def test_save_mesh_value_collection(tempdir, encoding, data_type, cell_type):
dtype_str, dtype = data_type
mesh = UnitCubeMesh(MPI.comm_world, 4, 4, 4, cell_type)
tdim = mesh.topology.dim
meshfn = MeshFunction(dtype_str, mesh, mesh.topology.dim, False)
meshfn.name = "volume_marker"
mp = cpp.mesh.midpoints(mesh, tdim, range(mesh.num_entities(tdim)))
for i in range(mesh.num_cells()):
if mp[i, 1] > 0.1:
meshfn.values[i] = 1
if mp[i, 1] > 0.9:
meshfn.values[i] = 2
for mvc_dim in range(0, tdim + 1):
mvc = MeshValueCollection(dtype_str, mesh, mvc_dim)
tag = "dim_{}_marker".format(mvc_dim)
mvc.name = tag
mesh.create_connectivity(mvc_dim, tdim)
mp = cpp.mesh.midpoints(mesh, mvc_dim,
range(mesh.num_entities(mvc_dim)))
for e in range(mesh.num_entities(mvc_dim)):
if (mp[e, 0] > 0.5):
mvc.set_value(e, dtype(1))
filename = os.path.join(tempdir, "mvc_{}.xdmf".format(mvc_dim))
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as xdmf:
xdmf.write(meshfn)
xdmf.write(mvc)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mvc_" + dtype_str)
mvc = read_function(mesh, tag)
def test_save_1d_mesh(tempdir, encoding):
filename = os.path.join(tempdir, "mf_1D.xdmf")
mesh = UnitIntervalMesh(MPI.comm_world, 32)
mf = MeshFunction("size_t", mesh, mesh.topology.dim, 0)
mf.values[:] = np.arange(mesh.num_entities(1))
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write(mf)
def test_save_and_read_meshfunction_3D(tempdir):
filename = os.path.join(tempdir, "meshfn-3d.h5")
# Write to file
mesh = UnitCubeMesh(MPI.comm_world, 2, 2, 2)
mf_file = HDF5File(mesh.mpi_comm(), filename, "w")
# save meshfuns to compare when reading back
meshfunctions = []
for i in range(0, 4):
mf = MeshFunction('double', mesh, i, 0.0)
mp = cpp.mesh.midpoints(mesh, i, range(mesh.num_entities(i)))
# NB choose a value to set which will be the same on every
# process for each entity
mf.values[:] = mp[:, 0]
meshfunctions.append(mf)
mf_file.write(mf, "/meshfunction/group/%d/meshfun" % i)
mf_file.close()
# Read back from file
mf_file = HDF5File(mesh.mpi_comm(), filename, "r")
for i in range(0, 4):
mf2 = mf_file.read_mf_double(mesh,
"/meshfunction/group/%d/meshfun" % i)
assert numpy.all(meshfunctions[i].values == mf2.values)
mf_file.close()
def test_mesh_function_assign_2D_facets():
mesh = UnitSquareMesh(MPI.comm_world, 3, 3)
mesh.create_entities(1)
tdim = mesh.topology.dim
num_cell_facets = cpp.mesh.cell_num_entities(mesh.topology.cell_type,
tdim - 1)
f = MeshFunction("int", mesh, tdim - 1, 25)
connectivity = mesh.topology.connectivity(tdim, tdim - 1)
for c in range(mesh.num_cells()):
facets = connectivity.links(c)
for i in range(num_cell_facets):
assert 25 == f.values[facets[i]]
g = MeshValueCollection("int", mesh, 1)
g.assign(f)
assert mesh.num_entities(tdim - 1) == len(f.values)
assert mesh.num_cells() * 3 == g.size()
for c in range(mesh.num_cells()):
for i in range(num_cell_facets):
assert 25 == g.get_value(c, i)
f2 = MeshFunction("int", mesh, g, 0)
connectivity = mesh.topology.connectivity(tdim, tdim - 1)
for c in range(mesh.num_cells()):
facets = connectivity.links(c)
for i in range(num_cell_facets):
assert f2.values[facets[i]] == g.get_value(c, i)
def test_mesh_function_assign_2D_cells():
mesh = UnitSquareMesh(MPI.comm_world, 3, 3)
ncells = mesh.num_cells()
f = MeshFunction("int", mesh, mesh.topology.dim, 0)
for c in range(ncells):
f.values[c] = ncells - c
g = MeshValueCollection("int", mesh, 2)
g.assign(f)
assert ncells == len(f.values)
assert ncells == g.size()
f2 = MeshFunction("int", mesh, g, 0)
for c in range(mesh.num_cells()):
value = ncells - c
assert value == g.get_value(c, 0)
assert f2.values[c] == g.get_value(c, 0)
h = MeshValueCollection("int", mesh, 2)
global_indices = mesh.topology.index_map(2).global_indices(True)
ncells_global = mesh.num_entities_global(2)
for c in range(mesh.num_cells()):
if global_indices[c] in [5, 8, 10]:
continue
value = ncells_global - global_indices[c]
h.set_value(c, int(value))
f3 = MeshFunction("int", mesh, h, 0)
values = f3.values
values[values > ncells_global] = 0.
assert MPI.sum(mesh.mpi_comm(), values.sum() * 1.0) == 140.
def test_save_3D_vertex_function(tempdir, encoding, data_type, cell_type):
dtype_str, dtype = data_type
filename = os.path.join(tempdir, "mf_vertex_3D_%s.xdmf" % dtype_str)
mesh = UnitCubeMesh(MPI.comm_world, 4, 4, 4, cell_type)
mf = MeshFunction(dtype_str, mesh, 0, 0)
mf.values[:] = np.arange(mesh.num_entities(0), dtype=dtype)
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write(mf)
def test_facet_normals(cell_type):
"""Test that FacetNormal is outward facing"""
for count in range(5):
mesh = unit_cell(cell_type)
V = VectorFunctionSpace(mesh, ("Lagrange", 1))
normal = FacetNormal(mesh)
num_facets = mesh.num_entities(mesh.topology.dim - 1)
v = Function(V)
facet_function = MeshFunction("size_t", mesh, mesh.topology.dim - 1, 1)
facet_function.values[:] = range(num_facets)
# For each facet, check that the inner product of the normal and
# the vector that has a positive normal component on only that facet
# is positive
for i in range(num_facets):
if cell_type == CellType.interval:
co = mesh.geometry.points[i]
v.interpolate(lambda x: x[0] - co[0])
if cell_type == CellType.triangle:
co = mesh.geometry.points[i]
# Vector function that is zero at `co` and points away from `co`
# so that there is no normal component on two edges and the integral
# over the other edge is 1
v.interpolate(lambda x: ((x[0] - co[0]) / 2,
(x[1] - co[1]) / 2))
elif cell_type == CellType.tetrahedron:
co = mesh.geometry.points[i]
# Vector function that is zero at `co` and points away from `co`
# so that there is no normal component on three faces and the integral
# over the other edge is 1
v.interpolate(lambda x: ((x[0] - co[0]) / 3, (x[1] - co[1]) /
3, (x[2] - co[2]) / 3))
elif cell_type == CellType.quadrilateral:
# function that is 0 on one edge and points away from that edge
# so that there is no normal component on three edges
v.interpolate(lambda x: tuple(x[j] - i % 2 if j == i // 2 else
0 * x[j] for j in range(2)))
elif cell_type == CellType.hexahedron:
# function that is 0 on one face and points away from that face
# so that there is no normal component on five faces
v.interpolate(lambda x: tuple(x[j] - i % 2 if j == i // 3 else
0 * x[j] for j in range(3)))
# assert that the integrals these functions dotted with the normal over a face
# is 1 on one face and 0 on the others
ones = 0
for j in range(num_facets):
a = inner(v, normal) * ds(subdomain_data=facet_function,
subdomain_id=j)
result = fem.assemble_scalar(a)
if np.isclose(result, 1):
ones += 1
else:
assert np.isclose(result, 0)
assert ones == 1
def test_append_and_load_mesh_value_collections(tempdir, encoding, data_type,
cell_type):
dtype_str, dtype = data_type
mesh = UnitCubeMesh(MPI.comm_world, 2, 2, 2, cell_type)
mesh.create_connectivity_all()
mvc_v = MeshValueCollection(dtype_str, mesh, 0)
mvc_v.name = "vertices"
mvc_e = MeshValueCollection(dtype_str, mesh, 1)
mvc_e.name = "edges"
mvc_f = MeshValueCollection(dtype_str, mesh, 2)
mvc_f.name = "facets"
mvc_c = MeshValueCollection(dtype_str, mesh, 3)
mvc_c.name = "cells"
mvcs = [mvc_v, mvc_e, mvc_f, mvc_c]
filename = os.path.join(tempdir, "appended_mvcs.xdmf")
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
for mvc in mvcs:
# global_indices = mesh.topology.global_indices(mvc.dim)
map = mesh.topology.index_map(mvc.dim)
global_indices = map.global_indices(True)
for ent in range(mesh.num_entities(mvc.dim)):
assert (mvc.set_value(ent, global_indices[ent]))
xdmf.write(mvc)
mvc_v_in = MeshValueCollection(dtype_str, mesh, 0)
mvc_e_in = MeshValueCollection(dtype_str, mesh, 1)
mvc_f_in = MeshValueCollection(dtype_str, mesh, 2)
mvc_c_in = MeshValueCollection(dtype_str, mesh, 3)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mvc_" + dtype_str)
mvc_v_in = read_function(mesh, "vertices")
mvc_e_in = read_function(mesh, "edges")
mvc_f_in = read_function(mesh, "facets")
mvc_c_in = read_function(mesh, "cells")
mvcs_in = [mvc_v_in, mvc_e_in, mvc_f_in, mvc_c_in]
for (mvc, mvc_in) in zip(mvcs, mvcs_in):
mf = MeshFunction(dtype_str, mesh, mvc, 0)
mf_in = MeshFunction(dtype_str, mesh, mvc_in, 0)
diff = mf_in.values - mf.values
assert np.all(diff == 0)
def test_save_3D_cell_function(tempdir, encoding, data_type, cell_type):
dtype_str, dtype = data_type
mesh = UnitCubeMesh(MPI.comm_world, 4, 4, 4, cell_type)
mf = MeshFunction(dtype_str, mesh, mesh.topology.dim, 0)
mf.name = "cells"
mf.values[:] = np.arange(mesh.num_entities(3), dtype=dtype)
filename = os.path.join(tempdir, "mf_3D_%s.xdmf" % dtype_str)
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write(mf)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mf_" + dtype_str)
mf_in = read_function(mesh, "cells")
diff = mf_in.values - mf.values
assert np.all(diff == 0)
def test_save_2D_vertex_function(tempdir, encoding, data_type, cell_type):
dtype_str, dtype = data_type
mesh = UnitSquareMesh(MPI.comm_world, 32, 32, cell_type)
mf = MeshFunction(dtype_str, mesh, 0, 0)
mf.name = "vertices"
global_indices = mesh.topology.index_map(0).global_indices(False)
mf.values[:] = global_indices[:]
filename = os.path.join(tempdir, "mf_vertex_2D_%s.xdmf" % dtype_str)
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as file:
file.write(mf)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mf_" + dtype_str)
mf_in = read_function(mesh, "vertices")
diff = mf_in.values - mf.values
assert np.all(diff == 0)
def test_save_3D_facet_function(tempdir, encoding, data_type, cell_type):
dtype_str, dtype = data_type
mesh = UnitCubeMesh(MPI.comm_world, 4, 4, 4, cell_type)
tdim = mesh.topology.dim
mf = MeshFunction(dtype_str, mesh, tdim - 1, 0)
mf.name = "facets"
global_indices = mesh.topology.global_indices(tdim - 1)
mf.values[:] = global_indices[:]
filename = os.path.join(tempdir, "mf_facet_3D_%s.xdmf" % dtype_str)
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as xdmf:
xdmf.write(mf)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mf_" + dtype_str)
mf_in = read_function(mesh, "facets")
diff = mf_in.values - mf.values
assert np.all(diff == 0)
def test_mesh_function_assign_2D_vertices():
mesh = UnitSquareMesh(MPI.comm_world, 3, 3)
mesh.create_entities(0)
f = MeshFunction("int", mesh, 0, 25)
g = MeshValueCollection("int", mesh, 0)
g.assign(f)
assert mesh.num_entities(0) == len(f.values)
assert mesh.num_cells() * 3 == g.size()
f2 = MeshFunction("int", mesh, g, 0)
num_cell_vertices = cpp.mesh.cell_num_vertices(mesh.topology.cell_type)
tdim = mesh.topology.dim
connectivity = mesh.topology.connectivity(tdim, 0)
for c in range(mesh.num_cells()):
vertices = connectivity.links(c)
for i in range(num_cell_vertices):
assert 25 == g.get_value(c, i)
assert f2.values[vertices[i]] == g.get_value(c, i)
def test_save_1d_meshfunctions(tempfile, mesh_function_types, file_options,
type_conv):
mesh = UnitIntervalMesh(MPI.comm_world, 32)
for d in range(mesh.topology.dim + 1):
for t in mesh_function_types:
mf = MeshFunction(t, mesh, mesh.topology.dim - d, type_conv[t](1))
VTKFile(tempfile + "mf.pvd").write(mf)
f = VTKFile(tempfile + "mf.pvd")
f.write(mf, 0.)
f.write(mf, 1.)
def test_save_3d_meshfunctions(tempfile, mesh_function_types, file_options,
type_conv, cell_types_3D):
mesh = UnitCubeMesh(MPI.comm_world, 8, 8, 8)
for d in range(mesh.topology.dim + 1):
for t in mesh_function_types:
for cell_type in cell_types_3D:
mf = MeshFunction(t, mesh, mesh.topology.dim - d, type_conv[t](1))
VTKFile(tempfile + "mf_{0:d}_{1:s}.pvd".format(mesh.topology.dim - d,
str(cell_type).split(".")[-1])).write(mf)
f = VTKFile(tempfile + "mf{0:d}_{1:s}.pvd".format(mesh.topology.dim - d,
str(cell_type).split(".")[-1]))
f.write(mf, 0.)
f.write(mf, 1.)
def test_save_and_read_meshfunction_2D(tempdir):
filename = os.path.join(tempdir, "meshfn-2d.h5")
# Write to file
mesh = UnitSquareMesh(MPI.comm_world, 20, 20)
with HDF5File(mesh.mpi_comm(), filename, "w") as mf_file:
# save meshfuns to compare when reading back
meshfunctions = []
for i in range(0, 3):
mf = MeshFunction('double', mesh, i, 0.0)
# NB choose a value to set which will be the same on every
# process for each entity
mf.values[:] = cpp.mesh.midpoints(mesh, i,
range(mesh.num_entities(i)))[:,
0]
meshfunctions.append(mf)
mf_file.write(mf, "/meshfunction/meshfun%d" % i)
# Read back from file
with HDF5File(mesh.mpi_comm(), filename, "r") as mf_file:
for i in range(0, 3):
mf2 = mf_file.read_mf_double(mesh, "/meshfunction/meshfun%d" % i)
assert numpy.all(meshfunctions[i].values == mf2.values)
def test_facet_integral(cell_type):
"""Test that the integral of a function over a facet is correct"""
for count in range(5):
mesh = unit_cell(cell_type)
V = FunctionSpace(mesh, ("Lagrange", 2))
num_facets = mesh.num_entities(mesh.topology.dim - 1)
v = Function(V)
facet_function = MeshFunction("size_t", mesh, mesh.topology.dim - 1, 1)
facet_function.values[:] = range(num_facets)
# Functions that will have the same integral over each facet
if cell_type == CellType.triangle:
root = 3**0.25 # 4th root of 3
v.interpolate(lambda x: (x[0] - 1 / root)**2 +
(x[1] - root / 3)**2)
elif cell_type == CellType.quadrilateral:
v.interpolate(lambda x: x[0] * (1 - x[0]) + x[1] * (1 - x[1]))
elif cell_type == CellType.tetrahedron:
s = 2**0.5 * 3**(1 / 3) # side length
v.interpolate(lambda x: (x[0] - s / 2)**2 +
(x[1] - s / 2 / np.sqrt(3))**2 +
(x[2] - s * np.sqrt(2 / 3) / 4)**2)
elif cell_type == CellType.hexahedron:
v.interpolate(lambda x: x[0] * (1 - x[0]) + x[1] *
(1 - x[1]) + x[2] * (1 - x[2]))
# assert that the integral of these functions over each face are equal
out = []
for j in range(num_facets):
a = v * ds(subdomain_data=facet_function, subdomain_id=j)
result = fem.assemble_scalar(a)
out.append(result)
assert np.isclose(result, out[0])
def test_multiple_datasets(tempdir, encoding, cell_type):
mesh = UnitSquareMesh(MPI.comm_world, 4, 4, cell_type)
cf0 = MeshFunction('size_t', mesh, 2, 11)
cf0.name = 'cf0'
cf1 = MeshFunction('size_t', mesh, 2, 22)
cf1.name = 'cf1'
filename = os.path.join(tempdir, "multiple_mf.xdmf")
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as xdmf:
xdmf.write(mesh)
xdmf.write(cf0)
xdmf.write(cf1)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
mesh = xdmf.read_mesh(cpp.mesh.GhostMode.none)
cf0 = xdmf.read_mf_size_t(mesh, "cf0")
cf1 = xdmf.read_mf_size_t(mesh, "cf1")
assert (cf0.values[0] == 11 and cf1.values[0] == 22)
def amg_solve(N, method):
# Elasticity parameters
E = 1.0e9
nu = 0.3
mu = E / (2.0 * (1.0 + nu))
lmbda = E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))
# Stress computation
def sigma(v):
return 2.0 * mu * sym(grad(v)) + lmbda * tr(sym(
grad(v))) * Identity(2)
# Define problem
mesh = UnitSquareMesh(MPI.comm_world, N, N)
V = VectorFunctionSpace(mesh, 'Lagrange', 1)
bc0 = Function(V)
with bc0.vector.localForm() as bc_local:
bc_local.set(0.0)
def boundary(x):
return np.full(x.shape[1], True)
facetdim = mesh.topology.dim - 1
mf = MeshFunction("size_t", mesh, facetdim, 0)
mf.mark(boundary, 1)
bndry_facets = np.where(mf.values == 1)[0]
bdofs = locate_dofs_topological(V.sub(0), V, facetdim, bndry_facets)
bc = DirichletBC(bc0, bdofs, V.sub(0))
u = TrialFunction(V)
v = TestFunction(V)
# Forms
a, L = inner(sigma(u), grad(v)) * dx, dot(ufl.as_vector(
(1.0, 1.0)), v) * dx
# Assemble linear algebra objects
A = assemble_matrix(a, [bc])
A.assemble()
b = assemble_vector(L)
apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc])
# Create solution function
u = Function(V)
# Create near null space basis and orthonormalize
null_space = build_nullspace(V, u.vector)
# Attached near-null space to matrix
A.set_near_nullspace(null_space)
# Test that basis is orthonormal
assert null_space.is_orthonormal()
# Create PETSC smoothed aggregation AMG preconditioner, and
# create CG solver
solver = PETSc.KSP().create(mesh.mpi_comm)
solver.setType("cg")
# Set matrix operator
solver.setOperators(A)
# Compute solution and return number of iterations
return solver.solve(b, u.vector)
def test_data_types(dtype, mesh):
dtype_str, dtype = dtype
mf = MeshFunction(dtype_str, mesh, 0, 0)
assert isinstance(mf.values[0], dtype)
def f(mesh):
return MeshFunction('int', mesh, 0, 0)
def test_numpy_access(dtype, mesh):
dtype_str, dtype = dtype
mf = MeshFunction(dtype_str, mesh, 0, 0)
values = mf.values
values[:] = numpy.random.rand(len(values))
assert numpy.all(values == mf.values)
def dx_from_measure(mesh):
subdomains = MeshFunction("size_t", mesh, mesh.topology.dim, 1)
dx = Measure("dx")(subdomain_data=subdomains, domain=mesh)
dx = dx(1)
return dx
def dS_from_measure(mesh):
boundaries = MeshFunction("size_t", mesh, mesh.topology.dim - 1, 1)
dS = Measure("dS")(subdomain_data=boundaries, domain=mesh)
return dS
def test_append_and_load_mesh_functions(tempdir, encoding, data_type):
dtype_str, dtype = data_type
meshes = [
UnitSquareMesh(MPI.comm_world, 12, 12),
UnitCubeMesh(MPI.comm_world, 2, 2, 2),
UnitSquareMesh(MPI.comm_world, 12, 12, CellType.quadrilateral),
UnitCubeMesh(MPI.comm_world, 2, 2, 2, CellType.hexahedron)
]
for mesh in meshes:
dim = mesh.topology.dim
vf = MeshFunction(dtype_str, mesh, 0, 0)
vf.name = "vertices"
ff = MeshFunction(dtype_str, mesh, mesh.topology.dim - 1, 0)
ff.name = "facets"
cf = MeshFunction(dtype_str, mesh, mesh.topology.dim, 0)
cf.name = "cells"
# vf.values[:] = mesh.topology.global_indices(0)[:]
map = mesh.topology.index_map(0)
vf.values[:] = map.global_indices(True)
map = mesh.topology.index_map(dim - 1)
ff.values[:] = map.global_indices(True)
map = mesh.topology.index_map(dim)
cf.values[:] = map.global_indices(True)
filename = os.path.join(
tempdir, "appended_mf_{0:d}_{1:s}.xdmf".format(
dim, str(mesh.topology.cell_type)))
with XDMFFile(mesh.mpi_comm(), filename, encoding=encoding) as xdmf:
xdmf.write(mesh)
xdmf.write(vf)
xdmf.write(ff)
xdmf.write(cf)
with XDMFFile(mesh.mpi_comm(), filename) as xdmf:
read_function = getattr(xdmf, "read_mf_" + dtype_str)
vf_in = read_function(mesh, "vertices")
ff_in = read_function(mesh, "facets")
cf_in = read_function(mesh, "cells")
diff_vf = vf_in.values - vf.values
diff_ff = ff_in.values - ff.values
diff_cf = cf_in.values - cf.values
assert np.all(diff_vf == 0)
assert np.all(diff_ff == 0)
assert np.all(diff_cf == 0)
