def get_facet_areas(mesh):
"""
Compute area of each facet of `mesh`.
The facet areas are stored as a HDiv
trace field.
Note that the plus sign is arbitrary
and could equally well be chosen as minus.
:arg mesh: the input mesh to do computations on
:rtype: firedrake.function.Function facet_areas with
facet area data
"""
HDivTrace = firedrake.FunctionSpace(mesh, "HDiv Trace", 0)
v = firedrake.TestFunction(HDivTrace)
u = firedrake.TrialFunction(HDivTrace)
facet_areas = firedrake.Function(HDivTrace, name="Facet areas")
mass_term = v("+") * u("+") * ufl.dS + v * u * ufl.ds
rhs = v("+") * ufl.FacetArea(mesh) * ufl.dS + v * ufl.FacetArea(mesh) * ufl.ds
sp = {
"snes_type": "ksponly",
"ksp_type": "preonly",
"pc_type": "jacobi",
}
firedrake.solve(mass_term == rhs, facet_areas, solver_parameters=sp)
return facet_areas
def test_interior_facet_integral_sides():
n = 1
mesh = UnitSquareMesh(n, n)
markers = CellFunctionSizet(mesh)
subdomain = AutoSubDomain(lambda x, on_boundary: x[0] > x[1] - DOLFIN_EPS)
V = FunctionSpace(mesh, "DG", 0)
f = interpolate(Expression("x[0]"), V)
# Define forms picking value of f from + and - sides
scale = 1.0 / ufl.FacetArea(mesh)
Mp = f('+') * scale * dS(domain=mesh)
Mm = f('-') * scale * dS(domain=mesh)
# Hack to attach cell markers to dS integral... Need to find a UFL
# solution to this.
Mh = Constant(0) * dx(99, domain=mesh, subdomain_data=markers)
Mp = Mp + Mh
Mm = Mm + Mh
# Case A: subdomain is 1, rest is 0
markers.set_all(0)
subdomain.mark(markers, 1)
assert abs(assemble(Mp) - 2.0 / 3.0) < 1e-8
assert abs(assemble(Mm) - 1.0 / 3.0) < 1e-8
# Case B: subdomain is 0, rest is 1
markers.set_all(1)
subdomain.mark(markers, 0)
assert abs(assemble(Mp) - 1.0 / 3.0) < 1e-8
assert abs(assemble(Mm) - 2.0 / 3.0) < 1e-8
def testFacetArea():
references = [(UnitIntervalMesh(MPI.comm_world, 1), 2, 2),
(UnitSquareMesh(MPI.comm_world, 1, 1), 4, 4),
(UnitCubeMesh(MPI.comm_world, 1, 1, 1), 6, 3)]
for mesh, surface, ref_int in references:
c0 = ufl.FacetArea(mesh)
c1 = dolfinx.FacetArea(mesh)
assert (c0)
assert (c1)
def testFacetArea():
references = [(UnitIntervalMesh(MPI.comm_world, 1), 2, 2),
(UnitSquareMesh(MPI.comm_world, 1, 1), 4, 4),
(UnitCubeMesh(MPI.comm_world, 1, 1, 1), 6, 3)]
for mesh, surface, ref_int in references:
c = Constant(1, mesh.ufl_cell()) # FIXME
c0 = ufl.FacetArea(mesh)
c1 = dolfin.FacetArea(mesh)
assert (c)
assert (c0)
assert (c1)
def test_facet_area1D():
mesh = create_unit_interval(MPI.COMM_WORLD, 10)
# NOTE: Area of a vertex is defined to 1 in ufl
c0 = ufl.FacetArea(mesh)
c = Constant(mesh, ScalarType(1))
ds = ufl.Measure("ds", domain=mesh)
a0 = mesh.comm.allreduce(assemble_scalar(form(c * ds)), op=MPI.SUM)
a = mesh.comm.allreduce(assemble_scalar(form(c0 * ds)), op=MPI.SUM)
assert numpy.isclose(a.real, 2)
assert numpy.isclose(a0.real, 2)
def testFacetArea():
references = [(UnitIntervalMesh(1), 2, 2),\
(UnitSquareMesh(1,1), 4, 4),\
(UnitCubeMesh(1,1,1), 6, 3)]
for mesh, surface, ref_int in references:
c = Constant(1, mesh.ufl_cell()) # FIXME
c0 = ufl.FacetArea(mesh)
c1 = dolfin.FacetArea(mesh)
assert round(assemble(c * dx(mesh)) - 1, 7) == 0
assert round(assemble(c * ds(mesh)) - surface, 7) == 0
assert round(assemble(c0 * ds(mesh)) - ref_int, 7) == 0
assert round(assemble(c1 * ds(mesh)) - ref_int, 7) == 0
def testFacetArea(self):
if MPI.size(mpi_comm_world()) == 1:
references = [(UnitIntervalMesh(1), 2, 2),\
(UnitSquareMesh(1,1), 4, 4),\
(UnitCubeMesh(1,1,1), 6, 3)]
for mesh, surface, ref_int in references:
c = Constant(1, mesh.ufl_cell()) # FIXME
c0 = ufl.FacetArea(mesh)
c1 = dolfin.FacetArea(mesh)
self.assertAlmostEqual(assemble(c * dx, mesh=mesh), 1)
self.assertAlmostEqual(assemble(c * ds, mesh=mesh), surface)
self.assertAlmostEqual(assemble(c0 * ds, mesh=mesh), ref_int)
self.assertAlmostEqual(assemble(c1 * ds, mesh=mesh), ref_int)
def test_facet_area(mesh_factory):
"""
Compute facet area of cell. UFL currently only supports affine cells for this computation
"""
# NOTE: UFL only supports facet area calculations of affine cells
func, args, exact_area = mesh_factory
mesh = func(*args)
c0 = ufl.FacetArea(mesh)
c = Constant(mesh, ScalarType(1))
tdim = mesh.topology.dim
num_faces = 4 if tdim == 2 else 6
ds = ufl.Measure("ds", domain=mesh)
a = mesh.comm.allreduce(assemble_scalar(form(c * ds)), op=MPI.SUM)
a0 = mesh.comm.allreduce(assemble_scalar(form(c0 * ds)), op=MPI.SUM)
assert numpy.isclose(a.real, num_faces)
assert numpy.isclose(a0.real, num_faces * exact_area)
