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_cell(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)
# We want to embed
mappings = left.parent_entity_map[mesh.id()]
# Is it correct?
xi, x = left.coordinates(), mesh.coordinates()
assert min(
np.linalg.norm(
xi[list(mappings[0].keys())] - x[list(mappings[0].values())], 2,
1)) < tol
tdim = mesh.topology().dim()
c2v = mesh.topology()(tdim, 0)
icells = left.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[c2v(val)])
for key, val in list(mappings[tdim].items())
])
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_translate_markers_3d_facet(n=4):
'''
|----|
| [] |
|----|
'''
# Let there be a background mesh with facet functions
mesh = UnitCubeMesh(n, n, n)
bdries = MeshFunction('size_t', mesh, mesh.topology().dim() - 1, 0)
CompiledSubDomain('near(x[0], 0)').mark(bdries, 10)
CompiledSubDomain('near(x[0], 1)').mark(bdries, 20)
CompiledSubDomain('near(x[1], 0)').mark(bdries, 30)
CompiledSubDomain('near(x[1], 1)').mark(bdries, 40)
CompiledSubDomain(
'near(x[0], 0.25) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))'
).mark(bdries, 1)
CompiledSubDomain(
'near(x[0], 0.75) && ((x[1] > 0.25-DOLFIN_EPS) && (x[1] < 0.75+DOLFIN_EPS))'
).mark(bdries, 2)
CompiledSubDomain(
'near(x[1], 0.25) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))'
).mark(bdries, 3)
CompiledSubDomain(
'near(x[1], 0.75) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))'
).mark(bdries, 4)
# It will have subdomains
cell_f = MeshFunction('size_t', mesh, mesh.topology().dim(), 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)
inside = EmbeddedMesh(cell_f, 2)
values = inside.translate_markers(bdries, (1, 2, 3, 4, 10, 20, 30, 40))
assert set(np.unique(values)) == set((0, 1, 2, 3, 4))
# And they are in the right place
x, y = mesh.coordinates(), inside.coordinates()
_, f2v_x = (mesh.init(1, 0), mesh.topology()(mesh.topology().dim() - 1, 0))
_, f2v_y = (inside.init(1, 0), inside.topology()(mesh.topology().dim() - 1,
0))
for tag in (1, 2, 3, 4):
entities_x, = np.where(bdries.array() == tag)
entities_y, = np.where(values.array() == tag)
assert len(entities_x) == len(entities_y)
nodes_x = np.unique(np.hstack([f2v_x(e) for e in entities_x]))
nodes_y = np.unique(np.hstack([f2v_y(e) for e in entities_y]))
assert len(nodes_x) == len(nodes_y)
xx = sorted(map(tuple, x[nodes_x]))
yy = sorted(map(tuple, y[nodes_y]))
assert xx == yy
def test_3d(n=4, tol=1E-10):
'''[|]'''
mesh = UnitCubeMesh(n, n, n)
cell_f = MeshFunction('size_t', mesh, 3, 2)
CompiledSubDomain('x[0] < 0.5+DOLFIN_EPS').mark(cell_f, 1)
left = EmbeddedMesh(cell_f, 1)
facet_f = MeshFunction('size_t', left, 2, 0)
CompiledSubDomain('near(x[0], 0.5)').mark(facet_f, 1)
iface = EmbeddedMesh(facet_f, 1)
# We want to embed
mappings = iface.parent_entity_map[left.id()]
# Is it correct?
xi, x = iface.coordinates(), left.coordinates()
assert min(
np.linalg.norm(
xi[list(mappings[0].keys())] - x[list(mappings[0].values())], 2,
1)) < tol
tdim = left.topology().dim() - 1
left.init(tdim, 0)
f2v = left.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())
])
V = FunctionSpace(left, 'CG', 1)
u = interpolate(Expression('x[0] + x[1]', degree=1), V)
dx_ = Measure('dx', domain=iface)
assert abs(ii_assemble(Trace(u, iface) * dx_) - 1.0) < tol
def test_3d_performance(n=4, tol=1E-10, strict=False):
'''[|]'''
mesh = UnitCubeMesh(n, n, n)
bdries1 = MeshFunction('size_t', mesh, 2, 0)
DomainBoundary().mark(bdries1, 1)
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, 1)
CompiledSubDomain(
'near(x[1], 0.25) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))'
).mark(bdries1, 1)
CompiledSubDomain(
'near(x[1], 0.75) && ((x[0] > 0.25-DOLFIN_EPS) && (x[0] < 0.75+DOLFIN_EPS))'
).mark(bdries1, 1)
t = Timer('embed')
iface = EmbeddedMesh(bdries1, 1)
dt = t.stop()
if strict:
# We want to embed
mappings = iface.parent_entity_map[mesh.id()]
# Is it correct?
xi, x = iface.coordinates(), mesh.coordinates()
assert min(
np.linalg.norm(
xi[list(mappings[0].keys())] - x[list(mappings[0].values())],
2, 1)) < tol
tdim = mesh.topology().dim() - 1
mesh.init(tdim, 0)
f2v = mesh.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())
])
return (dt, mesh.num_cells(), iface.num_cells())
def load(scale, curve_gen):
'''Load meshes for 3d-1d problems'''
h5_file = generate(scale)
comm = df.mpi_comm_world()
h5 = df.HDF5File(comm, h5_file, 'r')
mesh3d = df.Mesh()
h5.read(mesh3d, 'mesh', False)
# 1d mesh from tagged edges
edge_f, bc_vertex = curve_gen(mesh3d)
mesh1d = EmbeddedMesh(edge_f, 1)
# Check thet we really have only on surface point
bdry = df.CompiledSubDomain(
'near(std::max(std::max(std::abs(x[0]), std::abs(x[1])), std::abs(x[2])), 1, tol)',
tol=TOL)
e = sum(int(bdry.inside(x, False)) for x in mesh1d.coordinates())
assert e == 1, e
return mesh3d, mesh1d, bc_vertex
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
from dolfin import *
from xii import OuterNormal, EmbeddedMesh
import numpy as np
mesh = UnitSquareMesh(10, 10)
f = MeshFunction('size_t', mesh, 1, 0)
CompiledSubDomain('near(x[1], 0)').mark(f, 1)
CompiledSubDomain('near(x[1], 1)').mark(f, 1)
bmesh = EmbeddedMesh(f, 1)
n = OuterNormal(bmesh, [0.5, 0.5])
# Top?
for x in bmesh.coordinates():
if near(x[1], 1.0):
assert np.linalg.norm(n(x) - np.array([0, 1.])) < 1E-13
# Bottom
for x in bmesh.coordinates():
if near(x[1], 0.0):
assert np.linalg.norm(n(x) - np.array([0, -1.])) < 1E-13
def test_2d_color(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)
# And interface
bmesh = EmbeddedMesh(bdries1, (1, 2, 3, 4))
# Embedded it viewwed from stokes
mappings = bmesh.parent_entity_map[mesh1.id()]
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())
])
# Now color specific
cf = bmesh.marking_function
assert set(cf.array()) == set((1, 2, 3, 4))
assert all(bdries1[v] == cf[k] for k, v in list(mappings[tdim].items()))