def poincare_const(o, p, d=1):
# Vectorial Poincare, see [Blechta, Malek, Vohralik 2016]
if d != 1 and p != 2.0:
return d**abs(0.5-1.0/p) * poincare_const(o, p)
if isinstance(o, Mesh):
raise NotImplementedError("Poincare constant not implemented on mesh!")
if isinstance(o, Cell):
assert _is_simplex(o), "Poincare constant not " \
"implemented on non-simplicial cells!"
h = max(e.length() for e in edges(o))
return h*_poincare_convex(p)
if isinstance(o, CellType):
assert _is_simplex(o), "Poincare constant not " \
"implemented on non-simplicial cells!"
return _poincare_convex(p)
if isinstance(o, Vertex):
# TODO: fix using ghosted mesh
not_working_in_parallel("Poincare computation on patch")
h = max(v0.point().distance(v1.point())
for c0 in cells(o) for v0 in vertices(c0)
for c1 in cells(o) for v1 in vertices(c1))
# FIXME: Implement a check for convexity of the patch
_warn_poincare_convex()
return h*_poincare_convex(p)
raise NotImplementedError
def compare_split_matrices(eq, mat, vec, Wv, Wu, eps=1e-14):
# Assemble coupled system
M, v = dolfin.system(eq)
M = assemble(M).array()
v = assemble(v).get_local()
Ni, Nj = mat.shape
def compute_diff(coupled, split):
diff = abs(coupled - split).flatten().max()
return diff
# Rebuild coupled system from split parts
M2 = numpy.zeros_like(M)
v2 = numpy.zeros_like(v)
for i in range(Ni):
dm_Wi = Wv.sub(i).dofmap()
if vec[i] is not None:
data = assemble(vec[i]).get_local()
dm_Vi = vec[i].arguments()[0].function_space().dofmap()
for cell in dolfin.cells(Wv.mesh()):
dofs_Wi = dm_Wi.cell_dofs(cell.index())
dofs_Vi = dm_Vi.cell_dofs(cell.index())
v2[dofs_Wi] = data[dofs_Vi]
dofs_i = dm_Wi.dofs()
diff = compute_diff(v[dofs_i], v2[dofs_i])
print(
'Vector part %d has error %10.3e' % (i, diff), '<---' if diff > eps else ''
)
for j in range(Nj):
dm_Wj = Wv.sub(j).dofmap()
if mat[i, j] is not None:
data = assemble(mat[i, j]).array()
dm_Vi = mat[i, j].arguments()[0].function_space().dofmap()
dm_Vj = mat[i, j].arguments()[1].function_space().dofmap()
for cell in dolfin.cells(Wv.mesh()):
dofs_Wi = dm_Wi.cell_dofs(cell.index())
dofs_Wj = dm_Wj.cell_dofs(cell.index())
dofs_Vi = dm_Vi.cell_dofs(cell.index())
dofs_Vj = dm_Vj.cell_dofs(cell.index())
W_idx = numpy.ix_(dofs_Wi, dofs_Wj)
V_idx = numpy.ix_(dofs_Vi, dofs_Vj)
M2[W_idx] = data[V_idx]
dofs_j = dm_Wj.dofs()
idx = numpy.ix_(dofs_i, dofs_j)
diff = compute_diff(M[idx], M2[idx])
print(
'Matrix part (%d, %d) has error %10.3e' % (i, j, diff),
'<---' if diff > eps else '',
)
# Check that the original and rebuilt systems are identical
assert compute_diff(M, M2) < eps
assert compute_diff(v, v2) < eps
def create_measures(self):
for rom_cell_counter, rom_cell in enumerate(df.cells(
self._mesh_coarse)):
form = FluxForm(df.Function(self._V), df.Function(self._Vc))
facetfct = df.MeshFunction('size_t', self._mesh_fine,
self._mesh_fine.topology().dim() - 1)
facetfct.set_all(0)
for local_facet_id, rom_facet in enumerate(df.facets(rom_cell)):
for fom_facet in df.facets(self._mesh_fine):
mp = fom_facet.midpoint()
p0 = df.Vertex(self._mesh_coarse, rom_facet.entities(0)[0])
p1 = df.Vertex(self._mesh_coarse, rom_facet.entities(0)[1])
p0 = df.Point(np.array([p0.x(0), p0.x(1)]))
p1 = df.Point(np.array([p1.x(0), p1.x(1)]))
eps = mp.distance(p0) + mp.distance(p1) - p0.distance(p1)
if eps < 1e-12:
facetfct.set_value(fom_facet.index(),
local_facet_id + 1)
if self._rom_exterior_facets[rom_facet.index()]:
form.append_ds(
df.Measure('ds',
domain=self._mesh_fine,
subdomain_data=facetfct,
subdomain_id=local_facet_id + 1))
else:
form.append_dS(
df.Measure('dS',
domain=self._mesh_fine,
subdomain_data=facetfct,
subdomain_id=local_facet_id + 1))
cellfct = df.MeshFunction('size_t', self._mesh_fine,
self._mesh_fine.topology().dim())
cellfct.set_all(0)
for fom_cell in df.cells(self._mesh_fine):
if rom_cell.contains(fom_cell.midpoint()):
cellfct.set_value(fom_cell.index(), 1)
form.append_dx(
df.Measure('dx',
domain=self._mesh_fine,
subdomain_data=cellfct,
subdomain_id=1))
self._flux_forms.append(form)
self._initialized = True
def friedrichs_const(o, p):
if isinstance(o, Vertex):
# TODO: fix using ghosted mesh
not_working_in_parallel("Friedrichs computation on patch")
d = max(v0.point().distance(v1.point())
for c0 in cells(o) for v0 in vertices(c0)
for c1 in cells(o) for v1 in vertices(c1))
# FIXME: Implement the check
_warn_friedrichs_lines()
return d
raise NotImplementedError
def make_submesh(mesh, use_indices):
'''Submesh + mapping of child to parent cell and vertex indices'''
length0 = sum(c.volume() for c in df.cells(mesh))
tdim = mesh.topology().dim()
f = df.MeshFunction('size_t', mesh, tdim, 0)
f.array()[use_indices] = 1
submesh = df.SubMesh(mesh, f, 1)
length1 = sum(c.volume() for c in df.cells(submesh))
print_red('Reduced mesh has %g volume of original' %
(length1 / length0, ))
return (submesh, submesh.data().array('parent_cell_indices', tdim),
submesh.data().array('parent_vertex_indices', 0))
def refine_maxh(self, maxh, uniform=False):
"""Refine mesh of FEM basis such that maxh of mesh is smaller than given value."""
if maxh <= 0 or self.mesh.hmax() < maxh:
return self, self.project_onto, self.project_onto, 0
ufl = self._fefs.ufl_element()
mesh = self.mesh
num_cells_refined = 0
if uniform:
while mesh.hmax() > maxh:
num_cells_refined += mesh.num_cells()
mesh = refine(mesh) # NOTE: this global refine results in a red-refinement as opposed to bisection in the adaptive case
else:
while mesh.hmax() > maxh:
cell_markers = CellFunction("bool", mesh)
cell_markers.set_all(False)
for c in cells(mesh):
if c.diameter() > maxh:
cell_markers[c.index()] = True
num_cells_refined += 1
mesh = refine(mesh, cell_markers)
if self._fefs.num_sub_spaces() > 1:
new_fefs = VectorFunctionSpace(mesh, ufl.family(), ufl.degree())
else:
new_fefs = FunctionSpace(mesh, ufl.family(), ufl.degree())
new_basis = FEniCSBasis(new_fefs)
prolongate = new_basis.project_onto
restrict = self.project_onto
return new_basis, prolongate, restrict, num_cells_refined
def is_continuous(mesh):
'''
We say that the embedded mesh is continuous if for each 2 cells
there exists a continuous path of mesh (other) cells between
the two cells
'''
import networkx as nx
assert mesh.topology().dim() < mesh.geometry().dim()
# This mounts to the graph of the mesh having only one connected
# component
G = nx.Graph()
if mesh.topology().dim() == 1:
mesh.init(1, 0)
G.add_edges_from((tuple(cell.entities(0)) for cell in df.cells(mesh)))
else:
tdim = mesh.topology().dim() == 2
graph_edges = set()
# Geome edge cell connectivity to define the graph edges
mesh.init(tdim-1, tdim)
e2c = mesh.topology()(tdim-1, tdim)
for e in range(mesh.num_entities(tdim-1)):
cells = sorted(e2c(e))
graph_edges.update(zip(cells[:-1], cells[1:]))
G.add_edges_from(graph_edges)
return nx.number_connected_components(G) == 1
def from_mesh(cls, mesh, initial_point, k):
print 'Creating Mesh from dolfin.Mesh data.'
# Make sure it is the right kind of mesh.
print 'Initializing mesh attributes (edges, faces, etc.)'
mesh.init() # This will do nothing if already called.
check_mesh_type(mesh)
# Compute extra data not stored on the object.
print 'Reading vertex list from the mesh object'
vertex_list = list(dolfin.vertices(mesh))
print 'Reading edge list from the mesh object'
edge_list = list(dolfin.edges(mesh))
print 'Reading facets list from the mesh object'
# Use facets since they have facet.exterior() set.
facets_list = list(dolfin.facets(mesh))
# Get values specific to motion on the mesh.
print 'Reading cell list from the mesh object'
cell_list = list(dolfin.cells(mesh))
initial_face_index = get_face(dolfin.Point(*initial_point),
mesh, cell_list)
print 'Parsing exterior faces and creating Face objects'
(all_vertices, triangles, face_local_bases, neighbor_faces,
initial_face_index) = get_face_data(vertex_list, edge_list,
facets_list, initial_face_index)
return cls(k, initial_point, initial_face_index,
all_vertices, triangles, face_local_bases, neighbor_faces)
def create_3d_mesh(self, mesh):
nv = mesh.num_vertices()
nc = mesh.num_cells()
h = self.thickness
mesh3 = df.Mesh()
editor = df.MeshEditor()
editor.open(mesh3, 3, 3)
editor.init_vertices(2 * nv)
editor.init_cells(3 * nc)
for v in df.vertices(mesh):
i = v.index()
p = v.point()
editor.add_vertex(i, p.x(), p.y(), 0)
editor.add_vertex(i + nv, p.x(), p.y(), h)
gid = 0
for c in df.cells(mesh):
i, j, k = c.entities(0)
editor.add_cell(gid, i, j, k, i + nv)
gid = gid + 1
editor.add_cell(gid, j, j + nv, k, i + nv)
gid = gid + 1
editor.add_cell(gid, k, k + nv, j + nv, i + nv)
gid = gid + 1
editor.close()
return mesh3
def assert_dof_map_two_blocks_no_restriction(V1, V2, block_V):
local_dimension1 = V1.dofmap().ownership_range()[1] - V1.dofmap().ownership_range()[0]
local_dimension2 = V2.dofmap().ownership_range()[1] - V2.dofmap().ownership_range()[0]
block_local_dimension = block_V.block_dofmap().ownership_range()[1] - block_V.block_dofmap().ownership_range()[0]
assert local_dimension1 + local_dimension2 == block_local_dimension
global_dimension1 = V1.dofmap().global_dimension()
global_dimension2 = V2.dofmap().global_dimension()
block_global_dimension = block_V.block_dofmap().global_dimension()
assert global_dimension1 + global_dimension2 == block_global_dimension
for c in cells(block_V.mesh()):
V1_cell_dofs = V1.dofmap().cell_dofs(c.index())
V1_cell_owned_local_dofs = [a for a in V1_cell_dofs if a < local_dimension1]
V1_cell_unowned_local_dofs = [a for a in V1_cell_dofs if a >= local_dimension1]
V2_cell_dofs = V2.dofmap().cell_dofs(c.index())
V2_cell_owned_local_dofs = [a + local_dimension1 for a in V2_cell_dofs if a < local_dimension2]
V2_cell_unowned_local_dofs = [a + local_dimension1 for a in V2_cell_dofs if a >= local_dimension2]
V_cell_owned_local_dofs = concatenate((V1_cell_owned_local_dofs, V2_cell_owned_local_dofs))
V_cell_unowned_local_dofs = concatenate((V1_cell_unowned_local_dofs, V2_cell_unowned_local_dofs))
block_V_cell_dofs = block_V.block_dofmap().cell_dofs(c.index())
block_V_cell_owned_local_dofs = [b for b in block_V_cell_dofs if b < block_local_dimension]
block_V_cell_unowned_local_dofs = [b for b in block_V_cell_dofs if b >= block_local_dimension]
assert_owned_local_dofs(V_cell_owned_local_dofs, block_V_cell_owned_local_dofs)
assert_unowned_local_dofs(V_cell_unowned_local_dofs, block_V_cell_unowned_local_dofs)
V_dof_coordinates = concatenate((V1.tabulate_dof_coordinates(), V2.tabulate_dof_coordinates()))
block_V_dof_coordinates = block_V.tabulate_dof_coordinates()
assert_tabulated_dof_coordinates(V_dof_coordinates, block_V_dof_coordinates)
def get_regional_midpoints(strain_markers, mesh):
coords = {
region: {coord: []
for coord in range(3)}
for region in range(18)
}
import dolfin
for cell in dolfin.cells(mesh):
# Get coordinates to cell midpoint
x = cell.midpoint().x()
y = cell.midpoint().y()
z = cell.midpoint().z()
# Get index of cell
index = cell.index()
region = strain_markers.array()[index]
coords[region][0].append(x)
coords[region][1].append(y)
coords[region][2].append(z)
mean_coords = {region: np.zeros(3) for region in range(18)}
for i in range(18):
for j in range(3):
mean_coords[i][j] = np.mean(coords[i][j])
return mean_coords, coords
def is_continuous(mesh):
'''
We say that the embedded mesh is continuous if for each 2 cells
there exists a continuous path of mesh (other) cells between
the two cells
'''
assert mesh.topology().dim() < mesh.geometry().dim()
# This mounts to the graph of the mesh having only one connected
# component
G = nx.Graph()
if mesh.topology().dim() == 1:
mesh.init(1, 0)
G.add_edges_from((tuple(cell.entities(0)) for cell in df.cells(mesh)))
else:
tdim = mesh.topology().dim() == 2
graph_edges = set()
# Geome edge cell connectivity to define the graph edges
mesh.init(tdim - 1, tdim)
e2c = mesh.topology()(tdim - 1, tdim)
for e in range(mesh.num_entities(tdim - 1)):
cells = sorted(e2c(e))
graph_edges.update(zip(cells[:-1], cells[1:]))
G.add_edges_from(graph_edges)
return nx.number_connected_components(G) == 1
def __init__(self, mesh, orientation):
# Manifold assumption
assert 1 <= mesh.topology().dim() < mesh.geometry().dim()
gdim = mesh.geometry().dim()
# Orientation from inside point
if isinstance(orientation, (list, np.ndarray, tuple)):
assert len(orientation) == gdim
kwargs = {'x0%d' % i: val for i, val in enumerate(orientation)}
orientation = ['x[%d] - x0%d' % (i, i) for i in range(gdim)]
orientation = df.Expression(orientation, degree=1, **kwargs)
assert orientation.ufl_shape == (gdim, )
V = df.VectorFunctionSpace(mesh, 'DG', 0, gdim)
df.Function.__init__(self, V)
n_values = self.vector().get_local()
values = []
for cell in df.cells(mesh):
n = cell.cell_normal().array()[:gdim]
x = cell.midpoint().array()[:gdim]
# Disagree?
if np.inner(orientation(x), n) < 0:
n *= -1
values.append(n/np.linalg.norm(n))
values = np.array(values)
for sub in range(gdim):
dofs = V.sub(sub).dofmap().dofs()
n_values[dofs] = values[:, sub]
self.vector().set_local(n_values)
self.vector().apply('insert')
def relocate(self):
# Relocate particles on cells and processors
p_map = self.particle_map
# Map such that map[old_cell] = [(new_cell, particle_id), ...]
# Ie new destination of particles formerly in old_cell
new_cell_map = defaultdict(list)
for cwp in p_map.itervalues():
for i, particle in enumerate(cwp.particles):
point = df.Point(*particle.position)
# Search only if particle moved outside original cell
if not cwp.contains(point):
found = False
# Check neighbor cells
for neighbor in df.cells(cwp):
if neighbor.contains(point):
new_cell_id = neighbor.index()
found = True
break
# Do a completely new search if not found by now
if not found:
new_cell_id = self.locate(particle)
# Record to map
new_cell_map[cwp.index()].append((new_cell_id, i))
# Rebuild locally the particles that end up on the process. Some
# have cell_id == -1, i.e. they are on other process
list_of_escaped_particles = []
for old_cell_id, new_data in new_cell_map.iteritems():
# We iterate in reverse becasue normal order would remove some
# particle this shifts the whole list!
for (new_cell_id, i) in sorted(new_data,
key=lambda t: t[1],
reverse=True):
particle = p_map.pop(old_cell_id, i)
if new_cell_id == -1 or new_cell_id == __UINT32_MAX__ :
list_of_escaped_particles.append(particle)
else:
p_map += self.mesh, new_cell_id, particle
# Create a list of how many particles escapes from each processor
self.my_escaped_particles[0] = len(list_of_escaped_particles)
# Make all processes aware of the number of escapees
comm.Allgather(self.my_escaped_particles, self.tot_escaped_particles)
# Send particles to root
if self.myrank != 0:
for particle in list_of_escaped_particles:
particle.send(0)
# Receive the particles escaping from other processors
if self.myrank == 0:
for proc in self.other_processes:
for i in range(self.tot_escaped_particles[proc]):
self.particle0.recv(proc)
list_of_escaped_particles.append(copy.deepcopy(self.particle0))
# Put all travelling particles on all processes, then perform new search
travelling_particles = comm.bcast(list_of_escaped_particles, root=0)
self.add_particles(travelling_particles)
def _adaptive_mesh_refinement(dx, phi, mu, sigma, omega, conv, voltages):
from dolfin import cells, refine
eta = _error_estimator(dx, phi, mu, sigma, omega, conv, voltages)
mesh = phi.function_space().mesh()
level = 0
TOL = 1.0e-4
E = sum([e * e for e in eta])
E = sqrt(MPI.sum(E))
info('Level %d: E = %g (TOL = %g)' % (level, E, TOL))
# Mark cells for refinement
REFINE_RATIO = 0.5
cell_markers = MeshFunction('bool', mesh, mesh.topology().dim())
eta_0 = sorted(eta, reverse=True)[int(len(eta) * REFINE_RATIO)]
eta_0 = MPI.max(eta_0)
for c in cells(mesh):
cell_markers[c] = eta[c.index()] > eta_0
# Refine mesh
mesh = refine(mesh, cell_markers)
# Plot mesh
plot(mesh)
interactive()
exit()
## Compute error indicators
#K = array([c.volume() for c in cells(mesh)])
#R = array([abs(source([c.midpoint().x(), c.midpoint().y()])) for c in cells(mesh)])
#gam = h*R*sqrt(K)
return
def assemble_A_tilde_single_element(self):
"""
Assemble block diagonal à and Ã_inv matrices where the blocks
are the dofs in a single element
"""
Aglobal = self.M if self.a_tilde_is_mass else self.A
if self.A_tilde is None:
At = Aglobal.copy()
Ati = Aglobal.copy()
else:
At = self.A_tilde
Ati = self.A_tilde_inv
At.zero()
Ati.zero()
dm = self.Vuvw.dofmap()
N = dm.cell_dofs(0).shape[0]
Alocal = numpy.zeros((N, N), float)
# Loop over cells and get the block diagonal parts (should be moved to C++)
for cell in dolfin.cells(self.simulation.data['mesh'], 'regular'):
# Get global dofs
istart = Aglobal.local_range(0)[0]
dofs = dm.cell_dofs(cell.index()) + istart
# Get block diagonal part of A, invert and insert into approximations
Aglobal.get(Alocal, dofs, dofs)
Alocal_inv = numpy.linalg.inv(Alocal)
At.set(Alocal, dofs, dofs)
Ati.set(Alocal_inv, dofs, dofs)
return At, Ati
def plot(self, mpl_ax, levels=50, lw=0.3, mesh_alpha=0, mesh_lw=0.2):
"""
Plot the function on a matplotlib axes. Call .compute() first
to calculate the stream function
"""
if self._triangulation is None:
from matplotlib.tri import Triangulation
coords = self.mesh.coordinates()
triangles = []
for cell in df.cells(self.mesh):
cell_vertices = cell.entities(0)
triangles.append(cell_vertices)
self._triangulation = Triangulation(coords[:, 0], coords[:, 1],
triangles)
if mesh_alpha > 0:
mpl_ax.triplot(self._triangulation,
color='#000000',
alpha=mesh_alpha,
lw=mesh_lw)
Z = self.psi.compute_vertex_values()
if all(Z == 0):
return
mpl_ax.tricontour(
self._triangulation,
Z,
levels,
colors='#0000AA',
linewidths=lw,
linestyles='solid',
)
def convert_meshfunction_to_function(meshfunction, functionspace=None):
"""
Convert a meshfunction to a function with 'p0' elements.
Parameters
----------
meshfunction : dolfin.cpp.mesh.MeshFunctionDouble
The mesh function specifying a field that is constant over each cell.
functionspace : dolfin.FunctionSpace (default None)
The function space to be used for creating the dolfin.Function object.
A 'p0' function space is used if None is specified.
Returns
-------
func : dolfin.Function
The scalar-valued function storing the values of the mesh function.
"""
mesh = meshfunction.mesh()
if functionspace is None:
functionspace = dlf.FunctionSpace(mesh, "DG", 0)
func = dlf.Function(functionspace)
dofmap = functionspace.dofmap()
new_values = np.zeros(func.vector().local_size())
for cell in dlf.cells(mesh):
new_values[dofmap.cell_dofs(cell.index())] = meshfunction[cell]
func.vector().set_local(new_values)
return func
def distribute_DG0(Q, pop):
"""
Returns the charge volume density in DG0 (discontinuous Lagrange space of
order 0). The charge of all the particles inside a given cell is simply
added together and then divided by the volume of the cell.
Args:
Q (DOLFIN: FunctionSpace): DG0 function space
pop (PUNC: Population)
"""
assert Q.ufl_element().family() == 'Discontinuous Lagrange'
assert Q.ufl_element().degree() == 0
rho = df.Function(Q)
for cell in df.cells(Q.mesh()):
cellindex = cell.index()
dofindex = Q.dofmap().cell_dofs(cellindex)
accum = 0
for particle in pop[cellindex]:
accum += particle.q
accum /= cell.volume()
rho.vector()[dofindex] = accum
return rho
def assert_dof_map_single_block_no_restriction(V, block_V):
local_dimension = V.dofmap().ownership_range()[1] - V.dofmap().ownership_range()[0]
block_local_dimension = block_V.block_dofmap().ownership_range()[1] - block_V.block_dofmap().ownership_range()[0]
assert local_dimension == block_local_dimension
global_dimension = V.dofmap().global_dimension()
block_global_dimension = block_V.block_dofmap().global_dimension()
assert global_dimension == block_global_dimension
V_local_to_global_unowned = V.dofmap().local_to_global_unowned()
block_V_local_to_global_unowned = block_V.block_dofmap().local_to_global_unowned()
block_V_local_to_global_unowned = unique([b//V.dofmap().index_map().block_size() for b in block_V_local_to_global_unowned])
assert array_sorted_equal(V_local_to_global_unowned, block_V_local_to_global_unowned)
for c in cells(block_V.mesh()):
V_cell_dofs = V.dofmap().cell_dofs(c.index())
V_cell_owned_local_dofs = [a for a in V_cell_dofs if a < local_dimension]
V_cell_unowned_local_dofs = [a for a in V_cell_dofs if a >= local_dimension]
V_cell_global_dofs = [V.dofmap().local_to_global_index(a) for a in V_cell_dofs]
block_V_cell_dofs = block_V.block_dofmap().cell_dofs(c.index())
block_V_cell_owned_local_dofs = [b for b in block_V_cell_dofs if b < block_local_dimension]
block_V_cell_unowned_local_dofs = [b for b in block_V_cell_dofs if b >= block_local_dimension]
block_V_cell_global_dofs = [block_V.block_dofmap().local_to_global_index(b) for b in block_V_cell_dofs]
assert_owned_local_dofs(V_cell_owned_local_dofs, block_V_cell_owned_local_dofs)
assert_unowned_local_dofs(V_cell_unowned_local_dofs, block_V_cell_unowned_local_dofs)
assert_global_dofs(V_cell_global_dofs, block_V_cell_global_dofs)
V_dof_coordinates = V.tabulate_dof_coordinates()
block_V_dof_coordinates = block_V.tabulate_dof_coordinates()
assert_tabulated_dof_coordinates(V_dof_coordinates, block_V_dof_coordinates)
def morph_mesh(self):
"""
Move the mesh and update cached geometry information. It is assumed
that the mesh velocities u_mesh0, u_mesh1 etc are already populated
"""
sim = self.simulation
# Get the mesh displacement
for d in range(sim.ndim):
umi = sim.data['u_mesh%d' % d]
self.assigners[d].assign(self.displacement.sub(d), umi)
self.displacement.vector()[:] *= sim.dt
# Save the cell volumes before morphing
mesh = sim.data['mesh']
cvolp = sim.data['cvolp']
dofmap_cvol = cvolp.function_space().dofmap()
for cell in dolfin.cells(mesh):
dofs = dofmap_cvol.cell_dofs(cell.index())
assert len(dofs) == 1
cvolp.vector()[dofs[0]] = cell.volume()
# Move the mesh according to the given displacements
dolfin.ALE.move(mesh, self.displacement)
mesh.bounding_box_tree().build(mesh)
sim.update_mesh_data(connectivity_changed=False)
def write_function(self, func, t):
"""
Write a function to XDMF file. The function is from the original
function space, but will be written in the subdivided function space
with truely discontinuous elements
"""
f = self.subdivided_function
V = self.subdivided_function_space
dm = V.dofmap()
gdim = self.subdivided_mesh.geometry().dim()
dof_coords = V.tabulate_dof_coordinates().reshape((-1, gdim))
all_values = f.vector().get_local()
f.rename(func.name(), func.name())
vals = numpy.zeros(1, float)
crds = numpy.zeros(2, float)
# Evaluate the function at all subcell dof locations
for subcell in dolfin.cells(self.subdivided_mesh):
subcell_id = subcell.index()
for dof in dm.cell_dofs(subcell_id):
crds[:] = dof_coords[dof]
parent_cell = dolfin.Cell(self.mesh,
self.parent_cell[subcell_id])
func.eval_cell(vals, crds, parent_cell)
all_values[dof] = vals[0]
f.vector().set_local(all_values)
f.vector().apply('insert')
self.xdmf.write(f, float(t))
def __init__(self, V, geo, name, f):
self.V = V
# get dofs lying in subdomain
dofmap = V.dofmap()
tup = geo.physicaldomain(name)
sub = geo.subdomains
mesh = geo.mesh
subdofs = set()
for i, cell in enumerate(dolfin.cells(mesh)):
if sub[cell] in tup:
celldofs = dofmap.cell_dofs(i)
subdofs.update(celldofs)
subdofs = np.array(list(subdofs), dtype="intc")
d2v = dolfin.dof_to_vertex_map(V)
co = mesh.coordinates()
# create function with desired values
# could also be implemented with Expression.eval_cell like pwconst
bc_f = dolfin.Function(V)
for dof in subdofs:
x = co[d2v[dof]]
bc_f.vector()[dof] = f(x)
self.bc_f = bc_f
self.dof_set = subdofs
def invert_block_diagonal_matrix(V, M, Minv=None):
"""
Given a block diagonal matrix (DG mass matrix or similar), use local
dense inverses to compute the inverse matrix and return it, optionally
reusing the given Minv tensor
"""
mesh = V.mesh()
dm = V.dofmap()
N = dm.cell_dofs(0).shape[0]
Mlocal = numpy.zeros((N, N), float)
if Minv is None:
Minv = dolfin.as_backend_type(M.copy())
# Loop over cells and get the block diagonal parts (should be moved to C++)
istart = M.local_range(0)[0]
for cell in dolfin.cells(mesh, 'regular'):
# Get global dofs
dofs = dm.cell_dofs(cell.index()) + istart
# Get block diagonal part of approx_A, invert it and insert into M⁻¹
M.get(Mlocal, dofs, dofs)
Mlocal_inv = numpy.linalg.inv(Mlocal)
Minv.set(Mlocal_inv, dofs, dofs)
Minv.apply('insert')
return Minv
def mark_biv_mesh(
mesh, ffun=None, markers=None, tol=0.01, values={"lv": 0, "septum": 1, "rv": 2}
):
from .ldrb import scalar_laplacians
scalars = scalar_laplacians(mesh=mesh, ffun=ffun, markers=markers)
for cell in df.cells(mesh):
lv = scalars["lv"](cell.midpoint())
rv = scalars["rv"](cell.midpoint())
epi = scalars["epi"](cell.midpoint())
print(cell.index(), "lv = {}, rv = {}".format(lv, rv))
if (lv > tol or epi > 1 - tol) and rv < tol:
print("LV")
value = values["lv"]
if lv < tol and rv > lv:
value = values["rv"]
elif (rv > tol or epi > 1 - tol) and lv < tol:
print("RV")
value = values["rv"]
else:
print("SEPTUM")
value = values["septum"]
mesh.domains().set_marker((cell.index(), value), 3)
sfun = df.MeshFunction("size_t", mesh, 3, mesh.domains())
return sfun
def taylor_to_DG1_matrix_3D(V):
"""
Create the per cell matrices that when matrix multiplied with the
Taylor cell dofs return a vector of Lagrange cell dofs.
This implementation handles DG1 function space V in 3D
"""
mesh = V.mesh()
vertices = mesh.coordinates()
tdim = mesh.topology().dim()
num_cells_owned = mesh.topology().ghost_offset(tdim)
x = numpy.zeros((4, 3), float)
A = numpy.zeros((num_cells_owned, 4, 4), float)
for cell in cells(mesh):
icell = cell.index()
verts = cell.entities(0)
x[0] = vertices[verts[0]]
x[1] = vertices[verts[1]]
x[2] = vertices[verts[2]]
x[3] = vertices[verts[3]]
xc = (x[0] + x[1] + x[2] + x[3]) / 4
for i in range(4):
dx, dy, dz = x[i, 0] - xc[0], x[i, 1] - xc[1], x[i, 2] - xc[2]
A[icell, i, 0] = 1
A[icell, i, 1] = dx
A[icell, i, 2] = dy
A[icell, i, 3] = dz
return A
def preprocess(simulation, level_set_view):
"""
Compute distance between dofs
"""
V = level_set_view.function_space()
mesh = V.mesh()
dm = V.dofmap()
# Get coordinates of both regular and ghost dofs
dofs_x, Nlocal = all_dof_coordinates(V)
cell_dofs = [None] * mesh.num_cells()
dof_cells = [[] for _ in range(V.dim())]
dof_dist = {}
for cell in dolfin.cells(mesh, 'all'):
cid = cell.index()
dofs = dm.cell_dofs(cid)
cell_dofs[cid] = list(dofs)
for dof in dofs:
dof_cells[dof].append(cid)
# Store distance between the cell dofs
for dof2 in dofs:
if dof == dof2:
continue
p1 = dofs_x[dof]
p2 = dofs_x[dof2]
vec = p1 - p2
d = (vec[0]**2 + vec[1]**2 + vec[2]**2)**0.5
dof_dist[(dof, dof2)] = d
dof_dist[(dof2, dof)] = d
return dofs_x, dof_dist, cell_dofs, dof_cells
def test_cell_midpoints(D):
from ocellaris.solver_parts.slope_limiter.limiter_cpp_utils import SlopeLimiterInput
if D == 2:
mesh = dolfin.UnitSquareMesh(4, 4)
else:
mesh = dolfin.UnitCubeMesh(2, 2, 2)
Vx = dolfin.FunctionSpace(mesh, 'DG', 2)
V0 = dolfin.FunctionSpace(mesh, 'DG', 0)
py_inp = SlopeLimiterInput(mesh, Vx, V0)
cpp_inp = py_inp.cpp_obj
all_ok = True
for cell in dolfin.cells(mesh):
cid = cell.index()
mp = cell.midpoint()
cpp_mp = cpp_inp.cell_midpoints[cid]
for d in range(D):
ok = dolfin.near(mp[d], cpp_mp[d])
if not ok:
print(
'%3d %d - %10.3e %10.3e' % (cid, d, mp[d], cpp_mp[d]),
'<--- ERROR' if not ok else '',
)
all_ok = False
assert all_ok
def assert_dof_map_test_two_blocks_with_restriction(V1, V2, block_V):
local_dimension1 = V1.dofmap().ownership_range()[1] - V1.dofmap().ownership_range()[0]
local_dimension2 = V2.dofmap().ownership_range()[1] - V2.dofmap().ownership_range()[0]
block_local_dimension = block_V.block_dofmap().ownership_range()[1] - block_V.block_dofmap().ownership_range()[0]
# Create a map from all dofs to subset of kept dofs
map_block_to_original1 = block_V.block_dofmap().block_to_original(0)
map_block_to_original2 = block_V.block_dofmap().block_to_original(1)
kept_dofs1 = map_block_to_original1.values()
kept_dofs2 = map_block_to_original2.values()
map_block_to_original = dict()
for (b1, a1) in map_block_to_original1.items():
map_block_to_original[b1] = a1
for (b2, a2) in map_block_to_original2.items():
map_block_to_original[b2] = a2 + local_dimension1
# Assert equality
for c in cells(block_V.mesh()):
V1_cell_dofs = V1.dofmap().cell_dofs(c.index())
V1_cell_owned_local_dofs = [a1 for a1 in V1_cell_dofs if a1 in kept_dofs1 and a1 < local_dimension1]
V1_cell_unowned_local_dofs = [a1 for a1 in V1_cell_dofs if a1 in kept_dofs1 and a1 >= local_dimension1]
V2_cell_dofs = V2.dofmap().cell_dofs(c.index())
V2_cell_owned_local_dofs = [a2 + local_dimension1 for a2 in V2_cell_dofs if a2 in kept_dofs2 and a2 < local_dimension2]
V2_cell_unowned_local_dofs = [a2 + local_dimension1 for a2 in V2_cell_dofs if a2 in kept_dofs2 and a2 >= local_dimension2]
V_cell_owned_local_dofs = concatenate((V1_cell_owned_local_dofs, V2_cell_owned_local_dofs))
V_cell_unowned_local_dofs = concatenate((V1_cell_unowned_local_dofs, V2_cell_unowned_local_dofs))
block_V_cell_dofs = block_V.block_dofmap().cell_dofs(c.index())
block_V_cell_owned_local_dofs = [map_block_to_original[b] for b in block_V_cell_dofs if b < block_local_dimension]
block_V_cell_unowned_local_dofs = [map_block_to_original[b] for b in block_V_cell_dofs if b >= block_local_dimension]
assert_owned_local_dofs(V_cell_owned_local_dofs, block_V_cell_owned_local_dofs)
assert_unowned_local_dofs(V_cell_unowned_local_dofs, block_V_cell_unowned_local_dofs)
def delta_dg(mesh, expr):
V = df.FunctionSpace(mesh, "DG", 0)
m = df.interpolate(expr, V)
n = df.FacetNormal(mesh)
h = df.CellSize(mesh)
h_avg = (h('+') + h('-')) / 2
alpha = 1.0
gamma = 0.0
u = df.TrialFunction(V)
v = df.TestFunction(V)
# for DG 0 case, only term contain alpha is nonzero
a = df.dot(df.grad(v), df.grad(u))*df.dx \
- df.dot(df.avg(df.grad(v)), df.jump(u, n))*df.dS \
- df.dot(df.jump(v, n), df.avg(df.grad(u)))*df.dS \
+ alpha/h_avg*df.dot(df.jump(v, n), df.jump(u, n))*df.dS \
- df.dot(df.grad(v), u*n)*df.ds \
- df.dot(v*n, df.grad(u))*df.ds \
+ gamma/h*v*u*df.ds
K = df.assemble(a).array()
L = df.assemble(v * df.dx).array()
h = -np.dot(K, m.vector().array()) / (L)
xs = []
for cell in df.cells(mesh):
xs.append(cell.midpoint().x())
print len(xs), len(h)
return xs, h
def facet_dofmap(V):
"""
When working with Crouzeix-Raviart and DGT elements with dofs on the facets
it can be useful to get the dof corresponding to a facet index.
Returns a list mapping from local facet index to local dof
TODO: verify if dofmap.dofs(mesh, mesh.topology().dim()-1) is guaranteed to
always give the same result as this
"""
mesh = V.mesh()
dofmap = V.dofmap()
ndim = V.ufl_cell().topological_dimension()
# Loop through cells and get dofs for each cell
facet_dofmap = [None] * mesh.num_facets()
for cell in dolfin.cells(mesh, 'all'):
dofs = dofmap.cell_dofs(cell.index())
facet_idxs = cell.entities(ndim - 1)
assert len(dofs) == len(facet_idxs)
# Loop through connected facets and store dofs for each facet
for fidx, dof in zip(facet_idxs, dofs):
facet_dofmap[fidx] = dof
return facet_dofmap
def test_taylor_values(dim, degree):
"""
Check that the Lagrange -> Taylor projection gives the correct Taylor values
"""
if dim == 2:
mesh = dolfin.UnitSquareMesh(4, 4)
else:
mesh = dolfin.UnitCubeMesh(2, 2, 2)
# Setup Lagrange function with given derivatives and constants
V = dolfin.FunctionSpace(mesh, 'DG', degree)
u = dolfin.Function(V)
if dim == 2:
coeffs = [1, 2, -3.0] if degree == 1 else [1, 2, -3.0, -2.5, 4.2, -1.0]
else:
coeffs = ([1, 2, -3.0, 2.5] if degree == 1 else
[1, 2, -3.0, 2.5, -1.3, 4.2, -1.0, -4.2, 2.66, 3.14])
make_taylor_func(u, coeffs)
# Convert to Taylor
t = dolfin.Function(V)
lagrange_to_taylor(u, t)
# Check that the target values are obtained
dm = V.dofmap()
vals = t.vector().get_local()
for cell in dolfin.cells(mesh):
cell_dofs = dm.cell_dofs(cell.index())
cell_vals = vals[cell_dofs]
assert all(abs(cell_vals - coeffs) < 1e-13)
def save_inp_of_inital_m(m, file_name):
mesh = m.mesh()
data_type_number = 3
f = open(file_name, "w")
head = "%d %d %d 0 0\n" % (mesh.num_vertices(), mesh.num_cells(),
data_type_number)
f.write(head)
xyz = mesh.coordinates()
if np.max(xyz) < 0.5:
print "Converting unit_length from m to nm."
xyz = xyz * 1e9
for i in range(len(xyz)):
f.write("%d %0.15e %0.15e %0.15e\n" %
(i + 1, xyz[i][0], xyz[i][1], xyz[i][2]))
for c in df.cells(mesh):
id = c.index()
ce = c.entities(0)
f.write("%d 1 tet %d %d %d %d\n" %
(id + 1, ce[0] + 1, ce[1] + 1, ce[2] + 1, ce[3] + 1))
f.write("3 1 1 1\nM_x, none\nM_y, none\nM_z, none\n")
data = m.get_numpy_array_debug().reshape(3, -1)
for i in range(mesh.num_vertices()):
f.write("%d %0.15e %0.15e %0.15e\n" %
(i + 1, data[0][i], data[1][i], data[2][i]))
f.close()
def __init__(self, mesh, orientation):
# Manifold assumption
assert 1 <= mesh.topology().dim() < mesh.geometry().dim()
gdim = mesh.geometry().dim()
# Orientation from inside point
if isinstance(orientation, (list, np.ndarray, tuple)):
assert len(orientation) == gdim
kwargs = {'x0%d' % i: val for i, val in enumerate(orientation)}
orientation = ['x[%d] - x0%d' % (i, i) for i in range(gdim)]
orientation = df.Expression(orientation, degree=1, **kwargs)
assert orientation.ufl_shape == (gdim, )
V = df.VectorFunctionSpace(mesh, 'DG', 0, gdim)
df.Function.__init__(self, V)
n_values = self.vector().get_local()
values = []
for cell in df.cells(mesh):
n = cell.cell_normal().array()[:gdim]
x = cell.midpoint().array()[:gdim]
# Disagree?
if np.inner(orientation(x), n) < 0:
n *= -1
values.append(n / np.linalg.norm(n))
values = np.array(values)
for sub in range(gdim):
dofs = V.sub(sub).dofmap().dofs()
n_values[dofs] = values[:, sub]
self.vector().set_local(n_values)
self.vector().apply('insert')
def facet_info_and_dofmap(V):
"""
Return three lists
1) A list which maps facet index to dof
2) A list which maps facet index to facet area
2) A list which maps facet index to facet midpoint
"""
mesh = V.mesh()
dofmap = V.dofmap()
ndim = V.ufl_cell().topological_dimension()
# Loop through cells and get dofs for each cell
facet_dofs = [None] * mesh.num_facets()
facet_area = [None] * mesh.num_facets()
facet_midp = [None] * mesh.num_facets()
for cell in dolfin.cells(mesh):
dofs = dofmap.cell_dofs(cell.index())
facet_idxs = cell.entities(ndim - 1)
# Only works for functions with one dof on each facet
assert len(dofs) == len(facet_idxs)
# Loop through connected facets and store dofs for each facet
for i, fidx in enumerate(facet_idxs):
facet_dofs[fidx] = dofs[i]
facet_area[fidx] = cell.facet_area(i)
mp = dolfin.Facet(mesh, fidx).midpoint()
facet_midp[fidx] = (mp.x(), mp.y())
return facet_dofs, facet_area, facet_midp
def assert_dof_map_single_block_with_restriction(V, block_V):
local_dimension = V.dofmap().ownership_range()[1] - V.dofmap(
).ownership_range()[0]
block_local_dimension = block_V.block_dofmap().ownership_range(
)[1] - block_V.block_dofmap().ownership_range()[0]
# Create a map from all dofs to subset of kept dofs
map_block_to_original = block_V.block_dofmap().block_to_original(0)
kept_dofs = map_block_to_original.values()
# Assert equality
for c in cells(block_V.mesh()):
V_cell_dofs = V.dofmap().cell_dofs(c.index())
V_cell_owned_local_dofs = [
a for a in V_cell_dofs if a in kept_dofs and a < local_dimension
]
V_cell_unowned_local_dofs = [
a for a in V_cell_dofs if a in kept_dofs and a >= local_dimension
]
block_V_cell_dofs = block_V.block_dofmap().cell_dofs(c.index())
block_V_cell_owned_local_dofs = [
map_block_to_original[b] for b in block_V_cell_dofs
if b < block_local_dimension
]
block_V_cell_unowned_local_dofs = [
map_block_to_original[b] for b in block_V_cell_dofs
if b >= block_local_dimension
]
assert_owned_local_dofs(V_cell_owned_local_dofs,
block_V_cell_owned_local_dofs)
assert_unowned_local_dofs(V_cell_unowned_local_dofs,
block_V_cell_unowned_local_dofs)
def refine_perimeter(mesh):
"""Refine largest boundary triangles."""
mesh.init(1, 2)
perimeter = [c for c in cells(mesh)
if any([f.exterior() for f in facets(c)])]
marker = CellFunction('bool', mesh, False)
max_size = max([c.diameter() for c in perimeter])
for c in perimeter:
marker[c] = c.diameter() > 0.75 * max_size
return refine(mesh, marker)
def refine_cylinder(mesh):
'Refine mesh by cutting cells around the cylinder.'
h = mesh.hmin()
center = Point(c_x, c_y)
cell_f = CellFunction('bool', mesh, False)
for cell in cells(mesh):
if cell.midpoint().distance(center) < r + h:
cell_f[cell] = True
mesh = refine(mesh, cell_f)
return mesh
def build_cell_to_dof(V):
'''Build a dictionary between cell and dofs that it has.'''
mesh = V.mesh()
dofmap = V.dofmap()
cell_to_dof = {}
for cell in cells(mesh):
cell_to_dof[cell.index()] = []
for dof in dofmap.cell_dofs(cell.index()):
cell_to_dof[cell.index()].append(dof)
return cell_to_dof
def build_cell_to_edge(V):
'''Build mapping between cell and edges that form it.'''
cell_to_edge = {}
mesh = V.mesh()
mesh.init(1)
for cell in cells(mesh):
cell_to_edge[cell.index()] = []
for edge in edges(cell):
cell_to_edge[cell.index()].append(edge.index())
return cell_to_edge
def weighted_H1_norm(w, vec, piecewise=False):
if piecewise:
DG = FunctionSpace(vec.basis.mesh, "DG", 0)
s = TestFunction(DG)
ae = assemble(w * inner(nabla_grad(vec._fefunc), nabla_grad(vec._fefunc)) * s * dx)
norm_vec = np.array([sqrt(e) for e in ae])
# map DG dofs to cell indices
dofs = [DG.dofmap().cell_dofs(c.index())[0] for c in cells(vec.basis.mesh)]
norm_vec = norm_vec[dofs]
else:
ae = assemble(w * inner(nabla_grad(vec._fefunc), nabla_grad(vec._fefunc)) * dx)
norm_vec = sqrt(ae)
return norm_vec
def get_dof_coordinates(self):
V = self._fefs
# degrees of freedom
N = V.dofmap().global_dimension()
c4dof = np.zeros((N, V.mesh().geometry().dim()))
# evaluate nodes matrix by local-to-global map on each cells
for c in cells(V.mesh()):
# coordinates of nodes in current cell
cell_c4dof = V.dofmap().tabulate_coordinates(c)
# global indices of nodes in current cell
nodes = V.dofmap().cell_dofs(c.index())
# set global nodes coordinates
c4dof[nodes] = cell_c4dof
return c4dof
def refine_boundary_layers(mesh, s, d, x0, x1):
from dolfin import CellFunction, cells, refine, DOLFIN_EPS
h = mesh.hmax()
cell_markers = CellFunction('bool', mesh, mesh.topology().dim())
cell_markers.set_all(False)
for cell in cells(mesh):
x = cell.midpoint()
for i, d_ in enumerate(d):
if x[d_] > (x1[i]-s*h-DOLFIN_EPS) or x[d_] < (s*h + x0[i] + DOLFIN_EPS):
cell_markers[cell] = True
return refine(mesh, cell_markers)
def poincare_friedrichs_cutoff(o, p):
if isinstance(o, Mesh):
# TODO: easy fix - ghosted mesh + missing reduction
not_working_in_parallel("PF cutoff on mesh")
return max(poincare_friedrichs_cutoff(v, p) for v in vertices(o))
if isinstance(o, Vertex):
# TODO: fix using ghosted mesh
not_working_in_parallel("PF cutoff on patch")
hat_fun_grad = max(hat_function_grad(o, c) for c in cells(o))
if any(f.exterior() for f in facets(o)):
return 1.0 + friedrichs_const(o, p) * hat_fun_grad
else:
return 1.0 + poincare_const(o, p) * hat_fun_grad
raise NotImplementedError
def build_edge_to_dof(V, cell_to_edge):
'''Build mapping between edges and dofs on it.'''
edge_to_dof = {}
mesh = V.mesh()
dofmap = V.dofmap()
for cell in cells(mesh):
cell_edges = cell_to_edge[cell.index()]
for i in range(3): # there are 3 edges in cell
edge = cell_edges[i]
edge_dofs = dofmap.cell_dofs(cell.index())[dofmap.tabulate_facet_dofs(i)]
if edge in edge_to_dof:
for edge_dof in edge_dofs:
edge_to_dof[edge].add(edge_dof)
else:
edge_to_dof[edge] = set(edge_dofs)
return edge_to_dof
def computeEdgeCRDofArray(V, mesh, B=None):
# dof map, dim_V = 2 * num_E
num_E = mesh.num_facets()
dofmap = V.dofmap()
edgeCRDofArray = np.zeros((num_E, 2))
# loop over cells and fill array
for k, cell in enumerate(cells(mesh)):
# list of dof-indices for edges of the cell
dofs = dofmap.cell_dofs(cell.index())
for i, facet in enumerate(facets(cell)):
# print 'cell: %3g || i: %3g || facet: %3g || dof[i]: %3g' \
# % (cell.index(), i, facet.index(), dofs[i])
# corresponding DoFs (2 basisfct per edge)
edgeCRDofArray[facet.index()] = [dofs[i], dofs[i+3]]
# edgeCRDofArray[facet.index()] = [dofs[i], dofs[i]+1]
# every interior edge visited twice but EGAL!
return edgeCRDofArray
def _error_estimator(dx, phi, mu, sigma, omega, conv, voltages):
'''Simple error estimator from
A posteriori error estimation and adaptive mesh-refinement techniques;
R. Verfürth;
Journal of Computational and Applied Mathematics;
Volume 50, Issues 1-3, 20 May 1994, Pages 67-83;
<https://www.sciencedirect.com/science/article/pii/0377042794902909>.
The strong PDE is
- div(1/(mu r) grad(rphi)) + <u, 1/r grad(rphi)> + i sigma omega phi
= sigma v_k / (2 pi r).
'''
from dolfin import cells
mesh = phi.function_space().mesh()
# Assemble the cell-wise residual in DG space
DG = FunctionSpace(mesh, 'DG', 0)
# get residual in DG
v = TestFunction(DG)
R = _residual_strong(dx, v, phi, mu, sigma, omega, conv, voltages)
r_r = assemble(R[0])
r_i = assemble(R[1])
r = r_r * r_r + r_i * r_i
visualize = True
if visualize:
# Plot the cell-wise residual
u = TrialFunction(DG)
a = zero() * dx(0)
subdomain_indices = mu.keys()
for i in subdomain_indices:
a += u * v * dx(i)
A = assemble(a)
R2 = Function(DG)
solve(A, R2.vector(), r)
plot(R2, title='||R||^2')
interactive()
K = r.array()
info('%r' % K)
h = numpy.array([c.diameter() for c in cells(mesh)])
eta = h * numpy.sqrt(K)
return eta
def plot_mesh(mesh,savefig = False,show = False):
n = mesh.num_vertices()
d = mesh.geometry().dim()
# Create the triangulation
mesh_coordinates = mesh.coordinates().reshape((n, d))
triangles = np.asarray([cell.entities(0) for cell in df.cells(mesh)])
triangulation = tri.Triangulation(mesh_coordinates[:, 0],
mesh_coordinates[:, 1],
triangles)
triangulation.x *=1e6
triangulation.y *=1e6
# Plot the mesh
fig = plt.figure(figsize=(7.0, 7.0))
plt.triplot(triangulation)
plt.xlabel(r'$x(\mu m)$')
plt.ylabel(r'$y(\mu m)$')
if savefig != False:
plt.savefig(savefig)
if show != False:
plt.show()
return None
editor.init_vertices(6)
editor.init_cells(2)
vertex_0 = Vertex(mesh, 0)
vertex_1 = Vertex(mesh, 1)
vertex_2 = Vertex(mesh, 2)
vertex_3 = Vertex(mesh, 3)
vertex_4 = Vertex(mesh, 4)
vertex_5 = Vertex(mesh, 5)
editor.add_cell(0, 1, 2, 3)
editor.add_cell(1, 0, 2, 3)
editor.close()
t = IonTag("foo", 3, "int", mesh)
for v in vertices(mesh):
t[v] = [1, 2, 3]
for c in cells(mesh):
t[c] = [4, 5, 6, 7]
v = MeshEntity(mesh, 0, 1)
print t[v]
def create_joint_mesh(meshes, destmesh=None, additional_refine=0):
if destmesh is None:
# start with finest mesh to avoid (most) refinements
# hmin = [m.hmin() for m in meshes]
# mind = hmin.index(min(hmin))
numcells = [m.num_cells() for m in meshes]
mind = numcells.index(max(numcells))
destmesh = meshes.pop(mind)
try:
# test for old FEniCS version < 1.2
destmesh.closest_cell(Point(0,0))
bbt = None
except:
# FEniCS > 1.2
bbt = destmesh.bounding_box_tree()
# setup parent cells
parents = {}
for c in cells(destmesh):
parents[c.index()] = [c.index()]
PM = []
# refinement loop for destmesh
for m in meshes:
# loop until all cells of destmesh are finer than the respective cells in the set of meshes
while True:
cf = CellFunction("bool", destmesh)
cf.set_all(False)
rc = 0 # counter for number of marked cells
# get cell sizes of current mesh
h = [c.diameter() for c in cells(destmesh)]
# check all cells with destination sizes and mark for refinement when destination mesh is coarser (=larger)
for c in cells(m):
p = c.midpoint()
if bbt is not None:
# FEniCS > 1.2
cid = bbt.compute_closest_entity(p)[0]
else:
# FEniCS < 1.2
cid = destmesh.closest_cell(p)
if h[cid] > c.diameter():
cf[cid] = True
rc += 1
# carry out refinement if any cells are marked
if rc:
# refine marked cells
newmesh = refine(destmesh, cf)
# determine parent cell association map
pc = newmesh.data().array("parent_cell", newmesh.topology().dim())
pmap = defaultdict(list)
for i, cid in enumerate(pc):
pmap[cid].append(i)
PM.append(pmap)
# set refined mesh as current mesh
destmesh = newmesh
else:
break
# carry out additional uniform refinements
for _ in range(additional_refine):
# refine uniformly
newmesh = refine(destmesh)
# determine parent cell association map
pc = newmesh.data().array("parent_cell", newmesh.topology().dim())
pmap = defaultdict(list)
for i, cid in enumerate(pc):
pmap[cid].append(i)
PM.append(pmap)
# set refined mesh as current mesh
destmesh = newmesh
# determine association to parent cells
for level in range(len(PM)):
for parentid, childids in parents.iteritems():
newchildids = []
for cid in childids:
for cid in PM[level][cid]:
newchildids.append(cid)
parents[parentid] = newchildids
return destmesh, parents
def _evaluateLocalEstimator(cls, mu, w, coeff_field, pde, f, quadrature_degree, epsilon=1e-5):
"""Evaluation of patch local equilibrated estimator."""
# prepare numerical flux and f
sigma_mu, f_mu = evaluate_numerical_flux(w, mu, coeff_field, f)
# ###################
# ## MIXED PROBLEM ##
# ###################
# get setup data for mixed problem
V = w[mu]._fefunc.function_space()
mesh = V.mesh()
mesh.init()
degree = element_degree(w[mu]._fefunc)
# data for nodal bases
V_dm = V.dofmap()
V_dofs = dict([(i, V_dm.cell_dofs(i)) for i in range(mesh.num_cells())])
V1 = FunctionSpace(mesh, 'CG', 1) # V1 is to define nodal base functions
phi_z = Function(V1)
phi_coeffs = np.ndarray(V1.dim())
vertex_dof_map = V1.dofmap().vertex_to_dof_map(mesh)
# vertex_dof_map = vertex_to_dof_map(V1)
dof_list = vertex_dof_map.tolist()
# DG0 localisation
DG0 = FunctionSpace(mesh, 'DG', 0)
DG0_dofs = dict([(c.index(),DG0.dofmap().cell_dofs(c.index())[0]) for c in cells(mesh)])
dg0 = TestFunction(DG0)
# characteristic function of patch
xi_z = Function(DG0)
xi_coeffs = np.ndarray(DG0.dim())
# mesh data
h = CellSize(mesh)
n = FacetNormal(mesh)
cf = CellFunction('size_t', mesh)
# setup error estimator vector
eq_est = np.zeros(DG0.dim())
# setup global equilibrated flux vector
DG = VectorFunctionSpace(mesh, "DG", degree)
DG_dofmap = DG.dofmap()
# define form functions
tau = TrialFunction(DG)
v = TestFunction(DG)
# define global tau
tau_global = Function(DG)
tau_global.vector()[:] = 0.0
# iterate vertices
for vertex in vertices(mesh):
# get patch cell indices
vid = vertex.index()
patch_cid, FF_inner, FF_boundary = get_vertex_patch(vid, mesh, layers=1)
# set nodal base function
phi_coeffs[:] = 0
phi_coeffs[dof_list.index(vid)] = 1
phi_z.vector()[:] = phi_coeffs
# set characteristic function and mark patch
cf.set_all(0)
xi_coeffs[:] = 0
for cid in patch_cid:
xi_coeffs[DG0_dofs[int(cid)]] = 1
cf[int(cid)] = 1
xi_z.vector()[:] = xi_coeffs
# determine local dofs
lDG_cell_dofs = dict([(cid, DG_dofmap.cell_dofs(cid)) for cid in patch_cid])
lDG_dofs = [cd.tolist() for cd in lDG_cell_dofs.values()]
lDG_dofs = list(iter.chain(*lDG_dofs))
# print "\nlocal DG subspace has dimension", len(lDG_dofs), "degree", degree, "cells", len(patch_cid), patch_cid
# print "local DG_cell_dofs", lDG_cell_dofs
# print "local DG_dofs", lDG_dofs
# create patch measures
dx = Measure('dx')[cf]
dS = Measure('dS')[FF_inner]
# define forms
alpha = Constant(1 / epsilon) / h
a = inner(tau,v) * phi_z * dx(1) + alpha * div(tau) * div(v) * dx(1) + avg(alpha) * jump(tau,n) * jump(v,n) * dS(1)\
+ avg(alpha) * jump(xi_z * tau,n) * jump(v,n) * dS(2)
L = -alpha * (div(sigma_mu) + f) * div(v) * phi_z * dx(1)\
- avg(alpha) * jump(sigma_mu,n) * jump(v,n) * avg(phi_z)*dS(1)
# print "L2 f + div(sigma)", assemble((f + div(sigma)) * (f + div(sigma)) * dx(0))
# assemble forms
lhs = assemble(a, form_compiler_parameters={'quadrature_degree': quadrature_degree})
rhs = assemble(L, form_compiler_parameters={'quadrature_degree': quadrature_degree})
# convert DOLFIN representation to scipy sparse arrays
rows, cols, values = lhs.data()
lhsA = sps.csr_matrix((values, cols, rows)).tocoo()
# slice sparse matrix and solve linear problem
lhsA = coo_submatrix_pull(lhsA, lDG_dofs, lDG_dofs)
lx = spsolve(lhsA, rhs.array()[lDG_dofs])
# print ">>> local solution lx", type(lx), lx
local_tau = Function(DG)
local_tau.vector()[lDG_dofs] = lx
# print "div(tau)", assemble(inner(div(local_tau),div(local_tau))*dx(1))
# add up local fluxes
tau_global.vector()[lDG_dofs] += lx
# evaluate estimator
# maybe TODO: re-define measure dx
eq_est = assemble( inner(tau_global, tau_global) * dg0 * (dx(0)+dx(1)),\
form_compiler_parameters={'quadrature_degree': quadrature_degree})
# reorder according to cell ids
eq_est = eq_est[DG0_dofs.values()].array()
global_est = np.sqrt(np.sum(eq_est))
# eq_est_global = assemble( inner(tau_global, tau_global) * (dx(0)+dx(1)), form_compiler_parameters={'quadrature_degree': quadrature_degree} )
# global_est2 = np.sqrt(np.sum(eq_est_global))
return global_est, FlatVector(np.sqrt(eq_est))#, tau_global
def _evaluateResidualEstimator(cls, mu, w, coeff_field, pde, f, quadrature_degree):
"""Evaluate the residual error according to EGSZ (5.7) which consists of volume terms (5.3) and jump terms (5.5).
.. math:: \eta_{\mu,T}(w_N) &:= h_T || \overline{a}^{-1/2} (f\delta_{\mu,0} + \nabla\overline{a}\cdot\nabla w_{N,\mu}
+ \sum_{m=1}^\infty \nabla a_m\cdot\nabla( \alpha^m_{\mu_m+1}\Pi_\mu^{\mu+e_m} w_{N,\mu+e_m}
- \alpha_{\mu_m}^m w_{N,\mu} + \alpha_{\mu_m-1}^m\Pi_\mu^{\mu_m-e_m} w_{N,\mu-e_m} ||_{L^2(T)}\\
\eta_{\mu,S}(w_N) &:= h_S^{-1/2} || \overline{a}^{-1/2} [(\overline{a}\nabla w_{N,\mu} + \sum_{m=1}^\infty a_m\nabla
( \alpha_{\mu_m+1}^m\Pi_\mu^{\mu+e_m} w_{N,\mu+e_m} - \alpha_{\mu_m}^m w_{N,\mu}
+ \alpha_{\mu_m-1}^m\Pi_\mu^{\mu-e_m} w_{N,\mu-e_m})\cdot\nu] ||_{L^2(S)}\\
"""
# set quadrature degree
quadrature_degree_old = parameters["form_compiler"]["quadrature_degree"]
parameters["form_compiler"]["quadrature_degree"] = quadrature_degree
logger.debug("residual quadrature order = " + str(quadrature_degree))
# get pde residual terms
r_T = pde.volume_residual
r_E = pde.edge_residual
r_Nb = pde.neumann_residual
# get mean field of coefficient
a0_f = coeff_field.mean_func
# prepare some FEM variables
V = w[mu]._fefunc.function_space()
mesh = V.mesh()
nu = FacetNormal(mesh)
# initialise volume and edge residual with deterministic part
# R_T = dot(nabla_grad(a0_f), nabla_grad(w[mu]._fefunc))
R_T = r_T(a0_f, w[mu]._fefunc)
if not mu:
R_T = R_T + f
# R_E = a0_f * dot(nabla_grad(w[mu]._fefunc), nu)
R_E = r_E(a0_f, w[mu]._fefunc, nu)
# get Neumann residual
homogeneousNBC = False if mu.order == 0 else True
R_Nb = r_Nb(a0_f, w[mu]._fefunc, nu, mesh, homogeneous=homogeneousNBC)
# iterate m
Lambda = w.active_indices()
maxm = w.max_order
if len(coeff_field) < maxm:
logger.warning("insufficient length of coefficient field for MultiVector (%i < %i)", len(coeff_field), maxm)
maxm = len(coeff_field)
# assert coeff_field.length >= maxm # ensure coeff_field expansion is sufficiently long
for m in range(maxm):
am_f, am_rv = coeff_field[m]
# prepare polynom coefficients
beta = am_rv.orth_polys.get_beta(mu[m])
# mu
res = -beta[0] * w[mu]
# mu+1
mu1 = mu.inc(m)
if mu1 in Lambda:
w_mu1 = w.get_projection(mu1, mu)
res += beta[1] * w_mu1
# mu-1
mu2 = mu.dec(m)
if mu2 in Lambda:
w_mu2 = w.get_projection(mu2, mu)
res += beta[-1] * w_mu2
# add volume contribution for m
# r_t = dot(nabla_grad(am_f), nabla_grad(res._fefunc))
R_T = R_T + r_T(am_f, res._fefunc)
# add edge contribution for m
# r_e = am_f * dot(nabla_grad(res._fefunc), nu)
R_E = R_E + r_E(am_f, res._fefunc, nu)
# prepare more FEM variables for residual assembly
DG = FunctionSpace(mesh, "DG", 0)
s = TestFunction(DG)
h = CellSize(mesh)
# scaling of residual terms and definition of residual form
a0_s = a0_f[0] if isinstance(a0_f, tuple) else a0_f # required for elasticity parameters
res_form = (h ** 2 * (1 / a0_s) * dot(R_T, R_T) * s * dx
+ avg(h) * dot(avg(R_E) / avg(a0_s), avg(R_E)) * 2 * avg(s) * dS)
resT = h ** 2 * (1 / a0_s) * dot(R_T, R_T) * s * dx
resE = 0 * s * dx + avg(h) * dot(avg(R_E) / avg(a0_s), avg(R_E)) * 2 * avg(s) * dS
resNb = 0 * s * dx
# add Neumann residuals
if R_Nb is not None:
for rj, dsj in R_Nb:
res_form = res_form + h * (1 / a0_s) * dot(rj, rj) * s * dsj
resNb += h * (1 / a0_s) * dot(rj, rj) * s * dsj
# FEM evaluate residual on mesh
eta = assemble(res_form)
eta_indicator = np.array([sqrt(e) for e in eta])
# map DG dofs to cell indices
dofs = [DG.dofmap().cell_dofs(c.index())[0] for c in cells(mesh)]
eta_indicator = eta_indicator[dofs]
global_error = sqrt(sum(e for e in eta))
# debug ---
if False:
etaT = assemble(resT)
etaT_indicator = etaT #np.array([sqrt(e) for e in etaT])
etaT = sqrt(sum(e for e in etaT))
etaE = assemble(resE)
etaE_indicator = etaE #np.array([sqrt(e) for e in etaE])
etaE = sqrt(sum(e for e in etaE))
etaNb = assemble(resNb)
etaNb_indicator = etaNb #np.array([sqrt(e) for e in etaNb])
etaNb = sqrt(sum(e for e in etaNb))
print "==========RESIDUAL ESTIMATOR============"
print "eta", eta
print "eta_indicator", eta_indicator
print "global =", global_error
print "volume =", etaT
print "edge =", etaE
print "Neumann =", etaNb
if False:
plot_indicators(((eta, "overall residual"), (etaT_indicator, "volume residual"), (etaE_indicator, "edge residual"), (etaNb_indicator, "Neumann residual")), mesh)
# ---debug
# restore quadrature degree
parameters["form_compiler"]["quadrature_degree"] = quadrature_degree_old
return (FlatVector(eta_indicator), global_error)
def _evaluateGlobalMixedEstimator(cls, mu, w, coeff_field, pde, f, quadrature_degree, vectorspace_type='BDM'):
"""Evaluation of global mixed equilibrated estimator."""
# set quadrature degree
# quadrature_degree_old = parameters["form_compiler"]["quadrature_degree"]
# parameters["form_compiler"]["quadrature_degree"] = quadrature_degree
# logger.debug("residual quadrature order = " + str(quadrature_degree))
# prepare numerical flux and f
sigma_mu, f_mu = evaluate_numerical_flux(w, mu, coeff_field, f)
# ###################
# ## MIXED PROBLEM ##
# ###################
# get setup data for mixed problem
V = w[mu]._fefunc.function_space()
mesh = V.mesh()
degree = element_degree(w[mu]._fefunc)
# create function spaces
DG0 = FunctionSpace(mesh, 'DG', 0)
DG0_dofs = [DG0.dofmap().cell_dofs(c.index())[0] for c in cells(mesh)]
RT = FunctionSpace(mesh, vectorspace_type, degree)
W = RT * DG0
# setup boundary conditions
# bcs = pde.create_dirichlet_bcs(W.sub(1))
# debug ===
# from dolfin import DOLFIN_EPS, DirichletBC
# def boundary(x):
# return x[0] < DOLFIN_EPS or x[0] > 1.0 + DOLFIN_EPS or x[1] < DOLFIN_EPS or x[1] > 1.0 + DOLFIN_EPS
# bcs = [DirichletBC(W.sub(1), Constant(0.0), boundary)]
# === debug
# create trial and test functions
(sigma, u) = TrialFunctions(W)
(tau, v) = TestFunctions(W)
# define variational form
a_eq = (dot(sigma, tau) + div(tau) * u + div(sigma) * v) * dx
L_eq = (- f_mu * v + dot(sigma_mu, tau)) * dx
# compute solution
w_eq = Function(W)
solve(a_eq == L_eq, w_eq)
(sigma_mixed, u_mixed) = w_eq.split()
# #############################
# ## EQUILIBRATION ESTIMATOR ##
# #############################
# evaluate error estimator
dg0 = TestFunction(DG0)
eta_mu = inner(sigma_mu, sigma_mu) * dg0 * dx
eta_T = assemble(eta_mu, form_compiler_parameters={'quadrature_degree': quadrature_degree})
eta_T = np.array([sqrt(e) for e in eta_T])
# evaluate global error
eta = sqrt(sum(i**2 for i in eta_T))
# reorder array entries for local estimators
eta_T = eta_T[DG0_dofs]
# restore quadrature degree
# parameters["form_compiler"]["quadrature_degree"] = quadrature_degree_old
return eta, FlatVector(eta_T)
def trace_3d1d_matrix(V, TV, reduced_mesh):
'''Trace from 3d to 1d. Makes sense only for CG space'''
assert reduced_mesh.id() == TV.mesh().id()
assert V.ufl_element().family() == 'Lagrange'
mesh = V.mesh()
line_mesh = TV.mesh()
# The idea for point evaluation/computing dofs of TV is to minimize
# the number of evaluation. I mean a vector dof if done naively would
# have to evaluate at same x number of component times.
value_size = TV.ufl_element().value_size()
# We use the map to get (1d cell -> [3d edge) -> 3d cell]
if hasattr(reduced_mesh, 'parent_entity_map'):
# ( )
mapping = reduced_mesh.parent_entity_map[mesh.id()][1]
# [ ]
mesh.init(1)
mesh.init(1, 3)
e2c = mesh.topology()(1, 3)
# From 1d cell (by index)
get_cell3d = lambda c, d1d3=mapping, d3d3=e2c: d3d3(d1d3[c.index()])[0]
# Tree collision by midpoint
else:
tree = mesh.bounding_box_tree()
limit = mesh.num_cells()
get_cell3d = lambda c, tree=tree, bound=limit: (
lambda index: index if index<bound else None
)(tree.compute_first_entity_collision(c.midpoint()))
TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1))
TV_dm = TV.dofmap()
V_dm = V.dofmap()
# For non scalar we plan to make compoenents by shift
if value_size > 1:
TV_dm = TV.sub(0).dofmap()
Vel = V.element()
basis_values = np.zeros(V.element().space_dimension()*value_size)
with petsc_serial_matrix(TV, V) as mat:
for line_cell in cells(line_mesh):
# Get the tangent => orthogonal tangent vectors
# The idea is now to minimize the point evaluation
scalar_dofs = TV_dm.cell_dofs(line_cell.index())
scalar_dofs_x = TV_coordinates[scalar_dofs]
# Let's get a 3d cell to use for getting the V values
# CG assumption allows taking any
tet_cell = get_cell3d(line_cell)
if tet_cell is None: continue
Vcell = Cell(mesh, tet_cell)
vertex_coordinates = Vcell.get_vertex_coordinates()
cell_orientation = 0
# Columns are determined by V cell! I guess the sparsity
# could be improved if for x_dofs of TV only x_dofs of V
# were considered
column_indices = np.array(V_dm.cell_dofs(tet_cell), dtype='int32')
for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x):
# 3d at point
Vel.evaluate_basis_all(basis_values, avg_point, vertex_coordinates, cell_orientation)
# The thing now is that with data we can assign to several
# rows of the matrix. Shift determines the (x, y, ... ) or
# (xx, xy, yx, ...) component of Q
data = basis_values.reshape((-1, value_size)).T
for shift, column_values in enumerate(data):
row = scalar_row + shift
mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES)
# On to next avg point
# On to next cell
return PETScMatrix(mat)
def sphere_average_matrix(V, TV, radius, quad_degree):
'''Averaging matrix over the sphere'''
mesh = V.mesh()
line_mesh = TV.mesh()
# Lebedev below need off degrees
if quad_degree % 2 == 0: quad_degree += 1
# NOTE: this is a dependency
from quadpy.sphere import Lebedev
integrator = Lebedev(quad_degree)
xq = integrator.points
wq = integrator.weights
if is_number(radius):
radius = lambda x, radius=radius: radius
mesh_x = TV.mesh().coordinates()
# The idea for point evaluation/computing dofs of TV is to minimize
# the number of evaluation. I mean a vector dof if done naively would
# have to evaluate at same x number of component times.
value_size = TV.ufl_element().value_size()
# Eval at points will require serch
tree = mesh.bounding_box_tree()
limit = mesh.num_cells()
TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1))
TV_dm = TV.dofmap()
V_dm = V.dofmap()
# For non scalar we plan to make compoenents by shift
if value_size > 1:
TV_dm = TV.sub(0).dofmap()
Vel = V.element()
basis_values = np.zeros(V.element().space_dimension()*value_size)
with petsc_serial_matrix(TV, V) as mat:
for line_cell in cells(line_mesh):
# The idea is now to minimize the point evaluation
scalar_dofs = TV_dm.cell_dofs(line_cell.index())
scalar_dofs_x = TV_coordinates[scalar_dofs]
for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x):
# Get radius and integration points
rad = radius(avg_point)
# Scale and shift the unit sphere to the point
integration_points = xq*rad + avg_point
data = {}
for index, ip in enumerate(integration_points):
c = tree.compute_first_entity_collision(Point(*ip))
if c >= limit: continue
Vcell = Cell(mesh, c)
vertex_coordinates = Vcell.get_vertex_coordinates()
cell_orientation = Vcell.orientation()
Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation)
cols_ip = V_dm.cell_dofs(c)
values_ip = basis_values*wq[index]
# Add
for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))):
if col in data:
data[col] += value
else:
data[col] = value
# The thing now that with data we can assign to several
# rows of the matrix
column_indices = np.array(data.keys(), dtype='int32')
for shift in range(value_size):
row = scalar_row + shift
column_values = np.array([data[col][shift] for col in column_indices])
mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES)
# On to next avg point
# On to next cell
return PETScMatrix(mat)
def OverlapMesh(mesh1, mesh2, tol=1E-14):
'''
Given two subdomain meshes which share a single unique common tag in
their marking function we create here a mesh of cells corresponding
to that tag. The new mesh cells can be mapped to mesh1/2 cells.
'''
assert isinstance(mesh1, SubDomainMesh), type(mesh1)
assert isinstance(mesh2, SubDomainMesh)
tdim = mesh1.topology().dim()
assert mesh2.topology().dim() == tdim
assert mesh1.geometry().dim() == mesh2.geometry().dim()
# Overlap has to be unique as well (for now)
tags1 = set(mesh1.marking_function.array())
tags2 = set(mesh2.marking_function.array())
common_tags = tags1 & tags2
assert len(common_tags) == 1
tag = int(common_tags.pop())
# A bit of wishful thinking here: create overlap mesh from mesh1
# and hope it makes sense for mesh2 as well
emesh = SubDomainMesh(mesh1.marking_function, tag)
# Now we have a mesh from cells of omega to cells in mesh1. Let's
# build a map for mesh2 simlar to `build_embedding_map`
tree = mesh2.bounding_box_tree()
# Localize first the vertex in mesh2
mesh2.init(tdim) # Then we want to find a cell in mesh2 which
mesh2.init(tdim, 0) # has the same vertices
c2v = mesh2.topology()(tdim, 0)
mesh_x = mesh2.coordinates()
emesh_x = emesh.coordinates()
# Get som idea of mesh size to make relative comparison of coords
scale = max(emesh_x.max(axis=0) - emesh_x.min(axis=0))
# Also build the map for vertices
entity_map = {0: [None]*emesh.num_vertices(), tdim: [None]*emesh.num_cells()}
vertex_map = entity_map[0]
cell_map = entity_map[tdim]
collided_cells = {}
for cell in df.cells(emesh):
# The idea is the there is exactly on the_cell which will be
# found in every point-cell collision patches
the_cell = set()
for vertex in cell.entities(0):
# Try to be less efficient by computing each vertex collision
# only once
if vertex in collided_cells:
mcells = collided_cells[vertex]
else:
vertex_x = emesh_x[vertex]
mcells = tree.compute_entity_collisions(df.Point(*vertex_x))
# What is the id of vertex in the mesh
mcell_vertices = c2v(next(iter(mcells)))
the_vertex = min(mcell_vertices, key=lambda v: np.linalg.norm(vertex_x-mesh_x[v]))
error = np.linalg.norm(vertex_x - mesh_x[the_vertex])/scale
assert error < tol, 'Found a hanging node %16f' % error
vertex_map[vertex] = the_vertex
collided_cells[vertex] = mcells
if not the_cell:
the_cell.update(mcells)
else:
the_cell = the_cell & set(mcells)
assert len(the_cell) == 1, the_cell
# Insert
cell_map[cell.index()] = the_cell.pop()
# Sanity
assert not any(v is None for v in entity_map[0])
assert not any(v is None for v in entity_map[tdim])
# At this point we can build add the map
emesh.parent_entity_map[mesh2.id()] = entity_map
return emesh
return emesh
# -------------------------------------------------------------------
if __name__ == '__main__':
mesh = df.UnitSquareMesh(4, 4)
subdomains = df.MeshFunction('size_t', mesh, mesh.topology().dim(), 3)
df.CompiledSubDomain('x[0] < 0.25+DOLFIN_EPS').mark(subdomains, 1)
df.CompiledSubDomain('x[0] > 0.75-DOLFIN_EPS').mark(subdomains, 2)
mesh1 = SubDomainMesh(subdomains, (1, 3))
mesh2 = SubDomainMesh(subdomains, (2, 3))
mesh12 = OverlapMesh(mesh1, mesh2)
# FIXME: split the file!
map1 = mesh12.parent_entity_map[mesh1.id()][2]
map2 = mesh12.parent_entity_map[mesh2.id()][2]
# Cell check out
for c, c1, c2 in zip(df.cells(mesh12), map1, map2):
assert df.near(c.midpoint().distance(df.Cell(mesh1, c1).midpoint()), 0, 1E-14)
assert df.near(c.midpoint().distance(df.Cell(mesh2, c2).midpoint()), 0, 1E-14)
# Vertices are not that important but anyways
x1 = mesh1.coordinates(); map1 = mesh12.parent_entity_map[mesh1.id()][0]
x2 = mesh2.coordinates(); map2 = mesh12.parent_entity_map[mesh2.id()][0]
for x, i1, i2 in zip(mesh12.coordinates(), map1, map2):
assert np.linalg.norm(x - x1[i1]) < 1E-13
assert np.linalg.norm(x - x2[i2]) < 1E-13
def cylinder_average_matrix(V, TV, radius, quad_degree):
'''Averaging matrix'''
mesh = V.mesh()
line_mesh = TV.mesh()
# We are going to perform the integration with Gauss quadrature at
# the end (PI u)(x):
# A cell of mesh (an edge) defines a normal vector. Let P be the plane
# that is defined by the normal vector n and some point x on Gamma. Let L
# be the circle that is the intersect of P and S. The value of q (in Q) at x
# is defined as
#
# q(x) = (1/|L|)*\int_{L}g(x)*dL
#
# which simplifies to g(x) = (1/(2*pi*R))*\int_{-pi}^{pi}u(L)*R*d(theta) and
# or = (1/2) * \int_{-1}^{1} u (L(pi*s)) * ds
# This can be integrated no problemo once we figure out L. To this end, let
# t_1 and t_2 be two unit mutually orthogonal vectors that are orthogonal to
# n. Then L(pi*s) = p + R*t_1*cos(pi*s) + R*t_2*sin(pi*s) can be seen to be
# such that i) |x-p| = R and ii) x.n = 0 [i.e. this the suitable
# parametrization]
# Clearly we can scale the weights as well as precompute
# cos and sin terms.
xq, wq = leggauss(quad_degree)
wq *= 0.5
cos_xq = np.cos(np.pi*xq).reshape((-1, 1))
sin_xq = np.sin(np.pi*xq).reshape((-1, 1))
if is_number(radius):
radius = lambda x, radius=radius: radius
mesh_x = TV.mesh().coordinates()
# The idea for point evaluation/computing dofs of TV is to minimize
# the number of evaluation. I mean a vector dof if done naively would
# have to evaluate at same x number of component times.
value_size = TV.ufl_element().value_size()
# Eval at points will require serch
tree = mesh.bounding_box_tree()
limit = mesh.num_cells()
TV_coordinates = TV.tabulate_dof_coordinates().reshape((TV.dim(), -1))
TV_dm = TV.dofmap()
V_dm = V.dofmap()
# For non scalar we plan to make compoenents by shift
if value_size > 1:
TV_dm = TV.sub(0).dofmap()
Vel = V.element()
basis_values = np.zeros(V.element().space_dimension()*value_size)
with petsc_serial_matrix(TV, V) as mat:
for line_cell in cells(line_mesh):
# Get the tangent => orthogonal tangent vectors
v0, v1 = mesh_x[line_cell.entities(0)]
n = v0 - v1
t1 = np.array([n[1]-n[2], n[2]-n[0], n[0]-n[1]])
t2 = np.cross(n, t1)
t1 /= np.linalg.norm(t1)
t2 = t2/np.linalg.norm(t2)
# The idea is now to minimize the point evaluation
scalar_dofs = TV_dm.cell_dofs(line_cell.index())
scalar_dofs_x = TV_coordinates[scalar_dofs]
for scalar_row, avg_point in zip(scalar_dofs, scalar_dofs_x):
# Get radius and integration points
rad = radius(avg_point)
integration_points = avg_point + rad*t1*sin_xq + rad*t2*cos_xq
data = {}
for index, ip in enumerate(integration_points):
c = tree.compute_first_entity_collision(Point(*ip))
if c >= limit: continue
Vcell = Cell(mesh, c)
vertex_coordinates = Vcell.get_vertex_coordinates()
cell_orientation = Vcell.orientation()
Vel.evaluate_basis_all(basis_values, ip, vertex_coordinates, cell_orientation)
cols_ip = V_dm.cell_dofs(c)
values_ip = basis_values*wq[index]
# Add
for col, value in zip(cols_ip, values_ip.reshape((-1, value_size))):
if col in data:
data[col] += value
else:
data[col] = value
# The thing now that with data we can assign to several
# rows of the matrix
column_indices = np.array(data.keys(), dtype='int32')
for shift in range(value_size):
row = scalar_row + shift
column_values = np.array([data[col][shift] for col in column_indices])
mat.setValues([row], column_indices, column_values, PETSc.InsertMode.INSERT_VALUES)
# On to next avg point
# On to next cell
return PETScMatrix(mat)
