500, -0.00195],
[0.00000, 0.25000, 0.00195],
[0.00000, 0.12500, -0.00195],
[0.12500, 0.12500, -0.00195],
[0.75000, 0.12500, -0.00195],
[0.12500, 0.75000, 0.00195],
[0.25000, 0.12500, -0.00195],
[0.37500, 0.12500, -0.00195],
[0.50000, 0.12500, -0.00195],
[0.62500, 0.12500, -0.00195],
[0.62500, 0.25000, 0.00195],
[0.50000, 0.37500, -0.00195],
[0.37500, 0.50000, 0.00195],
[0.25000, 0.62500, -0.00195],
[0.12500, 0.62500, -0.00195],
[0.12500, 0.50000, 0.00195],
[0.12500, 0.37500, -0.00195],
[0.12500, 0.25000, 0.00195],
[0.25000, 0.25000, 0.00195],
[0.50000, 0.25000, 0.00195],
[0.25000, 0.50000, 0.00195],
[0.37500, 0.25000, 0.00195],
[0.37500, 0.37500, -0.00195],
[0.25000, 0.37500, -0.00195]])
mesh = Mesh(MPI.comm_world, CellType.triangle, points, cells, [],
GhostMode.none)
# Find nodes corresponding to y axis
nodes = []
for j in range(points.shape[0]):
if np.isclose(points[j][0], 0):
nodes.append(j)
def e2(x):
return x[2] + x[0] * x[1]
# For solution to be in functionspace
V = FunctionSpace(mesh, ("CG", max(2, order)))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
quad_order = 30
intu = assemble_scalar(u * dx(metadata={"quadrature_degree": quad_order}))
intu = MPI.sum(mesh.mpi_comm(), intu)
ref = scipy_one_cell(points, nodes)
assert ref == pytest.approx(intu, rel=3e-3)
def test_fourth_order_quad(L, H, Z):
"""Test by comparing integration of z+x*y against sympy/scipy integration
of a quad element. Z>0 implies curved element.
*---------* 20-21-22-23-24-41--42--43--44
| | | | |
| | 15 16 17 18 19 37 38 39 40
| | | | |
| | 10 11 12 13 14 33 34 35 36
| | | | |
| | 5 6 7 8 9 29 30 31 32
| | | | |
*---------* 0--1--2--3--4--25--26--27--28
"""
points = np.array([
[0, 0, 0],
[L / 4, 0, 0],
[L / 2, 0, 0], # 0 1 2
[3 * L / 4, 0, 0],
[L, 0, 0], # 3 4
[0, H / 4, -Z / 3],
[L / 4, H / 4, -Z / 3],
[L / 2, H / 4, -Z / 3], # 5 6 7
[3 * L / 4, H / 4, -Z / 3],
[L, H / 4, -Z / 3], # 8 9
[0, H / 2, 0],
[L / 4, H / 2, 0],
[L / 2, H / 2, 0], # 10 11 12
[3 * L / 4, H / 2, 0],
[L, H / 2, 0], # 13 14
[0, (3 / 4) * H, 0],
[L / 4, (3 / 4) * H, 0], # 15 16
[L / 2, (3 / 4) * H, 0],
[3 * L / 4, (3 / 4) * H, 0], # 17 18
[L, (3 / 4) * H, 0],
[0, H, Z],
[L / 4, H, Z], # 19 20 21
[L / 2, H, Z],
[3 * L / 4, H, Z],
[L, H, Z], # 22 23 24
[(5 / 4) * L, 0, 0],
[(6 / 4) * L, 0, 0], # 25 26
[(7 / 4) * L, 0, 0],
[2 * L, 0, 0], # 27 28
[(5 / 4) * L, H / 4, -Z / 3],
[(6 / 4) * L, H / 4, -Z / 3], # 29 30
[(7 / 4) * L, H / 4, -Z / 3],
[2 * L, H / 4, -Z / 3], # 31 32
[(5 / 4) * L, H / 2, 0],
[(6 / 4) * L, H / 2, 0], # 33 34
[(7 / 4) * L, H / 2, 0],
[2 * L, H / 2, 0], # 35 36
[(5 / 4) * L, 3 / 4 * H, 0], # 37
[(6 / 4) * L, 3 / 4 * H, 0], # 38
[(7 / 4) * L, 3 / 4 * H, 0],
[2 * L, 3 / 4 * H, 0], # 39 40
[(5 / 4) * L, H, Z],
[(6 / 4) * L, H, Z], # 41 42
[(7 / 4) * L, H, Z],
[2 * L, H, Z]
]) # 43 44
# VTK ordering
cells = np.array([[
0, 4, 24, 20, 1, 2, 3, 9, 14, 19, 21, 22, 23, 5, 10, 15, 6, 7, 8, 11,
12, 13, 16, 17, 18
],
[
4, 28, 44, 24, 25, 26, 27, 32, 36, 40, 41, 42, 43, 9,
14, 19, 29, 30, 31, 33, 34, 35, 37, 38, 39
]])
cells = permute_cell_ordering(
cells, permutation_vtk_to_dolfin(CellType.quadrilateral,
cells.shape[1]))
mesh = Mesh(MPI.comm_world, CellType.quadrilateral, points, cells, [],
GhostMode.none)
def e2(x):
return x[2] + x[0] * x[1]
V = FunctionSpace(mesh, ("CG", 4))
u = Function(V)
cmap = fem.create_coordinate_map(mesh.ufl_domain())
mesh.geometry.coord_mapping = cmap
u.interpolate(e2)
intu = assemble_scalar(u * dx(mesh))
intu = MPI.sum(mesh.mpi_comm(), intu)
nodes = [0, 5, 10, 15, 20]
ref = sympy_scipy(points, nodes, 2 * L, H)
assert ref == pytest.approx(intu, rel=1e-5)
def test_mesh_order_unchanged_tetrahedron():
points = [[0, 0, 0], [1, 0, 0], [1, 1, 0], [0, 0, 1]]
cells = [[0, 1, 2, 3]]
mesh = Mesh(MPI.comm_world, CellType.tetrahedron, points, cells, [],
cpp.mesh.GhostMode.none)
assert (mesh.cells()[0] == cells[0]).all()
