def compute_vertex_periodicity(mesh, master, slave, to_master):
'''Compute mapping from slave vertices to master vertices'''
f = MeshFunction('size_t', mesh, 0, 0) # As a vertex function
master.mark(f, 2)
slave.mark(f, 3)
master_vertices = [v.index() for v in SubsetIterator(f, 2)]
slave_vertices = set(v.index() for v in SubsetIterator(f, 3))
assert len(master_vertices) == len(slave_vertices), (len(master_vertices),
len(slave_vertices))
x = mesh.coordinates()
error, mapping = 0., {}
while slave_vertices:
s = slave_vertices.pop()
xs = x[s]
mapped = to_master(xs)
# Local to master_vertex_x
master_vertex_x = x[master_vertices]
dist = np.sqrt(np.sum((master_vertex_x - mapped)**2, axis=1))
mapped_index = np.argmin(dist)
# Wrt to vertex numbering
m = master_vertices[mapped_index]
mapping[s] = m
error = max(error, dist[mapped_index])
master_vertices.remove(m)
assert not slave_vertices and not master_vertices
return error, mapping
def compute_entity_periodicity(tdim, mesh, master, slave, to_master):
'''
Compute mapping from slave tdim entities to master tdim entities
INPUT:
mesh = dolfin.Mesh
master = dolfin.SubDomain instance (to mark master vertices)
slave = dolfin.SubDomain instance (to mark slave vertices)
to_mastar = x (a slave vertex coord) -> a master vertex coord
OUTPUT:
error = largest distance between master and slave vertex coordinates
mapping = dict{slave tdim entity index -> master tdim entity index}
'''
assert 0 <= tdim < mesh.topology().dim()
error, vertex_mapping = compute_vertex_periodicity(mesh, master, slave,
to_master)
# Done for vertices
if tdim == 0:
return error, vertex_mapping
# Other entities are established using their definition in terms
# of vertex indices
f = MeshFunction('size_t', mesh, tdim, 0)
master.mark(f, 2)
slave.mark(f, 3)
master_entities = (e.index() for e in SubsetIterator(f, 2))
slave_entities = (e.index() for e in SubsetIterator(f, 3))
mesh.init(tdim, 0)
e2v = mesh.topology()(tdim, 0)
# Define in terms of vertices. Invert for look up
master_vertices = {tuple(sorted(e2v(e))): e for e in master_entities}
# For slave we define via mapped vertices
slave_entities = {
e: tuple(sorted(vertex_mapping[v] for v in e2v(e)))
for e in slave_entities
}
assert len(master_vertices) == len(slave_entities)
mapping = {}
while slave_entities:
s, vertices = slave_entities.popitem()
# Look up the master entity
m = master_vertices[vertices]
mapping[s] = m
master_vertices.pop(vertices)
assert not slave_entities and not master_vertices
return error, mapping
def load_data(mesh, mesh_f, dim, data):
'''
Represent mesh_f over dim entities of mesh as collection of vertices.
Can have mesh as mesh function or (h5_file, data_set)
'''
try:
h5_file, data_set = mesh_f
mf = MeshFunction('size_t', mesh, dim, 0)
h5_file.read(mf, data_set)
except ValueError:
mf = mesh_f
data_set = '%d dim entites' % mf.dim()
# Mapf for encoding entities as vertices
mesh.init(dim, 0)
e2v = mesh.topology()(dim, 0)
tags = set(mf.array())
# Don't encode zero - we initialize to it
if 0 in tags: tags.remove(0)
info('%s evolves tags %r' % (data_set, tags))
for tag in tags:
data[(dim, tag)] = np.array([e2v(e.index()) for e in SubsetIterator(mf, tag)],
dtype='uintp')
return data
def cell_chi(f, marker=1):
'''
Let f be a facet function. Build a DG0 function which is such
that cell connected to f == marker are 1 and are 0 otherwise.
'''
assert f.mesh().topology().dim() == 2
assert f.dim() == 1
mesh = f.mesh()
mesh.init(1, 2)
f2c = mesh.topology()(1, 2)
V = FunctionSpace(mesh, 'DG', 0)
dm = V.dofmap()
first, last = dm.ownership_range()
n = last - first
is_local = lambda i, f=first, l=last: f <= i + f < l
chi = Function(V)
values = chi.vector().get_local()
for facet in SubsetIterator(f, marker):
fi = facet.index()
for c in f2c(fi):
dofs = filter(is_local, dm.cell_dofs(c))
values[dofs] = 1.
# Sync
chi.vector().set_local(values)
as_backend_type(chi.vector()).update_ghost_values()
return chi
def compute_vertex_periodicity(mesh, master, slave, to_master):
'''
Compute mapping from slave vertices to master vertices
INPUT:
mesh = dolfin.Mesh
master = dolfin.SubDomain instance (to mark master vertices)
slave = dolfin.SubDomain instance (to mark slave vertices)
to_mastar = x (a slave vertex coord) -> a master vertex coord
OUTPUT:
error = largest distance between master and slave vertex coordinates
mapping = dict{slave vertex index -> master vertex index}
'''
f = MeshFunction('size_t', mesh, 0, 0) # As a vertex function
master.mark(f, 2)
slave.mark(f, 3)
master_vertices = [v.index() for v in SubsetIterator(f, 2)]
slave_vertices = set(v.index() for v in SubsetIterator(f, 3))
assert len(master_vertices) == len(slave_vertices), (len(master_vertices),
len(slave_vertices))
x = mesh.coordinates()
error, mapping = 0., {}
while slave_vertices:
s = slave_vertices.pop()
xs = x[s] # Its coord
mapped = to_master(xs) # Coord in master domain
# Local to master_vertex_x
master_vertex_x = x[master_vertices]
# Perform search to find closest master vertex
dist = np.sqrt(np.sum((master_vertex_x - mapped)**2, axis=1))
mapped_index = np.argmin(dist)
# Wrt to vertex numbering
m = master_vertices[mapped_index]
mapping[s] = m
# Do we have a match ?
error = max(error, dist[mapped_index])
# Assume we do so no more match possible
master_vertices.remove(m)
assert not slave_vertices and not master_vertices
return error, mapping
def DLT_trace_mat(V, TV, trace_mesh=None, tag_data=None):
'''Inject dofs from facets to DLT'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
try:
marking_function = trace_mesh.marking_function
tag_data = (marking_function, set(marking_function.array()))
except AttributeError:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set(
(0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
if TV.num_sub_spaces() == 0:
Tdmaps = [TV.dofmap()]
else:
Tdmaps = [TV.sub(i).dofmap() for i in range(TV.num_sub_spaces())]
if V.num_sub_spaces() == 0:
dmap = V.dofmap()
facet2dofs = [dmap.entity_dofs(mesh, fdim)]
else:
facet2dofs = [
V.sub(i).dofmap().entity_dofs(mesh, fdim)
for i in range(V.num_sub_spaces())
]
assert len(Tdmaps) == len(facet2dofs)
# Only look at tagged cells
trace_cells = list(
itertools.chain(*[
map(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag)) for tag in tags
]))
# Rows
with petsc_serial_matrix(TV, V) as mat:
for Tdmap, facet2dof in zip(Tdmaps, facet2dofs):
for trace_cell in trace_cells:
trace_dof, = Tdmap.cell_dofs(trace_cell)
DLT_dof = facet2dof[mapping[trace_cell]]
mat.setValues([trace_dof], [DLT_dof], [1.],
PETSc.InsertMode.INSERT_VALUES)
return mat
def compute_entity_periodicity(tdim, mesh, master, slave, to_master):
'''Mapping from slave entities of tdim to master'''
assert 0 <= tdim < mesh.topology().dim()
_, vertex_mapping = compute_vertex_periodicity(mesh, master, slave,
to_master)
# Done for vertices
if tdim == 0:
return vertex_mapping
f = MeshFunction('size_t', mesh, tdim, 0)
master.mark(f, 2)
slave.mark(f, 3)
master_entities = (e.index() for e in SubsetIterator(f, 2))
slave_entities = (e.index() for e in SubsetIterator(f, 3))
mesh.init(tdim, 0)
e2v = mesh.topology()(tdim, 0)
# Define in terms of vertices. Invert for loopup
master_vertices = {tuple(sorted(e2v(e))): e for e in master_entities}
# For slave we define via mapped vertices
slave_entities = {
e: tuple(sorted(vertex_mapping[v] for v in e2v(e)))
for e in slave_entities
}
assert len(master_vertices) == len(slave_entities)
mapping = {}
while slave_entities:
s, vertices = slave_entities.popitem()
m = master_vertices[vertices]
mapping[s] = m
master_vertices.pop(vertices)
assert not slave_entities and not master_vertices
return mapping
def analyse_connectivity(mesh, edge_f, subdomain):
'''
Compute connectivity between vertices of mesh and its edges that are marked
by edge function with value of subdomain.
'''
# We are only interested in gdim == tdim meshes
gdim = mesh.geometry().dim()
tdim = mesh.topology().dim()
assert gdim == tdim and tdim > 1
# And building 1d in gdim meshes
try:
edim = edge_f.dim()
assert edim == 1
edges = SubsetIterator(edge_f, subdomain)
except AttributeError:
assert isinstance(edge_f, list)
# Recreate edges from list
mesh.init(1)
edges = (Edge(mesh, index) for index in edge_f)
# First compute connectivity edge <--> vertex for edge, vertex on edge_f
mesh.init(1, 0)
topology = mesh.topology()
# Connect between all edge->c of mesh
all_edge_vertex_c = topology(1, 0)
# Connectivity edge->vertex on interval mesh
# Edge function - extract marked
# if isinstance(edge_f, MeshFunction):
edge_vertex_c = dict(
(edge.index(), set(all_edge_vertex_c(edge.index()))) for edge in edges)
# Only marked are given in list
# else:
# edge_vertex_c = dict((edge, set(all_edge_vertex_c(edge)))
# for edge in edge_f)
assert len(edge_vertex_c), 'No edges with value %d' % subdomain
# Connectivity vertex->edge on interval mesh
vertex_edge_c = defaultdict(list)
for edge, vertices in edge_vertex_c.iteritems():
for vertex in vertices:
vertex_edge_c[vertex].append(edge)
return edge_vertex_c, vertex_edge_c
def dof_chi(f, V, marker=1):
'''
Let f be a an edge function. Build a function in V which is such
that all dofs where f == marker are 1 and are 0 otherwise.
'''
tdim = f.mesh().topology().dim()
assert f.dim() == 1
assert V.mesh().id() == f.mesh().id()
assert V.ufl_element().family() == 'Lagrange'
mesh = V.mesh()
mesh.init(1, tdim)
mesh.init(tdim, 1)
e2c = mesh.topology()(1, tdim)
c2e = mesh.topology()(tdim, 1)
dm = V.dofmap()
first, last = dm.ownership_range()
n = last - first
is_local = lambda i, f=first, l=last: f <= i + f < l
# Triangle has 3 facets/edges, tet has 6 edges
nedges = mesh.ufl_cell().num_edges()
edge_dofs = [dm.tabulate_entity_closure_dofs(1, i) for i in range(nedges)]
chi = Function(V)
values = chi.vector().get_local()
for edge in SubsetIterator(f, marker):
edgei = edge.index()
c = e2c(edgei)[0] # Any cell
dofs = dm.cell_dofs(c)
local_edge = c2e(c).tolist().index(edgei)
dofs = filter(is_local, dofs[edge_dofs[local_edge]])
values[dofs] = 1.
# Sync
chi.vector().set_local(values)
as_backend_type(chi.vector()).update_ghost_values()
return chi
def convert(msh_file, h5_file, save_mvc=False):
'''Temporary version of convertin from msh to h5'''
root, _ = os.path.splitext(msh_file)
assert os.path.splitext(msh_file)[1] == '.msh'
assert os.path.splitext(h5_file)[1] == '.h5'
# Get the xml mesh
xml_file = '.'.join([root, 'xml'])
subprocess.call(['dolfin-convert %s %s' % (msh_file, xml_file)], shell=True)
# Success?
assert os.path.exists(xml_file)
mesh = Mesh(xml_file)
out = HDF5File(mesh.mpi_comm(), h5_file, 'w')
out.write(mesh, 'mesh')
print('Mesh has %d cells' % mesh.num_cells())
print('Mesh size %g %g' % (mesh.hmin(), mesh.hmax()))
# Save ALL data as facet_functions
names = ('surfaces', 'volumes')
if not save_mvc:
for name, region in zip(names, ('facet_region.xml', 'physical_region.xml')):
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
print('%d %s with 1' % (sum(1 for _ in SubsetIterator(f, 1)), name))
out.write(f, name)
return True
for name, region in zip(names, ('facet_region.xml', 'physical_region.xml')):
r_xml_file = '_'.join([root, region])
f = MeshFunction('size_t', mesh, r_xml_file)
# With mesh value collection we only store nonzero tags
mvc = MeshValueCollection('size_t', mesh, f.dim())
# Fill
fill_mvc_from_mf(f, mvc)
# And save
out.write(mvc, name)
return True
def test_tiling(self):
tile = UnitSquareMesh(2, 2)
mf = MeshFunction('size_t', tile, tile.topology().dim() - 1, 0)
CompiledSubDomain('near(x[0], 0.5) || near(x[1], 0.5)').mark(mf, 1)
mesh_data = {}
mesh_data = load_data(tile, mf, dim=1, data=mesh_data)
mesh, mesh_data = TileMesh(tile, shape=(23, 13), mesh_data=mesh_data)
f = mf_from_data(mesh, mesh_data)[1]
self.assertTrue(
np.linalg.norm(mesh.coordinates().min(axis=0) -
np.zeros(2)) < 1E-13)
self.assertTrue(
np.linalg.norm(mesh.coordinates().max(axis=0) -
np.array([23., 13.])) < 1E-13)
self.assertTrue(23 * 13 * 4 == sum(1 for _ in SubsetIterator(f, 1)))
def load_data(mesh, h5_file, data_set, dim, data):
'''
Fill the data dictionary with data_set representing mesh function with
dim over mesh read from h5_file according to key spec expected by tiling
algorithm.
'''
mf = MeshFunction('size_t', mesh, dim, 0)
h5_file.read(mf, data_set)
# Data to evolve
mesh.init(dim, 0)
e2v = tile.topology()(dim, 0)
tags = set(mf.array())
# Don't evolve zero - we initialize to it
if 0 in tags: tags.remove(0)
info('%s evolves tags %r' % (data_set, tags))
for tag in tags:
data[(dim, tag)] = np.array([e2v(e.index()) for e in SubsetIterator(mf, tag)],
dtype='uintp')
return data
def cells_of(cell_f, tag):
'''Cells of tagged volume'''
return list(
map(operator.methodcaller('index'), SubsetIterator(cell_f, tag)))
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set((0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = itertools.chain(*[
itertools.imap(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag))
for tag in tags
])
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in trace_cells:
# We might
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
def trace_mat_one_restrict(V,
TV,
restriction,
normal,
trace_mesh=None,
tag_data=None):
'''
Compute the trace values using +/- restriction. A + plus is the one
for which the vector cell.midpoint - facet.midpoint agrees in orientation
with the normal on the facet.
'''
mesh = V.mesh()
fdim = mesh.topology().dim() - 1
if trace_mesh is None: trace_mesh = TV.mesh()
# None means all
if tag_data is None:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set((0, )))
trace_mesh_subdomains, tags = tag_data
# Only look at tagged cells
trace_cells = itertools.chain(*[
itertools.imap(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag))
for tag in tags
])
# Init/extract entity map
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions
# of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
gdim = mesh.geometry().dim()
# Rows
visited_dofs = [False] * TV.dim()
# Column values
dof_values = np.zeros(V_basis_f.elm.space_dimension(), dtype='double')
with petsc_serial_matrix(TV, V) as mat:
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here
facet_cells = f2c(mapping[trace_cell])
assert 0 < len(facet_cells) < 3
# Ignore boundary facets
if len(facet_cells) == 1:
cell = facet_cells[0]
# Search which cell has the right sign
else:
signs = []
for fcell in facet_cells:
t_mp = Cell(trace_mesh,
trace_cell).midpoint().array()[:gdim]
mp = Cell(mesh, fcell).midpoint().array()[:gdim]
sign = '+' if np.inner(mp -
t_mp, normal(t_mp)) > 0 else '-'
signs.append(sign)
cell = facet_cells[signs.index(restriction)]
V_basis_f.cell = cell
dofs = dmap.cell_dofs(cell)
for local_T, dof_T in enumerate(trace_dofs):
if visited_dofs[dof_T]:
continue
else:
visited_dofs[dof_T] = True
# Define trace dof
TV_dof.dof = local_T
# Eval at V basis functions
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
dof_values[local] = TV_dof.eval(V_basis_f)
# Can fill the matrix now
col_indices = np.array(dofs, dtype='int32')
# Insert
mat.setValues([dof_T], col_indices, dof_values,
PETSc.InsertMode.INSERT_VALUES)
return mat
print('Area/Volume %.3f, Area(!port)/Volume %.3f' %
((area_port + area_no_port) / volume, area_no_port / volume))
volume = intra + extra
print('Area/Volume %.3f, Area(!port)/Volume %.3f' %
((area_port + area_no_port) / volume, area_no_port / volume))
# Mesh size
mesh.init(2)
mesh.init(2, 0)
f2v = mesh.topology()(2, 0)
tri_area = lambda x: np.linalg.norm(np.cross(x[0] - x[1], x[0] - x[2]), 2
) / 2
x = mesh.coordinates()
areas = [tri_area(x[f2v(f.index())]) for f in SubsetIterator(surfaces, 1)]
min_l = sqrt(4 * np.min(areas) / sqrt(3))
max_l = sqrt(4 * np.max(areas) / sqrt(3))
print('Mesh size %g %g' % (min_l, max_l))
print('Domain sizes %g %g %g' %
tuple(np.max(x, axis=0) - np.min(x, axis=0)))
File('foo.pvd') << volumes
File('bar.pvd') << surfaces
map(
os.remove,
filter(lambda f: any(f.endswith(ext) for ext in ('.xml', '.msh')),
os.listdir('.')))
def test_convert_triangle(
self): # Disabled because it fails, see FIXME below
# test no. 1
from dolfin import Mesh, MPI
fname = os.path.join(os.path.dirname(__file__), "data", "triangle")
dfname = fname + ".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 96)
self.assertEqual(mesh.num_cells(), 159)
# Clean up
os.unlink(dfname)
# test no. 2
from dolfin import MPI, Mesh, MeshFunction, \
edges, Edge, faces, Face, \
SubsetIterator, facets
fname = os.path.join(os.path.dirname(__file__), "data",
"test_Triangle_3")
dfname = fname + ".xml"
dfname0 = fname + ".attr0.xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
mesh.init()
mfun = MeshFunction('double', mesh, dfname0)
self.assertEqual(mesh.num_vertices(), 58)
self.assertEqual(mesh.num_cells(), 58)
# Create a size_t MeshFunction and assign the values based on the
# converted Meshfunction
cf = MeshFunction("size_t", mesh, mesh.topology().dim())
cf.array()[mfun.array() == 10.0] = 0
cf.array()[mfun.array() == -10.0] = 1
# Meassure total area of cells with 1 and 2 marker
add = lambda x, y: x + y
area0 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 0)), 0.0)
area1 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 1)), 0.0)
total_area = reduce(add, (face.area() for face in faces(mesh)), 0.0)
# Check that all cells in the two domains are either above or below y=0
self.assertTrue(
all(cell.midpoint().y() < 0 for cell in SubsetIterator(cf, 0)))
self.assertTrue(
all(cell.midpoint().y() > 0 for cell in SubsetIterator(cf, 1)))
# Check that the areas add up
self.assertAlmostEqual(area0 + area1, total_area)
# Measure the edge length of the two edge domains
#edge_markers = mesh.domains().facet_domains()
edge_markers = mesh.domains().markers(mesh.topology().dim() - 1)
self.assertTrue(edge_markers is not None)
#length0 = reduce(add, (Edge(mesh, e.index()).length() \
# for e in SubsetIterator(edge_markers, 0)), 0.0)
length0, length1 = 0.0, 0.0
for item in list(edge_markers.items()):
if item[1] == 0:
e = Edge(mesh, int(item[0]))
length0 += Edge(mesh, int(item[0])).length()
elif item[1] == 1:
length1 += Edge(mesh, int(item[0])).length()
# Total length of all edges and total length of boundary edges
total_length = reduce(add, (e.length() for e in edges(mesh)), 0.0)
boundary_length = reduce(add, (Edge(mesh, f.index()).length() \
for f in facets(mesh) if f.exterior()), 0.0)
# Check that the edges add up
self.assertAlmostEqual(length0 + length1, total_length)
self.assertAlmostEqual(length1, boundary_length)
# Clean up
os.unlink(dfname)
os.unlink(dfname0)
def trace_mat_no_restrict(V, TV, trace_mesh=None, tag_data=None):
'''The first cell connected to the facet gets to set the values of TV'''
mesh = V.mesh()
if trace_mesh is None: trace_mesh = TV.mesh()
fdim = trace_mesh.topology().dim()
# None means all
if tag_data is None:
try:
marking_function = trace_mesh.marking_function
tag_data = (marking_function, set(marking_function.array()))
except AttributeError:
tag_data = (MeshFunction('size_t', trace_mesh,
trace_mesh.topology().dim(), 0), set(
(0, )))
trace_mesh_subdomains, tags = tag_data
# Init/extract the mapping
try:
assert get_entity_map(mesh, trace_mesh, trace_mesh_subdomains, tags)
except (AssertionError, IndexError):
warning('Using non-conforming trace')
# So non-conforming matrix returns PETSc.Mat
return nonconforming_trace_mat(V, TV)
if V.ufl_element().family() == 'HDiv Trace':
assert V.ufl_element().degree() == 0
# In this case
return DLT_trace_mat(V, TV, trace_mesh=trace_mesh, tag_data=tag_data)
# We can get it
mapping = trace_mesh.parent_entity_map[mesh.id()][
fdim] # Map cell of TV to cells of V
mesh.init(fdim, fdim + 1)
f2c = mesh.topology()(fdim, fdim + 1) # Facets of V to cell of V
# The idea is to evaluate TV's degrees of freedom at basis functions of V
Tdmap = TV.dofmap()
TV_dof = DegreeOfFreedom(TV)
dmap = V.dofmap()
V_basis_f = FEBasisFunction(V)
# Only look at tagged cells
trace_cells = list(
itertools.chain(*[
map(operator.methodcaller('index'),
SubsetIterator(trace_mesh_subdomains, tag)) for tag in tags
]))
ndofs_elm, nbasis_elm = TV_dof.elm.space_dimension(
), V_basis_f.elm.space_dimension()
local_values = np.zeros((nbasis_elm, ndofs_elm))
if len(trace_cells) > 10_000:
print(f'Trace mat {TV.ufl_element()} -> {V.ufl_element()}')
trace_cells = tqdm.tqdm(trace_cells, total=len(trace_cells))
rows, cols, values = [], [], []
# DG spaces don't share rows between cells so we take advantage of
# this in special branch
if TV.ufl_element().family() == 'Discontinuous Lagrange':
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs, nbasis_elm)
cols_ = np.repeat(dofs, ndofs_elm)
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values.flat)
# FIXME: Othewise we need to take care of duplicate entrieselse:
else:
needs_fill = np.ones(TV.dim(), dtype=bool)
for trace_cell in trace_cells:
TV_dof.cell = trace_cell
# Many rows at once
trace_dofs = Tdmap.cell_dofs(trace_cell)
# Don't add duplicates
unseen = needs_fill[trace_dofs] # Some will be true and
# For the future
needs_fill[trace_dofs[unseen]] = False
# Figure out the dofs of V to use here. Does not matter which
# cell of the connected ones we pick
cell = f2c(mapping[trace_cell])[0]
V_basis_f.cell = cell
# Columns for the rows
dofs = dmap.cell_dofs(cell)
for local, dof in enumerate(dofs):
# Set which basis foo
V_basis_f.dof = local
# Get all rows at once
local_values[local][:] = TV_dof.eval_dofs(V_basis_f)
# Indices for the filled piece
rows_ = np.tile(trace_dofs[unseen], nbasis_elm)
cols_ = np.repeat(dofs, sum(unseen))
rows.extend(rows_)
cols.extend(cols_)
values.extend(local_values[:, unseen].flat)
mat = csr_matrix((values, (rows, cols)), shape=(TV.dim(), V.dim()))
return PETSc.Mat().createAIJ(comm=PETSc.COMM_WORLD,
size=mat.shape,
csr=(mat.indptr, mat.indices, mat.data))
def deactivate_volumes(cell_f, tag, predicate):
'''Tagged cells of cell_f that satisfy the predicate'''
return [
cell.index() for cell in SubsetIterator(cell_f, tag) if predicate(cell)
]
def union_mesh(meshes, tol=1E-12):
'''Glue together meshes into a big one.'''
assert meshes
num_meshes = len(meshes)
# Nothing to do
if num_meshes == 1:
return meshes[0]
# Recurse
if num_meshes > 2:
return union_mesh([
union_mesh(meshes[:num_meshes / 2 + 1]),
union_mesh(meshes[num_meshes / 2 + 1:])
])
gdim, = set(m.geometry().dim() for m in meshes)
tdim, = set(m.topology().dim() for m in meshes)
fdim = tdim - 1
bdries = [MeshFunction('size_t', m, fdim, 0) for m in meshes]
[DomainBoundary().mark(bdry, 1) for bdry in bdries]
# We are after boundary vertices of both; NOTE that the assumption
# here is that the meshes share only the boundary vertices
[m.init(fdim) for m in meshes]
[m.init(fdim, 0) for m in meshes]
bdry_vertices0, bdry_vertices1 = map(
list,
(set(np.concatenate([f.entities(0) for f in SubsetIterator(bdry, 1)]))
for bdry in bdries))
x0, x1 = [m.coordinates() for m in meshes]
x1 = x1[bdry_vertices1]
shared_vertices = {}
while bdry_vertices0:
i = bdry_vertices0.pop()
x = x0[i]
# Try to match it
dist = np.linalg.norm(x1 - x, 2, axis=1)
imin = np.argmin(dist)
if dist[imin] < tol:
shared_vertices[bdry_vertices1[imin]] = i
x1 = np.delete(x1, imin, axis=0)
del bdry_vertices1[imin]
mesh0, mesh1 = meshes
# We make 0 the master - it adds all its vertices
# The other on add all but those that are not shared
unshared = list(
set(range(mesh1.num_vertices())) - set(shared_vertices.keys()))
merge_x = mesh0.coordinates()
offset = len(merge_x)
# Vertices of the merged mesh
merge_x = np.row_stack([merge_x, mesh1.coordinates()[unshared]])
# Mapping for cells from meshes
lg1 = {k: v for v, k in enumerate(unshared, offset)}
lg1.update(shared_vertices)
# Collapse to list
_, lg1 = zip(*sorted(lg1.items(), key=lambda v: v[0]))
lg1 = np.array(lg1)
mapped_cells = np.fromiter((lg1[v] for v in np.concatenate(mesh1.cells())),
dtype='uintp').reshape((mesh1.num_cells(), -1))
merged_cells = np.row_stack([mesh0.cells(), mapped_cells])
merged_mesh = make_mesh(coordinates=merge_x,
cells=merged_cells,
tdim=tdim,
gdim=gdim)
lg0 = np.arange(mesh0.num_vertices())
# Mapping from leafs
if not hasattr(mesh0, 'leafs'):
merged_mesh.leafs = [(mesh0.id(), lg0)]
else:
merged_mesh.leafs = mesh0.leafs
if not hasattr(mesh1, 'leafs'):
merged_mesh.leafs.append([mesh1.id(), lg1])
else:
for id_, map_ in mesh1.leafs:
merged_mesh.leafs.append((id_, lg1[map_]))
return merged_mesh
def vtk_surface(surfaces, tag, output, value):
assert surfaces.dim() == 2
mesh = surfaces.mesh()
mesh.init(2, 0)
f2v = mesh.topology()(2, 0)
ncells = sum(1 for _ in SubsetIterator(surfaces, tag))
nvertices = 3 * ncells
x = mesh.coordinates()
with open(output, 'w') as f:
f.write("<?xml version=\"1.0\"?>\n")
f.write(
"<VTKFile type=\"UnstructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n"
)
f.write(" <UnstructuredGrid>\n")
f.write(" <Piece NumberOfPoints=\"%i\" NumberOfCells=\"%i\">\n" %
(nvertices, ncells))
f.write(" <Points>\n")
f.write(
" <DataArray type=\"Float32\" Name=\"vertices\" NumberOfComponents=\"3\" format=\"ascii\">\n"
)
for e in SubsetIterator(surfaces, tag):
coords = x[f2v(e.index())]
for v in coords:
f.write("%g %g %g " % tuple(v))
f.write(" </DataArray>\n")
f.write(" </Points>\n")
f.write(" <Cells>\n")
f.write(
" <DataArray type=\"Int32\" Name=\"connectivity\" format=\"ascii\">\n"
)
f.write(" ".join(map(str, range(nvertices))))
f.write(" </DataArray>\n")
f.write(
" <DataArray type=\"Int32\" Name=\"offsets\" format=\"ascii\">\n"
)
f.write(' '.join(map(str, range(0, 3 * ncells, 3))))
f.write(" </DataArray>\n")
f.write(
" <DataArray type=\"UInt8\" Name=\"types\" format=\"ascii\">\n"
)
f.write('5 ' * ncells)
f.write(' </DataArray>\n')
f.write(" </Cells>\n")
value = '%d ' % value
print value
f.write(' <CellData Scalars="tags">\n')
f.write(
" <DataArray type=\"Float32\" Name=\"tags\" format=\"ascii\">\n"
)
f.write(value * ncells)
f.write(" </DataArray>\n")
f.write(" </CellData>\n")
f.write(" </Piece>\n")
f.write(" </UnstructuredGrid>\n")
f.write("</VTKFile>\n")
def test(path, type='mf'):
'''Evolve the tile in (n, n) pattern checking volume/surface properties'''
comm = mpi_comm_world()
h5 = HDF5File(comm, path, 'r')
tile = Mesh()
h5.read(tile, 'mesh', False)
init_container = lambda type, dim: (
MeshFunction('size_t', tile, dim, 0)
if type == 'mf' else MeshValueCollection('size_t', tile, dim))
for n in (2, 4):
data = {}
checks = {}
for dim, name in zip((2, 3), ('surfaces', 'volumes')):
# Get the collection
collection = init_container(type, dim)
h5.read(collection, name)
if type == 'mvc': collection = as_meshf(collection)
# Data to evolve
tile.init(dim, 0)
e2v = tile.topology()(dim, 0)
# Only want to evolve tag 1 (interfaces) for the facets.
data[(dim, 1)] = np.array(
[e2v(e.index()) for e in SubsetIterator(collection, 1)],
dtype='uintp')
if dim == 2:
check = lambda m, f: assemble(
FacetArea(m) * ds(domain=m,
subdomain_data=f,
subdomain_id=1) + avg(FacetArea(m)) *
dS(domain=m, subdomain_data=f, subdomain_id=1))
else:
check = lambda m, f: assemble(
CellVolume(m) * dx(
domain=m, subdomain_data=f, subdomain_id=1))
checks[
dim] = lambda m, f, t=tile, c=collection, n=n, check=check: abs(
check(m, f) - n**2 * check(t, c)) / (n**2 * check(t, c))
t = Timer('x')
mesh, mesh_data = TileMesh(tile, (n, n), mesh_data=data)
info('\tTiling took %g s. Ncells %d, nvertices %d, \n' %
(t.stop(), mesh.num_vertices(), mesh.num_cells()))
foos = mf_from_data(mesh, mesh_data)
# Mesh Functions
from_mf = np.array([checks[dim](mesh, foos[dim]) for dim in (2, 3)])
mvcs = mvc_from_data(mesh, mesh_data)
foos = as_meshf(mvcs)
# Mesh ValueCollections
from_mvc = np.array([checks[dim](mesh, foos[dim]) for dim in (2, 3)])
assert np.linalg.norm(from_mf - from_mvc) < 1E-13
# I ignore shared facets so there is bound to be some error in facets
# Volume should match well
print from_mf
# -------------------------------------------------------------------
if __name__ == '__main__':
from dolfin import (CompiledSubDomain, DomainBoundary, SubsetIterator,
UnitSquareMesh, Facet)
from xii import EmbeddedMesh
mesh = UnitSquareMesh(4, 4)
surfaces = MeshFunction('size_t', mesh, 2, 0)
CompiledSubDomain('x[0] > 0.5-DOLFIN_EPS').mark(surfaces, 1)
# What should be trasfered
f = MeshFunction('size_t', mesh, 1, 0)
DomainBoundary().mark(f, 1)
CompiledSubDomain('near(x[0], 0.5)').mark(f, 1)
# Assign funky colors
for i, e in enumerate(SubsetIterator(f, 1), 1): f[e] = i
ch_mesh = EmbeddedMesh(surfaces, 1)
ch_f = transfer_markers(ch_mesh, f)
# Every color in child is found in parent and we get the midpoint right
p_values, ch_values = list(f.array()), list(ch_f.array())
for ch_value in set(ch_f.array()) - set((0, )):
assert ch_value in p_values
x = Facet(mesh, p_values.index(ch_value)).midpoint()
y = Facet(ch_mesh, ch_values.index(ch_value)).midpoint()
assert x.distance(y) < 1E-13