def test_2d_incomplete(n=32, tol=1E-10):
'''[|]'''
mesh = UnitSquareMesh(n, n)
cell_f = MeshFunction('size_t', mesh, 2, 2)
CompiledSubDomain('x[0] < 0.5+DOLFIN_EPS').mark(cell_f, 1)
left = EmbeddedMesh(cell_f, 1)
right = EmbeddedMesh(cell_f, 2)
facet_f = MeshFunction('size_t', left, 1, 0)
CompiledSubDomain('near(x[0], 0.0)').mark(facet_f, 1)
CompiledSubDomain('near(x[0], 0.5)').mark(facet_f, 2)
CompiledSubDomain('near(x[1], 0.0)').mark(facet_f, 3)
CompiledSubDomain('near(x[1], 1.0)').mark(facet_f, 4)
# More complicated iface
iface = EmbeddedMesh(facet_f, (1, 2, 3, 4))
# Right will interact with it in a simpler way
facet_f = MeshFunction('size_t', right, 1, 0)
CompiledSubDomain('near(x[0], 0.5)').mark(facet_f, 2)
# We want to embed
mappings = iface.compute_embedding(facet_f, 2)
# Is it correct?
xi, x = iface.coordinates(), right.coordinates()
assert min(np.linalg.norm(xi[list(mappings[0].keys())]-x[list(mappings[0].values())], 2, 1)) < tol
tdim = right.topology().dim()-1
right.init(tdim, 0)
f2v = right.topology()(tdim, 0)
icells = iface.cells()
vertex_match = lambda xs, ys: all(min(np.linalg.norm(ys - x, 2, 1)) < tol for x in xs)
assert all([vertex_match(xi[icells[key]], x[f2v(val)]) for key, val in list(mappings[tdim].items())])
try:
iface.compute_embedding(facet_f, 2)
except ValueError:
pass
V = FunctionSpace(right, 'CG', 2)
u = interpolate(Expression('x[1]*x[1]', degree=1), V)
# FIXME: this passes but looks weird
dx_ = Measure('dx', domain=iface, subdomain_data=iface.marking_function)
assert abs(ii_assemble(Trace(u, iface, tag=2)*dx_(2)) - 1./3) < tol
def test_2d(n=32, tol=1E-10):
'''[|]'''
mesh = UnitSquareMesh(n, n)
cell_f = MeshFunction('size_t', mesh, 2, 2)
CompiledSubDomain('x[0] < 0.5+DOLFIN_EPS').mark(cell_f, 1)
left = EmbeddedMesh(cell_f, 1)
right = EmbeddedMesh(cell_f, 2)
facet_f = MeshFunction('size_t', left, 1, 0)
CompiledSubDomain('near(x[0], 0.5)').mark(facet_f, 1)
iface = EmbeddedMesh(facet_f, 1)
# Now suppose
facet_f = MeshFunction('size_t', right, 1, 0)
CompiledSubDomain('near(x[0], 0.5)').mark(facet_f, 2)
# We want to embed
mappings = iface.compute_embedding(facet_f, 2)
# Is it correct?
xi, x = iface.coordinates(), right.coordinates()
assert min(np.linalg.norm(xi[list(mappings[0].keys())]-x[list(mappings[0].values())], 2, 1)) < tol
tdim = right.topology().dim()-1
right.init(tdim, 0)
f2v = right.topology()(tdim, 0)
icells = iface.cells()
vertex_match = lambda xs, ys: all(min(np.linalg.norm(ys - x, 2, 1)) < tol for x in xs)
assert all([vertex_match(xi[icells[key]], x[f2v(val)]) for key, val in list(mappings[tdim].items())])
try:
iface.compute_embedding(facet_f, 2)
except ValueError:
pass
V = FunctionSpace(right, 'CG', 1)
u = interpolate(Expression('x[1]', degree=1), V)
dx_ = Measure('dx', domain=iface)
assert abs(ii_assemble(Trace(u, iface)*dx_) - 0.5) < tol
def test_2d_enclosed(n=32, tol=1E-10):
'''
|----|
| [] |
|----|
'''
mesh = UnitSquareMesh(n, n)
# Lets get the outer part
cell_f = MeshFunction('size_t', mesh, 2, 1)
inside = '(x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS) && (x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS)'
CompiledSubDomain(inside).mark(cell_f, 2)
# Stokes ---
mesh1 = EmbeddedMesh(cell_f, 1)
bdries1 = MeshFunction('size_t', mesh1, mesh1.topology().dim()-1, 0)
CompiledSubDomain('near(x[0], 0)').mark(bdries1, 10)
CompiledSubDomain('near(x[0], 1)').mark(bdries1, 20)
CompiledSubDomain('near(x[1], 0)').mark(bdries1, 30)
CompiledSubDomain('near(x[1], 1)').mark(bdries1, 40)
CompiledSubDomain('near(x[0], 0.25) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))').mark(bdries1, 1)
CompiledSubDomain('near(x[0], 0.75) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))').mark(bdries1, 2)
CompiledSubDomain('near(x[1], 0.25) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))').mark(bdries1, 3)
CompiledSubDomain('near(x[1], 0.75) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))').mark(bdries1, 4)
# Darcy ---
mesh2 = EmbeddedMesh(cell_f, 2)
bdries2 = MeshFunction('size_t', mesh2, mesh2.topology().dim()-1, 0)
CompiledSubDomain('near(x[0], 0.25) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))').mark(bdries2, 1)
CompiledSubDomain('near(x[0], 0.75) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))').mark(bdries2, 2)
CompiledSubDomain('near(x[1], 0.25) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))').mark(bdries2, 3)
CompiledSubDomain('near(x[1], 0.75) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))').mark(bdries2, 4)
# -----------------
# And interface
bmesh = EmbeddedMesh(bdries2, (1, 2, 3, 4))
# Embedded it viewwed from stokes
mappings = bmesh.compute_embedding(bdries1, (1, 2, 3, 4))
xi, x = bmesh.coordinates(), mesh1.coordinates()
assert min(np.linalg.norm(xi[list(mappings[0].keys())]-x[list(mappings[0].values())], 2, 1)) < tol
tdim = mesh1.topology().dim()-1
mesh1.init(tdim, 0)
f2v = mesh1.topology()(tdim, 0)
icells = bmesh.cells()
vertex_match = lambda xs, ys: all(min(np.linalg.norm(ys - x, 2, 1)) < tol for x in xs)
assert all([vertex_match(xi[icells[key]], x[f2v(val)]) for key, val in list(mappings[tdim].items())])
try:
bmesh.compute_embedding(bdries1, 2)
except ValueError:
pass
V = VectorFunctionSpace(mesh1, 'CG', 1)
u = interpolate(Expression(('x[1]', 'x[0]'), degree=1), V)
dx_ = Measure('dx', domain=bmesh)
n_ = OuterNormal(bmesh, [0.5, 0.5])
# Because it is divergence free
assert abs(ii_assemble(dot(n_, Trace(u, bmesh))*dx_)) < tol