def vtk_ug_to_dolfin_mesh(ug):
"""
Create a DOLFIN Mesh from a vtkUnstructuredGrid object
"""
if not isinstance(ug, vtk.vtkUnstructuredGrid):
raise TypeError("Expected a 'vtkUnstructuredGrid'")
# Get mesh data
num_cells = int(ug.GetNumberOfCells())
num_vertices = int(ug.GetNumberOfPoints())
# Get topological and geometrical dimensions
cell = ug.GetCell(0)
gdim = int(cell.GetCellDimension())
cell_type = cell.GetCellType()
if cell_type not in [vtk.VTK_TETRA, vtk.VTK_TRIANGLE]:
raise TypeError("DOLFIN only support meshes of triangles " + \
"and tetrahedrons.")
tdim = 3 if cell_type == vtk.VTK_TETRA else 2
# Create empty DOLFIN Mesh
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, tdim, gdim)
editor.init_cells(num_cells)
editor.init_vertices(num_vertices)
editor.close()
# Assign the cell and vertex informations directly from the vtk data
cells_array = array_handler.vtk2array(ug.GetCells().GetData())
# Get the assumed fixed size of indices and create an index array
cell_size = cell.GetPointIds().GetNumberOfIds()
cellinds = np.arange(len(cells_array))
# Each cell_ids_size:th data point need to be deleted from the
# index array
ind_delete = slice(0, len(cells_array), cell_size + 1)
# Check that the removed value all have the same value which should
# be the size of the data
if not np.all(cells_array[ind_delete] == cell_size):
raise ValueError("Expected all cells to be of the same size")
cellinds = np.delete(cellinds, ind_delete)
# Get cell data from mesh and make it writeable (cell data is non
# writeable by default) and update the values
mesh_cells = mesh.cells()
mesh_cells.flags.writeable = True
mesh_cells[:] = np.reshape(cells_array[cellinds], \
(num_cells , cell_size))
# Set coordinates from vtk data
vertex_array = array_handler.vtk2array(ug.GetPoints().GetData())
if vertex_array.shape[1] != gdim:
vertex_array = vertex_array[:, :gdim]
mesh.coordinates()[:] = vertex_array
return mesh
def vtk_ug_to_dolfin_mesh(ug):
"""
Create a DOLFIN Mesh from a vtkUnstructuredGrid object
"""
if not isinstance(ug, vtk.vtkUnstructuredGrid):
raise TypeError("Expected a 'vtkUnstructuredGrid'")
# Get mesh data
num_cells = int(ug.GetNumberOfCells())
num_vertices = int(ug.GetNumberOfPoints())
# Get topological and geometrical dimensions
cell = ug.GetCell(0)
gdim = int(cell.GetCellDimension())
cell_type = cell.GetCellType()
if cell_type not in [vtk.VTK_TETRA, vtk.VTK_TRIANGLE]:
raise TypeError("DOLFIN only support meshes of triangles " + \
"and tetrahedrons.")
tdim = 3 if cell_type == vtk.VTK_TETRA else 2
# Create empty DOLFIN Mesh
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, tdim, gdim)
editor.init_cells(num_cells)
editor.init_vertices(num_vertices)
editor.close()
# Assign the cell and vertex informations directly from the vtk data
cells_array = array_handler.vtk2array(ug.GetCells().GetData())
# Get the assumed fixed size of indices and create an index array
cell_size = cell.GetPointIds().GetNumberOfIds()
cellinds = np.arange(len(cells_array))
# Each cell_ids_size:th data point need to be deleted from the
# index array
ind_delete = slice(0, len(cells_array), cell_size+1)
# Check that the removed value all have the same value which should
# be the size of the data
if not np.all(cells_array[ind_delete]==cell_size):
raise ValueError("Expected all cells to be of the same size")
cellinds = np.delete(cellinds, ind_delete)
# Get cell data from mesh and make it writeable (cell data is non
# writeable by default) and update the values
mesh_cells = mesh.cells()
mesh_cells.flags.writeable = True
mesh_cells[:] = np.reshape(cells_array[cellinds], \
(num_cells , cell_size))
# Set coordinates from vtk data
vertex_array = array_handler.vtk2array(ug.GetPoints().GetData())
if vertex_array.shape[1] != gdim:
vertex_array = vertex_array[:,:gdim]
mesh.coordinates()[:] = vertex_array
return mesh
def convert(ifilename, handler):
""" Convert from Abaqus.
The Abaqus format first defines a node block, then there should be a number
of elements containing these nodes.
"""
# Dictionary of nodes (maps node id to coordinates)
nodes = {}
# Dictionary of elements (maps cell id to list of cell nodes)
elems = {}
# Lists of nodes for given name (key)
node_sets = {}
# Lists of cells for given name (key)
cell_sets = {}
# Lists of surfaces for given name (key) in the format:
# {'SS1': [set(['SS1_S1', 'S1']), set(['SS1_S4', 'S4'])]},
# where SS1 is the name of the surface, SS1_S1 is the name of the
# cell list whose first face is to be selected, ...
surface_sets = {}
# Open file Abaqus file
file = open(ifilename, 'r')
csv_file = csv.reader(file, delimiter=',', skipinitialspace=True)
node_set_name = None
generate = None
# Set intial state state
state = State.Init
# Read data from input file
for l in csv_file:
# Sanity check
if (len(l) == 0): print("Ooops, zero length.")
if l[0].startswith('**'): # Pass over comments
continue
elif l[0].startswith('*'): # Have a keyword
state = State.Unknown
if l[0].lower() == "*heading":
state = State.ReadHeading
elif l[0].lower() == "*part":
part_name = _read_part_name(l)
elif l[0].lower() == "*end part":
state = State.Invalid
elif l[0].lower() == "*node":
node_set_name = _create_node_list_entry(node_sets, l)
state = State.ReadNodes
elif l[0].lower() == "*element":
cell_type, cell_set_name = _read_element_keywords(cell_sets, l)
state = State.ReadCells
elif l[0].lower() == "*nset":
node_set_name, generate = _read_nset_keywords(node_sets, l)
state = State.ReadNodeSet
elif l[0].lower() == "*elset":
cell_set_name, generate = _read_elset_keywords(cell_sets, l)
if generate:
print("WARNING: generation of *elsets not tested.")
state = State.ReadCellSet
elif l[0].lower() == "*surface":
surface_set_name, generate = _read_surface_keywords(
surface_sets, l)
state = State.ReadSurfaceSet
else:
print("WARNING: unrecognised Abaqus input keyword:", l[0])
state = State.Unknown
else:
if state == State.ReadHeading:
model_name = _read_heading(l)
elif state == State.ReadNodes:
node_id = int(l[0]) - 1
coords = [float(c) for c in l[1:]]
nodes[node_id] = coords
if node_set_name is not None:
node_sets[node_set_name].add(node_id)
elif state == State.ReadCells:
cell_id = int(l[0]) - 1
cell_connectivity = [int(v) - 1 for v in l[1:]]
elems[cell_id] = cell_connectivity
if cell_set_name is not None:
cell_sets[cell_set_name].add(cell_id)
elif state == State.ReadNodeSet:
try:
if generate:
n0, n1, increment = l
node_range = list(
range(int(n0) - 1,
int(n1) - 1, int(increment)))
node_range.append(int(n1) - 1)
node_sets[node_set_name].update(node_range)
else:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
node_range = [int(n) - 1 for n in l]
node_sets[node_set_name].update(node_range)
except:
print("WARNING: Non-integer node sets not yet supported.")
elif state == State.ReadCellSet:
try:
if generate:
n0, n1, increment = l
cell_range = list(
range(int(n0) - 1,
int(n1) - 1, int(increment)))
cell_range.append(int(n1) - 1)
cell_sets[cell_set_name].update(cell_range)
else:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
cell_range = [int(n) - 1 for n in l]
cell_sets[cell_set_name].update(cell_range)
except:
print(
"WARNING: Non-integer element sets not yet supported.")
elif state == State.ReadSurfaceSet:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
surface_sets[surface_set_name].update([tuple(l)])
elif state == State.Invalid: # part
raise Exception("Inavlid Abaqus parser state..")
# Close CSV object
file.close()
del csv_file
# Write data to XML file
# Note that vertices/cells must be consecutively numbered, which
# isn't necessarily the case in Abaqus. Therefore we enumerate and
# translate original IDs to sequence indexes if gaps are present.
# FIXME
handler.set_mesh_type("tetrahedron", 3)
process_facets = len(surface_sets) > 0
if process_facets:
try:
from dolfin import MeshEditor, Mesh
except ImportError:
_error(
"DOLFIN must be installed to handle Abaqus boundary regions")
mesh = Mesh()
mesh_editor = MeshEditor()
mesh_editor.open(mesh, 3, 3)
node_ids_order = {}
# Check for gaps in vertex numbering
node_ids = list(iterkeys(nodes))
if len(node_ids) > 0:
vertex_gap = (min(node_ids) != 0 or max(node_ids) != len(node_ids) - 1)
for x, y in enumerate(node_ids):
node_ids_order[y] = x # Maps Abaqus IDs to Dolfin IDs
else:
vertex_gap = True
# Check for gaps in cell numbering
elemids = list(iterkeys(elems))
if len(elemids) > 0:
cell_gap = (min(elemids) != 0 or max(elemids) != len(elemids) - 1)
else:
cell_gap = True
# Write vertices to XML file
handler.start_vertices(len(nodes))
if process_facets:
mesh_editor.init_vertices_global(len(nodes), len(nodes))
if not vertex_gap:
for v_id, v_coords in list(iteritems(nodes)):
handler.add_vertex(v_id, v_coords)
if process_facets:
mesh_editor.add_vertex(v_id, np.array(v_coords,
dtype=np.float_))
else:
for idx, (v_id, v_coords) in enumerate(iteritems(nodes)):
handler.add_vertex(idx, v_coords)
if process_facets:
mesh_editor.add_vertex(idx, np.array(v_coords,
dtype=np.float_))
handler.end_vertices()
# Write cells to XML file
handler.start_cells(len(elems))
if process_facets:
mesh_editor.init_cells_global(len(elems), len(elems))
if not vertex_gap and not cell_gap:
for c_index, c_data in list(iteritems(elems)):
for v_id in c_data:
if not (0 <= v_id < len(nodes)):
handler.error(
"Element %s references non-existent node %s" %
(c_index, v_id))
handler.add_cell(c_index, c_data)
if process_facets:
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
mesh_editor.add_cell(c_index,
np.array(c_data_tmp, dtype=np.uintp))
elif not vertex_gap and cell_gap:
for idx, (c_index, c_data) in enumerate(iteritems(elems)):
for v_id in c_data:
if not (0 <= v_id < len(nodes)):
handler.error(
"Element %s references non-existent node %s" %
(c_index, v_id))
handler.add_cell(idx, c_data)
if process_facets:
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
mesh_editor.add_cell(idx, np.array(c_data_tmp, dtype=np.uintp))
else:
for idx, (c_id, c_data) in enumerate(iteritems(elems)):
c_nodes = []
for v_id in c_data:
try:
c_nodes.append(node_ids_order[v_id])
except ValueError:
handler.error(
"Element %s references non-existent node %s" %
(c_id, v_id))
handler.add_cell(idx, c_nodes)
if process_facets:
c_nodes.sort()
mesh_editor.add_cell(idx, np.array(c_nodes, dtype=np.uintp))
handler.end_cells()
# Write MeshValueCollections to XML file
handler.start_domains()
# Build a abaqus node ID -> dolfin cell ID map (which is not unique but that is irrelevant here)
# and its local entity.
if len(node_sets) > 0:
node_cell_map = {}
for c_dolfin_index, (c_index, c_data) in enumerate(iteritems(elems)):
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
for local_entity, n_index in enumerate(c_data_tmp):
node_cell_map[n_index] = (c_dolfin_index, local_entity)
# Write vertex/node sets
dim = 0
for value, (name, node_set) in enumerate(iteritems(node_sets)):
handler.start_mesh_value_collection(name, dim, len(node_set), "uint")
for node in node_set:
try:
cell, local_entity = node_cell_map[node]
handler.add_entity_mesh_value_collection(
dim, cell, value, local_entity=local_entity)
except KeyError:
print("Warning: Boundary references non-existent node %s" %
node)
handler.end_mesh_value_collection()
# Write cell/element sets
dim = 3
for name, s in list(iteritems(cell_sets)):
handler.start_mesh_value_collection(name, dim, len(s), "uint")
for cell in s:
handler.add_entity_mesh_value_collection(dim, cell, 0)
handler.end_mesh_value_collection()
# Write surface sets
if process_facets:
dim = 2
nodes_facet_map = _nodes_facet_map(mesh)
data = [int(0)] * mesh.num_facets()
S1 = [0, 1, 2]
S2 = [0, 3, 1]
S3 = [1, 3, 2]
S4 = [2, 3, 0]
node_selector = {
'S1': S1,
'S2': S2,
'S3': S3,
'S4': S4,
}
for index, (name, s) in enumerate(iteritems(surface_sets)):
cell_face_list = []
for cell_set_name, face_index in s:
cell_face_list += [(cell, face_index)
for cell in cell_sets[cell_set_name]]
for cell, face in cell_face_list:
cell_nodes = elems[cell]
# Extract the face nodes
face_nodes = [cell_nodes[i] for i in node_selector[face]]
dolfin_face_nodes = [node_ids_order[n] for n in face_nodes]
dolfin_face_nodes.sort()
# Convert the face_nodes to dolfin IDs
face_id = nodes_facet_map[tuple(dolfin_face_nodes)]
data[face_id] = index + 1
# Create and initialise the mesh function
handler.start_meshfunction("facet_region", dim, mesh.num_facets())
for index, physical_region in enumerate(data):
handler.add_entity_meshfunction(index, physical_region)
handler.end_meshfunction()
handler.end_domains()
def write_fenics_file(dim, ofilename):
ofile = File(ofilename + '.xml')
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, dim, dim)
editor.init_vertices(nodes.shape[1])
editor.init_cells(len(cell_map))
for i in range(nodes.shape[1]):
if dim == 2:
editor.add_vertex(i, nodes[0, i], nodes[1, i])
else:
editor.add_vertex(i, nodes[0, i], nodes[1, i], nodes[2, i])
for i in range(1, len(cell_map)+1):
if dim == 2:
editor.add_cell(i-1, cell_map[i][0]-1, cell_map[i][1]-1, cell_map[i][2]-1)
else:
editor.add_cell(i-1, cell_map[i][0]-1, cell_map[i][1]-1, cell_map[i][2]-1, cell_map[i][3]-1)
mesh.order()
mvc = mesh.domains().markers(dim-1)
for zone, cells in boundary_cells.iteritems():
for cell, nds in cells.iteritems():
dolfin_cell = Cell(mesh, cell-1)
nodes_of_cell = dolfin_cell.entities(0)
#print cell
#print nodes_of_cell
nodes_of_face = nds - 1
#print nodes_of_face
for jj, ff in enumerate(facets(dolfin_cell)):
facet_nodes = ff.entities(0)
#print facet_nodes
if all(map(lambda x: x in nodes_of_face, facet_nodes)):
local_index = jj
break
mvc.set_value(cell-1, local_index, zone)
ofile << mesh
from dolfin import plot
plot(mesh, interactive=True)
print 'Finished writing FEniCS mesh\n'
def Triangle(left, bottom):
""" Triangular mesh with just one triangular cell. """
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(3)
editor.init_cells(1)
editor.add_vertex(0, 0, 0)
editor.add_vertex(1, bottom, 0)
editor.add_vertex(2, 0, left)
editor.add_cell(0, 0, 1, 2)
editor.close()
return mesh
def get(self):
"""Build cells based on triangulated regular polygon."""
sides, h, x, y = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3) # dimension
editor.init_vertices(sides + 2)
editor.init_cells(sides)
editor.add_vertex(0, x, y, h)
for i in range(1, sides + 1):
editor.add_vertex(i,
cos(2 * pi * i / sides),
sin(2 * pi * i / sides),
0)
editor.add_vertex(sides + 1, 0, 0, 0)
for i in range(sides - 1):
editor.add_cell(i, 0, i + 1, i + 2, sides + 1)
editor.add_cell(sides - 1, 0, sides, 1, sides + 1)
editor.close()
return mesh
def fit2d(x0,
y0,
points,
cells,
eps,
degree=1,
verbose=False,
solver='spsolve'):
# Convert points, cells to dolfin mesh
editor = MeshEditor()
mesh = Mesh()
# topological and geometrical dimension 2
editor.open(mesh, 'triangle', 2, 2, 1)
editor.init_vertices(len(points))
editor.init_cells(len(cells))
for k, point in enumerate(points):
editor.add_vertex(k, point[:2])
for k, cell in enumerate(cells.astype(numpy.uintp)):
editor.add_cell(k, cell)
editor.close()
# Eps = numpy.array([[eps, eps], [eps, eps]])
# Eps = numpy.array([[eps, 0], [0, eps]])
Eps = numpy.array([[2 * eps, eps], [eps, 2 * eps]])
# Eps = numpy.array([[1.0, 1.0], [1.0, 1.0]])
return fit(x0,
y0,
mesh,
Eps,
degree=degree,
verbose=verbose,
solver=solver)
def get(self):
"""Two cells."""
a, b = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(4)
editor.init_cells(2)
editor.add_vertex(0, 0, 0)
editor.add_vertex(1, 1, 0)
editor.add_vertex(2, a, b)
editor.add_vertex(3, a, -b)
editor.add_cell(0, 0, 1, 2)
editor.add_cell(1, 0, 1, 3)
editor.close()
return mesh
def get(self):
"""Build mesh from the tree of triangles created by reflections."""
# get n
n, k, a, b = self.pad(self.values)
# adjust defaults based on n
self.full[2:4] = self.shape[n]
# get all parameters
n, k, a, b = self.pad(self.values)
if n == -1:
self.vertices = self.bothvertices[k]
else:
tree = self.trees[(n, k)]
self.triangles = []
# angles are 2pi/a, 2pi/b
side = np.sin(2 * pi / b) / np.sin(pi - 2 * pi / a - 2 * pi / b)
self.vertices = [
np.array([0.0, 0.0]), np.array([1.0, 0.0]), np.array(
[side * np.cos(2 * pi / a), side * np.sin(2 * pi / a)])]
self.generate(tree, [0, 1, 2])
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(len(self.vertices))
editor.init_cells(len(self.triangles))
for i, v in enumerate(self.vertices):
editor.add_vertex(i, *v)
for i, t in enumerate(self.triangles):
editor.add_cell(i, *t)
editor.close()
return mesh
def get(self):
"""Build cells based on triangulated regular polygon."""
sides, h, x, y = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3) # dimension
editor.init_vertices(sides + 2)
editor.init_cells(sides)
editor.add_vertex(0, x, y, h)
for i in range(1, sides + 1):
editor.add_vertex(i, cos(2 * pi * i / sides),
sin(2 * pi * i / sides), 0)
editor.add_vertex(sides + 1, 0, 0, 0)
for i in range(sides - 1):
editor.add_cell(i, 0, i + 1, i + 2, sides + 1)
editor.add_cell(sides - 1, 0, sides, 1, sides + 1)
editor.close()
return mesh
def reduced_mesh(mesh):
'''
Represent each branch only as a segment / single cell in the mesh.
The mesh has a map from new mesh to old mesh vertices
'''
terminals, _ = find_branches(mesh)
# Unique nodes, this is map from rmesh nodes to parent
nodes = map(int, set(sum(terminals, ())))
# Let's make reverse for purpose of creating the mesh
old2new = {old: new for new, old in enumerate(nodes)}
# Their coordinates
x = mesh.coordinates()[nodes]
rmesh = Mesh()
editor = MeshEditor()
editor.open(rmesh, 1, mesh.geometry().dim())
editor.init_vertices(len(x))
editor.init_cells(len(terminals))
# Add vertices
for vi, v in enumerate(x):
editor.add_vertex(vi, v)
# Add cells
for ci, c in enumerate(terminals):
editor.add_cell(ci, *map(lambda v: old2new[v], c))
editor.close()
# How to do this with MeshData
rmesh.parent_vertex_indices = nodes
return rmesh
def get(self):
"""One cell."""
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3)
editor.init_vertices(4)
editor.init_cells(1)
editor.add_vertex(0, 0, 0, 0)
editor.add_vertex(1, 1, 1, 0)
editor.add_vertex(2, 0, 1, 1)
editor.add_vertex(3, 1, 0, 1)
editor.add_cell(0, 0, 1, 2, 3)
editor.close()
return mesh
def get(self):
"""Eight cells."""
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3)
editor.init_vertices(7)
editor.init_cells(8)
editor.add_vertex(0, 1, 0, 0)
editor.add_vertex(1, 0, 1, 0)
editor.add_vertex(2, 0, 0, 1)
editor.add_vertex(3, -1, 0, 0)
editor.add_vertex(4, 0, -1, 0)
editor.add_vertex(5, 0, 0, -1)
editor.add_vertex(6, 0, 0, 0)
editor.add_cell(0, 6, 0, 1, 2)
editor.add_cell(1, 6, 0, 1, 5)
editor.add_cell(2, 6, 0, 4, 2)
editor.add_cell(3, 6, 0, 4, 5)
editor.add_cell(4, 6, 3, 1, 2)
editor.add_cell(5, 6, 3, 1, 5)
editor.add_cell(6, 6, 3, 4, 2)
editor.add_cell(7, 6, 3, 4, 5)
editor.close()
return mesh
def get(self):
"""One triangle per side in smaller, two triangles in larger."""
sides, R = self.pad(self.values)
mesh = Mesh()
large = [
np.array((cos(2 * pi * i / sides), sin(2 * pi * i / sides)))
for i in range(1, sides + 1)
]
small = np.array([v * R for v in large])
# centers of edges in large polygon
center = np.array([(v + w) / 2
for v, w in zip(large, large[1:] + [large[0]])])
large = np.array(large)
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(3 * sides)
editor.init_cells(3 * sides)
for i in range(sides):
editor.add_vertex(3 * i, *large[i])
editor.add_vertex(3 * i + 1, *small[i])
editor.add_vertex(3 * i + 2, *center[i])
for i, j in zip(range(sides), range(1, sides) + [0]):
editor.add_cell(3 * i, 3 * i, 3 * i + 1, 3 * i + 2)
editor.add_cell(3 * i + 1, 3 * i + 1, 3 * i + 2, 3 * j + 1)
editor.add_cell(3 * i + 2, 3 * i + 2, 3 * j + 1, 3 * j)
editor.close()
return mesh
def get(self):
"""Build mesh from the tree of triangles created by reflections."""
# get n
n, k, a, b = self.pad(self.values)
# adjust defaults based on n
self.full[2:4] = self.shape[n]
# get all parameters
n, k, a, b = self.pad(self.values)
if n == -1:
self.vertices = self.bothvertices[k]
else:
tree = self.trees[(n, k)]
self.triangles = []
# angles are 2pi/a, 2pi/b
side = np.sin(2 * pi / b) / np.sin(pi - 2 * pi / a - 2 * pi / b)
self.vertices = [
np.array([0.0, 0.0]),
np.array([1.0, 0.0]),
np.array(
[side * np.cos(2 * pi / a), side * np.sin(2 * pi / a)])
]
self.generate(tree, [0, 1, 2])
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(len(self.vertices))
editor.init_cells(len(self.triangles))
for i, v in enumerate(self.vertices):
editor.add_vertex(i, *v)
for i, t in enumerate(self.triangles):
editor.add_cell(i, *t)
editor.close()
return mesh
def get(self):
"""Build vertices from polar coordinates."""
angle, dist = self.values
if len(angle) < 3:
angle = np.array(range(int(angle[0]))) * 360.0 / angle[0]
while len(dist) < len(angle):
dist = dist * 2
dist = np.array(dist)
sides = len(angle)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(sides + 1)
editor.init_cells(sides)
editor.add_vertex(0, 0, 0)
for i in range(1, sides + 1):
editor.add_vertex(i, dist[i - 1] * cos(angle[i - 1] / 180.0 * pi),
dist[i - 1] * sin(angle[i - 1] / 180.0 * pi))
for i in range(sides - 1):
editor.add_cell(i, 0, i + 1, i + 2)
editor.add_cell(sides - 1, 0, sides, 1)
editor.close()
return mesh
def gmsh2xml(ifilename, handler):
"""Convert between .gmsh v2.0 format (http://www.geuz.org/gmsh/) and .xml,
parser implemented as a state machine:
0 = read 'MeshFormat'
1 = read mesh format data
2 = read 'EndMeshFormat'
3 = read 'Nodes'
4 = read number of vertices
5 = read vertices
6 = read 'EndNodes'
7 = read 'Elements'
8 = read number of cells
9 = read cells
10 = done
Afterwards, extract physical region numbers if they are defined in
the mesh file as a mesh function.
"""
print "Converting from Gmsh format (.msh, .gmsh) to DOLFIN XML format"
# The dimension of the gmsh element types supported here as well as the dolfin cell types for each dimension
gmsh_dim = {15: 0, 1: 1, 2: 2, 4: 3}
cell_type_for_dim = {1: "interval", 2: "triangle", 3: "tetrahedron" }
# the gmsh element types supported for conversion
supported_gmsh_element_types = [1, 2, 4, 15]
# Open files
ifile = open(ifilename, "r")
# Scan file for cell type
cell_type = None
highest_dim = 0
line = ifile.readline()
while line:
# Remove newline
if line[-1] == "\n":
line = line[:-1]
# Read dimension
if line.find("$Elements") == 0:
line = ifile.readline()
num_elements = int(line)
if num_elements == 0:
_error("No elements found in gmsh file.")
line = ifile.readline()
# Now iterate through elements to find largest dimension. Gmsh
# format might include elements of lower dimensions in the element list.
# We also need to count number of elements of correct dimensions.
# Also determine which vertices are not used.
dim_count = {0: 0, 1: 0, 2: 0, 3: 0}
vertices_used_for_dim = {0: [], 1: [], 2: [], 3: []}
# Array used to store gmsh tags for 1D (type 1/line), 2D (type 2/triangular) elements and 3D (type 4/tet) elements
tags_for_dim = {0: [], 1: [], 2: [], 3: []}
while line.find("$EndElements") == -1:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
if highest_dim < dim:
highest_dim = dim
node_num_list = [int(node) for node in element[3 + num_tags:]]
vertices_used_for_dim[dim].extend(node_num_list)
if num_tags > 0:
tags_for_dim[dim].append(tuple(int(tag) for tag in element[3:3+num_tags]))
dim_count[dim] += 1
else:
#TODO: output a warning here. "gmsh element type %d not supported" % elem_type
pass
line = ifile.readline()
else:
# Read next line
line = ifile.readline()
# Check that we got the cell type and set num_cells_counted
if highest_dim == 0:
_error("Unable to find cells of supported type.")
num_cells_counted = dim_count[highest_dim]
vertex_set = set(vertices_used_for_dim[highest_dim])
vertices_used_for_dim[highest_dim] = None
vertex_dict = {}
for n,v in enumerate(vertex_set):
vertex_dict[v] = n
# Step to beginning of file
ifile.seek(0)
# Set mesh type
handler.set_mesh_type(cell_type_for_dim[highest_dim], highest_dim)
# Initialise node list (gmsh does not export all vertexes in order)
nodelist = {}
# Current state
state = 0
# Write data
num_vertices_read = 0
num_cells_read = 0
# Only import the dolfin objects if facet markings exist
process_facets = False
if len(tags_for_dim[highest_dim-1]) > 0:
# first construct the mesh
try:
from dolfin import MeshEditor, Mesh
except ImportError:
_error("DOLFIN must be installed to handle Gmsh boundary regions")
mesh = Mesh()
mesh_editor = MeshEditor ()
mesh_editor.open( mesh, highest_dim, highest_dim )
process_facets = True
else:
# TODO: Output a warning or an error here
me = None
while state != 10:
# Read next line
line = ifile.readline()
if not line: break
# Skip comments
if line[0] == '#':
continue
# Remove newline
if line[-1] == "\n":
line = line[:-1]
if state == 0:
if line == "$MeshFormat":
state = 1
elif state == 1:
(version, file_type, data_size) = line.split()
state = 2
elif state == 2:
if line == "$EndMeshFormat":
state = 3
elif state == 3:
if line == "$Nodes":
state = 4
elif state == 4:
num_vertices = len(vertex_dict)
handler.start_vertices(num_vertices)
if process_facets:
mesh_editor.init_vertices ( num_vertices )
state = 5
elif state == 5:
(node_no, x, y, z) = line.split()
node_no = int(node_no)
x,y,z = [float(xx) for xx in (x,y,z)]
if vertex_dict.has_key(node_no):
node_no = vertex_dict[node_no]
else:
continue
nodelist[int(node_no)] = num_vertices_read
handler.add_vertex(num_vertices_read, [x, y, z])
if process_facets:
if highest_dim == 1:
coords = numpy.array([x])
elif highest_dim == 2:
coords = numpy.array([x, y])
elif highest_dim == 3:
coords = numpy.array([x, y, z])
mesh_editor.add_vertex(num_vertices_read, coords)
num_vertices_read +=1
if num_vertices == num_vertices_read:
handler.end_vertices()
state = 6
elif state == 6:
if line == "$EndNodes":
state = 7
elif state == 7:
if line == "$Elements":
state = 8
elif state == 8:
handler.start_cells(num_cells_counted)
if process_facets:
mesh_editor.init_cells( num_cells_counted )
state = 9
elif state == 9:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
else:
dim = 0
if dim == highest_dim:
node_num_list = [vertex_dict[int(node)] for node in element[3 + num_tags:]]
for node in node_num_list:
if not node in nodelist:
_error("Vertex %d of %s %d not previously defined." %
(node, cell_type_for_dim[dim], num_cells_read))
cell_nodes = [nodelist[n] for n in node_num_list]
handler.add_cell(num_cells_read, cell_nodes)
if process_facets:
cell_nodes = numpy.array([nodelist[n] for n in node_num_list], dtype=numpy.uintp)
mesh_editor.add_cell(num_cells_read, cell_nodes)
num_cells_read +=1
if num_cells_counted == num_cells_read:
handler.end_cells()
if process_facets:
mesh_editor.close()
state = 10
elif state == 10:
break
# Write mesh function based on the Physical Regions defined by
# gmsh, but only if they are not all zero. All zero physical
# regions indicate that no physical regions were defined.
if highest_dim not in [1,2,3]:
_error("Gmsh tags not supported for dimension %i. Probably a bug" % dim)
tags = tags_for_dim[highest_dim]
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
handler.start_meshfunction("physical_region", dim, num_cells_counted)
for i, physical_region in enumerate(physical_regions):
handler.add_entity_meshfunction(i, physical_region)
handler.end_meshfunction()
# Now process the facet markers
tags = tags_for_dim[highest_dim-1]
if (len(tags) > 0) and (mesh is not None):
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
mesh.init(highest_dim-1,0)
# Get the facet-node connectivity information (reshape as a row of node indices per facet)
if highest_dim==1:
# for 1d meshes the mesh topology returns the vertex to vertex map, which isn't what we want
# as facets are vertices
facets_as_nodes = numpy.array([[i] for i in range(mesh.num_facets())])
else:
facets_as_nodes = mesh.topology()(highest_dim-1,0)().reshape ( mesh.num_facets(), highest_dim )
# Build the reverse map
nodes_as_facets = {}
for facet in range(mesh.num_facets()):
nodes_as_facets[tuple(facets_as_nodes[facet,:])] = facet
data = [int(0*k) for k in range(mesh.num_facets()) ]
for i, physical_region in enumerate(physical_regions):
nodes = [n-1 for n in vertices_used_for_dim[highest_dim-1][highest_dim*i:(highest_dim*i+highest_dim)]]
nodes.sort()
if physical_region != 0:
try:
index = nodes_as_facets[tuple(nodes)]
data[index] = physical_region
except IndexError:
raise Exception ( "The facet (%d) was not found to mark: %s" % (i, nodes) )
# # Create and initialise the mesh function
handler.start_meshfunction("facet_region", highest_dim-1, mesh.num_facets() )
for index, physical_region in enumerate ( data ):
handler.add_entity_meshfunction(index, physical_region)
handler.end_meshfunction()
# Check that we got all data
if state == 10:
print "Conversion done"
else:
_error("Missing data, unable to convert \n\ Did you use version 2.0 of the gmsh file format?")
# Close files
ifile.close()
def get(self):
"""Part of the regular polygon construction."""
sides, angle = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2) # dimension
editor.init_vertices(angle + 2)
editor.init_cells(angle)
editor.add_vertex(0, 0, 0)
for i in range(0, angle + 1):
editor.add_vertex(i + 1,
cos(2 * pi * i / sides),
sin(2 * pi * i / sides))
editor.add_cell(0, 2, 1, 0)
for i in range(1, angle):
editor.add_cell(i, 0, i + 1, i + 2)
editor.close()
return mesh
def get(self):
"""Single cell."""
a, b, c, d, e = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3) # dimension
editor.init_vertices(4)
editor.init_cells(1)
editor.add_vertex(0, 0, 0, 0)
editor.add_vertex(1, 1, 0, 0)
editor.add_vertex(2, a, b, 0)
editor.add_vertex(3, c, d, e)
editor.add_cell(0, 0, 1, 2, 3)
editor.close()
return mesh
def get(self):
"""Just one cell."""
topx, topy = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(3)
editor.init_cells(1)
editor.add_vertex(0, 0, 0)
editor.add_vertex(1, 1, 0)
editor.add_vertex(2, topx, topy)
editor.add_cell(0, 0, 1, 2)
editor.close()
return mesh
def get(self):
"""One triangle per side with common vertex at (0,0)."""
sides = self.values[0]
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(sides + 1)
editor.init_cells(sides)
editor.add_vertex(0, 0, 0)
for i in range(1, sides + 1):
editor.add_vertex(i,
cos(2 * pi * i / sides),
sin(2 * pi * i / sides))
for i in range(sides - 1):
editor.add_cell(i, 0, i + 1, i + 2)
editor.add_cell(sides - 1, 0, sides, 1)
editor.close()
return mesh
def get_original_mesh(t_mesh_path, mesh, par):
def transform(coordinates, xi, rho):
S = np.exp(coordinates[:, 0] +
coordinates[:, 1] * rho / np.sqrt(1 - rho**2))
v = 50 * coordinates[:, 1] * xi / np.sqrt(1 - rho**2)
new_coords = np.column_stack((S, v))
return new_coords
if os.path.exists(t_mesh_path):
t_mesh = Mesh()
with XDMFFile(t_mesh_path) as f:
f.read(t_mesh)
return t_mesh
# Construct the mesh under transformed variables
new_coords = transform(mesh.coordinates(), xi=par.xi, rho=par.rho)
t_mesh = Mesh()
editor = MeshEditor()
editor.open(t_mesh, 'triangle', 2, 2)
editor.init_vertices(len(new_coords))
editor.init_cells(len(mesh.cells()))
for i, vertex in enumerate(new_coords):
editor.add_vertex(i, vertex)
for i, cell in enumerate(mesh.cells()):
editor.add_cell(i, cell)
editor.close()
with XDMFFile(t_mesh_path) as f:
f.write(t_mesh)
return t_mesh
def get(self):
"""Two cells."""
a, b = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(4)
editor.init_cells(2)
editor.add_vertex(0, 0, 0)
editor.add_vertex(1, 1, 0)
editor.add_vertex(2, a, b)
editor.add_vertex(3, a, -b)
editor.add_cell(0, 0, 1, 2)
editor.add_cell(1, 0, 1, 3)
editor.close()
return mesh
def barycentric_refine(mesh):
from dolfin import Mesh, MeshEditor
# the extension to 3d is straightforward but not yet implemented
assert mesh.topology().dim() is 2
# barycentric refinement
v = mesh.coordinates()
t = mesh.cells()
b = (v[t[:,0],:]+v[t[:,1],:]+v[t[:,2],:])/3
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2);
# add vertices to mesh
nv0 = len(v)
nv1 = nv0 + len(t)
editor.init_vertices(nv1)
for i, vi in enumerate(v):
editor.add_vertex(i, vi[0], vi[1])
for i, vi in enumerate(b):
editor.add_vertex(i + nv0, vi[0], vi[1])
# add cells to the mesh
nt1 = 3*len(t)
editor.init_cells(nt1)
for i, ti in enumerate(t):
editor.add_cell(i*3+0, ti[0], ti[1], nv0 + i)
editor.add_cell(i*3+1, ti[1], ti[2], nv0 + i)
editor.add_cell(i*3+2, ti[2], ti[0], nv0 + i)
# done: create and return mesh object
editor.close()
return mesh
def get(self):
"""One cell."""
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3)
editor.init_vertices(4)
editor.init_cells(1)
editor.add_vertex(0, 0, 0, 0)
editor.add_vertex(1, 1, 1, 0)
editor.add_vertex(2, 0, 1, 1)
editor.add_vertex(3, 1, 0, 1)
editor.add_cell(0, 0, 1, 2, 3)
editor.close()
return mesh
def __init__(self, centers, J, n):
self.centers = centers
self.J = J
self.target = 0.002
self.J /= self.target
# dir_path = os.path.dirname(os.path.realpath(__file__))
# with open(os.path.join(dir_path, '../colorio/data/gamut_triangulation.yaml')) as f:
# data = yaml.safe_load(f)
# self.points = numpy.column_stack([
# data['points'], numpy.zeros(len(data['points']))
# ])
# self.cells = numpy.array(data['cells'])
# self.points, self.cells = colorio.xy_gamut_mesh(0.15)
self.points, self.cells = meshzoo.triangle(n,
corners=numpy.array(
[[0.0, 0.0], [1.0, 0.0],
[0.0, 1.0]]))
# https://bitbucket.org/fenics-project/dolfin/issues/845/initialize-mesh-from-vertices
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh, "triangle", 2, 2)
editor.init_vertices(self.points.shape[0])
editor.init_cells(self.cells.shape[0])
for k, point in enumerate(self.points):
editor.add_vertex(k, point)
for k, cell in enumerate(self.cells):
editor.add_cell(k, cell)
editor.close()
self.V = FunctionSpace(mesh, "CG", 1)
self.Vgrad = VectorFunctionSpace(mesh, "DG", 0)
# self.ux0 = Function(self.V)
# self.uy0 = Function(self.V)
# 0 starting guess
# ax = numpy.zeros(self.V.dim())
# ay = numpy.zeros(self.V.dim())
# Use F(x, y) = (x, y) as starting guess
self.ux0 = project(Expression("x[0]", degree=1), self.V)
self.uy0 = project(Expression("x[1]", degree=1), self.V)
ax = self.ux0.vector().get_local()
ay = self.uy0.vector().get_local()
# Note that alpha doesn't contain the values in the order that one might expect,
# see
# <https://www.allanswered.com/post/awevg/projectexpressionx0-v-vector-get_local-not-in-order/>.
self.alpha = numpy.concatenate([ax, ay])
self.num_f_eval = 0
# Build L as scipy.csr_matrix
u = TrialFunction(self.V)
v = TestFunction(self.V)
L = assemble(dot(grad(u), grad(v)) * dx)
Lmat = as_backend_type(L).mat()
indptr, indices, data = Lmat.getValuesCSR()
size = Lmat.getSize()
self.L = sparse.csr_matrix((data, indices, indptr), shape=size)
self.LT = self.L.getH()
self.dx, self.dy = build_grad_matrices(self.V, centers)
self.dxT = self.dx.getH()
self.dyT = self.dy.getH()
return
def __setstate__(self, d):
"""pickling restore"""
# mesh
verts = d['coordinates']
elems = d['cells']
dim = verts.shape[1]
mesh = Mesh()
ME = MeshEditor()
ME.open(mesh, dim, dim)
ME.init_vertices(verts.shape[0])
ME.init_cells(elems.shape[0])
for i, v in enumerate(verts):
ME.add_vertex(i, v[0], v[1])
for i, c in enumerate(elems):
ME.add_cell(i, c[0], c[1], c[2])
ME.close()
# function space
if d['num_subspaces'] > 1:
V = VectorFunctionSpace(mesh, d['family'], d['degree'])
else:
V = FunctionSpace(mesh, d['family'], d['degree'])
# vector
v = Function(V)
v.vector()[:] = d['array']
self._fefunc = v
def main():
def round_trip_connect(start, end):
result = []
for i in range(start, end):
result.append((i, i+1))
result.append((end, start))
return result
corners, mesh1, mesh2 = generate_meshes(2, 1, 0.3)
points = get_vertices(corners, mesh1, mesh2)
print "points", np.array(points)
info = triangle.MeshInfo()
info.set_points(points)
info.set_facets(round_trip_connect(0, len(corners)-1))
mesh = triangle.build(info, allow_volume_steiner=False, allow_boundary_steiner=False, min_angle=60)
if False:
print "vertices:"
for i, p in enumerate(mesh.points):
print i, p
print "point numbers in triangles:"
for i, t in enumerate(mesh.elements):
print i, t
finemesh = Mesh()
ME = MeshEditor()
ME.open(finemesh,2,2)
ME.init_vertices(len(mesh.points))
ME.init_cells(len(mesh.elements))
for i,v in enumerate(mesh.points):
ME.add_vertex(i,v[0],v[1])
for i,c in enumerate(mesh.elements):
ME.add_cell(i,c[0],c[1],c[2])
ME.close()
triangle.write_gnuplot_mesh("triangles.dat", mesh)
plot(mesh1)
plot(mesh2)
plot(finemesh)
interactive()
def create_submesh(mesh, markers, marker):
"This function allows for a SubMesh-equivalent to be created in parallel"
# Build mesh
submesh = Mesh()
mesh_editor = MeshEditor()
mesh_editor.open(submesh,
mesh.ufl_cell().cellname(),
mesh.ufl_cell().topological_dimension(),
mesh.ufl_cell().geometric_dimension())
# Return empty mesh if no matching markers
if MPI.sum(mpi_comm_world(), int(marker in markers.array())) == 0:
cbc_warning(
"Unable to find matching markers in meshfunction. Submesh is empty."
)
mesh_editor.close()
return submesh
base_cell_indices = np.where(markers.array() == marker)[0]
base_cells = mesh.cells()[base_cell_indices]
base_vertex_indices = np.unique(base_cells.flatten())
base_global_vertex_indices = sorted(
[mesh.topology().global_indices(0)[vi] for vi in base_vertex_indices])
gi = mesh.topology().global_indices(0)
shared_local_indices = set(base_vertex_indices).intersection(
set(mesh.topology().shared_entities(0).keys()))
shared_global_indices = [gi[vi] for vi in shared_local_indices]
unshared_global_indices = list(
set(base_global_vertex_indices) - set(shared_global_indices))
unshared_vertices_dist = distribution(len(unshared_global_indices))
# Number unshared vertices on separate process
idx = sum(unshared_vertices_dist[:MPI.rank(mpi_comm_world())])
base_to_sub_global_indices = {}
for gi in unshared_global_indices:
base_to_sub_global_indices[gi] = idx
idx += 1
# Gather all shared process on process 0 and assign global index
all_shared_global_indices = gather(shared_global_indices,
on_process=0,
flatten=True)
all_shared_global_indices = np.unique(all_shared_global_indices)
shared_base_to_sub_global_indices = {}
idx = int(
MPI.max(mpi_comm_world(),
float(max(base_to_sub_global_indices.values() + [-1e16]))) + 1)
if MPI.rank(mpi_comm_world()) == 0:
for gi in all_shared_global_indices:
shared_base_to_sub_global_indices[int(gi)] = idx
idx += 1
# Broadcast global numbering of all shared vertices
shared_base_to_sub_global_indices = dict(
zip(broadcast(shared_base_to_sub_global_indices.keys(), 0),
broadcast(shared_base_to_sub_global_indices.values(), 0)))
# Join shared and unshared numbering in one dict
base_to_sub_global_indices = dict(
base_to_sub_global_indices.items() +
shared_base_to_sub_global_indices.items())
# Create mapping of local indices
base_to_sub_local_indices = dict(
zip(base_vertex_indices, range(len(base_vertex_indices))))
# Define sub-cells
sub_cells = [None] * len(base_cells)
for i, c in enumerate(base_cells):
sub_cells[i] = [base_to_sub_local_indices[j] for j in c]
# Store vertices as sub_vertices[local_index] = (global_index, coordinates)
sub_vertices = {}
for base_local, sub_local in base_to_sub_local_indices.items():
sub_vertices[sub_local] = (base_to_sub_global_indices[
mesh.topology().global_indices(0)[base_local]],
mesh.coordinates()[base_local])
## Done with base mesh
# Distribute meshdata on (if any) empty processes
sub_cells, sub_vertices = distribute_meshdata(sub_cells, sub_vertices)
global_cell_distribution = distribution(len(sub_cells))
#global_vertex_distribution = distribution(len(sub_vertices))
global_num_cells = MPI.sum(mpi_comm_world(), len(sub_cells))
global_num_vertices = sum(unshared_vertices_dist) + MPI.sum(
mpi_comm_world(), len(all_shared_global_indices))
mesh_editor.init_vertices(len(sub_vertices))
#mesh_editor.init_cells(len(sub_cells))
mesh_editor.init_cells_global(len(sub_cells), global_num_cells)
global_index_start = sum(
global_cell_distribution[:MPI.rank(mesh.mpi_comm())])
for index, cell in enumerate(sub_cells):
if LooseVersion(dolfin_version()) >= LooseVersion("1.6.0"):
mesh_editor.add_cell(index, *cell)
else:
mesh_editor.add_cell(int(index), global_index_start + index,
np.array(cell, dtype=np.uintp))
for local_index, (global_index, coordinates) in sub_vertices.items():
#print coordinates
mesh_editor.add_vertex_global(int(local_index), int(global_index),
coordinates)
mesh_editor.close()
submesh.topology().init(0, len(sub_vertices), global_num_vertices)
submesh.topology().init(mesh.ufl_cell().topological_dimension(),
len(sub_cells), global_num_cells)
# FIXME: Set up shared entities
# What damage does this do?
submesh.topology().shared_entities(0)[0] = []
# The code below sets up shared vertices, but lacks shared facets.
# It is considered incomplete, and therefore commented out
'''
#submesh.topology().shared_entities(0)[0] = []
from dolfin import compile_extension_module
cpp_code = """
void set_shared_entities(Mesh& mesh, std::size_t idx, const Array<std::size_t>& other_processes)
{
std::set<unsigned int> set_other_processes;
for (std::size_t i=0; i<other_processes.size(); i++)
{
set_other_processes.insert(other_processes[i]);
//std::cout << idx << " --> " << other_processes[i] << std::endl;
}
//std::cout << idx << " --> " << set_other_processes[0] << std::endl;
mesh.topology().shared_entities(0)[idx] = set_other_processes;
}
"""
set_shared_entities = compile_extension_module(cpp_code).set_shared_entities
base_se = mesh.topology().shared_entities(0)
se = submesh.topology().shared_entities(0)
for li in shared_local_indices:
arr = np.array(base_se[li], dtype=np.uintp)
sub_li = base_to_sub_local_indices[li]
set_shared_entities(submesh, base_to_sub_local_indices[li], arr)
'''
return submesh
def create_submesh(mesh, markers):
mpi_comm = mesh.mpi_comm()
if not has_pybind11():
mpi_comm = mpi_comm.tompi4py()
assert isinstance(markers, MeshFunctionBool)
assert markers.dim() == mesh.topology().dim()
marker_id = True
# == 1. Extract marked cells == #
# Dolfin does not support a distributed mesh that is empty on some processes.
# cbcpost gets around this by moving a single cell from the a non-empty processor to an empty one.
# Note that, however, this cannot work if the number of marked cell is less than the number of processors.
# In the interest of considering this case, we enable at least one cell (arbitrarily) on each processor.
# We find this solution acceptable for our purposes, despite the increase of the reduced mesh size,
# since we are never actually interested in solving a PDE on the reduced mesh, but rather only in
# assemblying tensors on it and extract their values at some locations.
backup_first_marker_id = None
if marker_id not in markers.array():
backup_first_marker_id = markers.array()[0]
markers.array()[0] = marker_id
assert marker_id in markers.array()
# == 2. Create submesh == #
submesh = Mesh(mesh.mpi_comm())
mesh_editor = MeshEditor()
mesh_editor.open(submesh,
mesh.ufl_cell().cellname(),
mesh.ufl_cell().topological_dimension(),
mesh.ufl_cell().geometric_dimension())
# Extract cells from mesh with specified marker_id
mesh_cell_indices = where(markers.array() == marker_id)[0]
mesh_cells = mesh.cells()[mesh_cell_indices]
mesh_global_cell_indices = sorted([mesh.topology().global_indices(mesh.topology().dim())[cell_index] for cell_index in mesh_cell_indices])
# Get vertices of extracted cells
mesh_vertex_indices = unique(mesh_cells.flatten())
mesh_global_vertex_indices = sorted([mesh.topology().global_indices(0)[vertex_index] for vertex_index in mesh_vertex_indices])
# Number vertices in a way which is independent from the number of processors. To do so ...
# ... first of all collect all vertices from all processors
allgathered_mesh_global_vertex_indices__non_empty_processors = list()
allgathered_mesh_global_vertex_indices__empty_processors = list()
for r in range(mpi_comm.size):
backup_first_marker_id_r = mpi_comm.bcast(backup_first_marker_id, root=r)
if backup_first_marker_id_r is None:
allgathered_mesh_global_vertex_indices__non_empty_processors.extend(mpi_comm.bcast(mesh_global_vertex_indices, root=r))
else:
allgathered_mesh_global_vertex_indices__empty_processors.extend(mpi_comm.bcast(mesh_global_vertex_indices, root=r))
allgathered_mesh_global_vertex_indices__non_empty_processors = sorted(unique(allgathered_mesh_global_vertex_indices__non_empty_processors))
allgathered_mesh_global_vertex_indices__empty_processors = sorted(unique(allgathered_mesh_global_vertex_indices__empty_processors))
# ... then create a dict that will contain the map from mesh global vertex index to submesh global vertex index.
# ... Here make sure to number first "real" vertices (those coming from non empty processors), since the other ones
# ... are just a side effect of the current partitioning!
allgathered_mesh_to_submesh_vertex_global_indices = dict()
_submesh_vertex_global_index = 0
for mesh_vertex_global_index in allgathered_mesh_global_vertex_indices__non_empty_processors:
assert mesh_vertex_global_index not in allgathered_mesh_to_submesh_vertex_global_indices
allgathered_mesh_to_submesh_vertex_global_indices[mesh_vertex_global_index] = _submesh_vertex_global_index
_submesh_vertex_global_index += 1
for mesh_vertex_global_index in allgathered_mesh_global_vertex_indices__empty_processors:
if mesh_vertex_global_index not in allgathered_mesh_to_submesh_vertex_global_indices:
allgathered_mesh_to_submesh_vertex_global_indices[mesh_vertex_global_index] = _submesh_vertex_global_index
_submesh_vertex_global_index += 1
# Number cells in a way which is independent from the number of processors. To do so ...
# ... first of all collect all cells from all processors
allgathered_mesh_global_cell_indices__non_empty_processors = list()
allgathered_mesh_global_cell_indices__empty_processors = list()
for r in range(mpi_comm.size):
backup_first_marker_id_r = mpi_comm.bcast(backup_first_marker_id, root=r)
if backup_first_marker_id_r is None:
allgathered_mesh_global_cell_indices__non_empty_processors.extend(mpi_comm.bcast(mesh_global_cell_indices, root=r))
else:
allgathered_mesh_global_cell_indices__empty_processors.extend(mpi_comm.bcast(mesh_global_cell_indices, root=r))
allgathered_mesh_global_cell_indices__non_empty_processors = sorted(unique(allgathered_mesh_global_cell_indices__non_empty_processors))
allgathered_mesh_global_cell_indices__empty_processors = sorted(unique(allgathered_mesh_global_cell_indices__empty_processors))
# ... then create a dict that will contain the map from mesh global cell index to submesh global cell index.
# ... Here make sure to number first "real" vertices (those coming from non empty processors), since the other ones
# ... are just a side effect of the current partitioning!
allgathered_mesh_to_submesh_cell_global_indices = dict()
_submesh_cell_global_index = 0
for mesh_cell_global_index in allgathered_mesh_global_cell_indices__non_empty_processors:
assert mesh_cell_global_index not in allgathered_mesh_to_submesh_cell_global_indices
allgathered_mesh_to_submesh_cell_global_indices[mesh_cell_global_index] = _submesh_cell_global_index
_submesh_cell_global_index += 1
for mesh_cell_global_index in allgathered_mesh_global_cell_indices__empty_processors:
assert mesh_cell_global_index not in allgathered_mesh_to_submesh_cell_global_indices
allgathered_mesh_to_submesh_cell_global_indices[mesh_cell_global_index] = _submesh_cell_global_index
_submesh_cell_global_index += 1
# Also create a mapping from mesh local vertex index to submesh local vertex index.
mesh_to_submesh_vertex_local_indices = dict(zip(mesh_vertex_indices, list(range(len(mesh_vertex_indices)))))
# Also create a mapping from mesh local cell index to submesh local cell index.
mesh_to_submesh_cell_local_indices = dict(zip(mesh_cell_indices, list(range(len(mesh_cell_indices)))))
# Now, define submesh cells
submesh_cells = list()
for i, c in enumerate(mesh_cells):
submesh_cells.append([mesh_to_submesh_vertex_local_indices[j] for j in c])
# Store vertices as submesh_vertices[local_index] = (global_index, coordinates)
submesh_vertices = dict()
for mesh_vertex_local_index, submesh_vertex_local_index in mesh_to_submesh_vertex_local_indices.items():
submesh_vertices[submesh_vertex_local_index] = (
allgathered_mesh_to_submesh_vertex_global_indices[mesh.topology().global_indices(0)[mesh_vertex_local_index]],
mesh.coordinates()[mesh_vertex_local_index]
)
# Collect the global number of vertices and cells
global_num_cells = mpi_comm.allreduce(len(submesh_cells), op=SUM)
global_num_vertices = len(allgathered_mesh_to_submesh_vertex_global_indices)
# Fill in mesh_editor
mesh_editor.init_vertices_global(len(submesh_vertices), global_num_vertices)
mesh_editor.init_cells_global(len(submesh_cells), global_num_cells)
for local_index, cell_vertices in enumerate(submesh_cells):
if has_pybind11():
mesh_editor.add_cell(local_index, cell_vertices)
else:
mesh_editor.add_cell(local_index, *cell_vertices)
for local_index, (global_index, coordinates) in submesh_vertices.items():
mesh_editor.add_vertex_global(local_index, global_index, coordinates)
mesh_editor.close()
# Initialize topology
submesh.topology().init(0, len(submesh_vertices), global_num_vertices)
submesh.topology().init(mesh.ufl_cell().topological_dimension(), len(submesh_cells), global_num_cells)
# Correct the global index of cells
for local_index in range(len(submesh_cells)):
submesh.topology().set_global_index(
submesh.topology().dim(),
local_index,
allgathered_mesh_to_submesh_cell_global_indices[mesh_global_cell_indices[local_index]]
)
# == 3. Store (local) mesh to/from submesh map for cells, facets and vertices == #
# Cells
submesh.mesh_to_submesh_cell_local_indices = mesh_to_submesh_cell_local_indices
submesh.submesh_to_mesh_cell_local_indices = mesh_cell_indices
# Vertices
submesh.mesh_to_submesh_vertex_local_indices = mesh_to_submesh_vertex_local_indices
submesh.submesh_to_mesh_vertex_local_indices = mesh_vertex_indices
# Facets
mesh_vertices_to_mesh_facets = dict()
mesh_facets_to_mesh_vertices = dict()
for mesh_cell_index in mesh_cell_indices:
mesh_cell = Cell(mesh, mesh_cell_index)
for mesh_facet in facets(mesh_cell):
mesh_facet_vertices = list()
for mesh_facet_vertex in vertices(mesh_facet):
mesh_facet_vertices.append(mesh_facet_vertex.index())
mesh_facet_vertices = tuple(sorted(mesh_facet_vertices))
if mesh_facet_vertices in mesh_vertices_to_mesh_facets:
assert mesh_vertices_to_mesh_facets[mesh_facet_vertices] == mesh_facet.index()
else:
mesh_vertices_to_mesh_facets[mesh_facet_vertices] = mesh_facet.index()
if mesh_facet.index() in mesh_facets_to_mesh_vertices:
assert mesh_facets_to_mesh_vertices[mesh_facet.index()] == mesh_facet_vertices
else:
mesh_facets_to_mesh_vertices[mesh_facet.index()] = mesh_facet_vertices
submesh_vertices_to_submesh_facets = dict()
submesh_facets_to_submesh_vertices = dict()
for submesh_facet in facets(submesh):
submesh_facet_vertices = list()
for submesh_facet_vertex in vertices(submesh_facet):
submesh_facet_vertices.append(submesh_facet_vertex.index())
submesh_facet_vertices = tuple(sorted(submesh_facet_vertices))
assert submesh_facet_vertices not in submesh_vertices_to_submesh_facets
submesh_vertices_to_submesh_facets[submesh_facet_vertices] = submesh_facet.index()
assert submesh_facet.index() not in submesh_facets_to_submesh_vertices
submesh_facets_to_submesh_vertices[submesh_facet.index()] = submesh_facet_vertices
mesh_to_submesh_facets_local_indices = dict()
for (mesh_facet_index, mesh_vertices) in mesh_facets_to_mesh_vertices.items():
submesh_vertices = tuple(sorted([submesh.mesh_to_submesh_vertex_local_indices[mesh_vertex] for mesh_vertex in mesh_vertices]))
submesh_facet_index = submesh_vertices_to_submesh_facets[submesh_vertices]
mesh_to_submesh_facets_local_indices[mesh_facet_index] = submesh_facet_index
submesh_to_mesh_facets_local_indices = dict()
for (submesh_facet_index, submesh_vertices) in submesh_facets_to_submesh_vertices.items():
mesh_vertices = tuple(sorted([submesh.submesh_to_mesh_vertex_local_indices[submesh_vertex] for submesh_vertex in submesh_vertices]))
mesh_facet_index = mesh_vertices_to_mesh_facets[mesh_vertices]
submesh_to_mesh_facets_local_indices[submesh_facet_index] = mesh_facet_index
submesh.mesh_to_submesh_facet_local_indices = mesh_to_submesh_facets_local_indices
submesh.submesh_to_mesh_facet_local_indices = list()
assert min(submesh_to_mesh_facets_local_indices.keys()) == 0
assert max(submesh_to_mesh_facets_local_indices.keys()) == len(submesh_to_mesh_facets_local_indices.keys()) - 1
for submesh_facet_index in range(len(submesh_to_mesh_facets_local_indices)):
submesh.submesh_to_mesh_facet_local_indices.append(submesh_to_mesh_facets_local_indices[submesh_facet_index])
# == 3bis. Prepare (temporary) global indices of facets == #
# Wrapper to DistributedMeshTools::number_entities
if has_pybind11():
cpp_code = """
#include <pybind11/pybind11.h>
#include <dolfin/mesh/DistributedMeshTools.h>
#include <dolfin/mesh/Mesh.h>
void initialize_global_indices(std::shared_ptr<dolfin::Mesh> mesh, std::size_t dim)
{
dolfin::DistributedMeshTools::number_entities(*mesh, dim);
}
PYBIND11_MODULE(SIGNATURE, m)
{
m.def("initialize_global_indices", &initialize_global_indices);
}
"""
initialize_global_indices = compile_cpp_code(cpp_code).initialize_global_indices
else:
cpp_code = """
void initialize_global_indices(Mesh & mesh, std::size_t dim)
{
DistributedMeshTools::number_entities(mesh, dim);
}
"""
initialize_global_indices = compile_extension_module(cpp_code, additional_system_headers=["dolfin/mesh/DistributedMeshTools.h"]).initialize_global_indices
initialize_global_indices(mesh, mesh.topology().dim() - 1)
# Prepare global indices of facets
mesh_facets_local_to_global_indices = dict()
for mesh_cell_index in mesh_cell_indices:
mesh_cell = Cell(mesh, mesh_cell_index)
for mesh_facet in facets(mesh_cell):
mesh_facets_local_to_global_indices[mesh_facet.index()] = mesh_facet.global_index()
mesh_facets_global_indices_in_submesh = list()
for mesh_facet_local_index in mesh_to_submesh_facets_local_indices.keys():
mesh_facets_global_indices_in_submesh.append(mesh_facets_local_to_global_indices[mesh_facet_local_index])
allgathered__mesh_facets_global_indices_in_submesh = list()
for r in range(mpi_comm.size):
allgathered__mesh_facets_global_indices_in_submesh.extend(mpi_comm.bcast(mesh_facets_global_indices_in_submesh, root=r))
allgathered__mesh_facets_global_indices_in_submesh = sorted(set(allgathered__mesh_facets_global_indices_in_submesh))
mesh_to_submesh_facets_global_indices = dict()
for (submesh_facet_global_index, mesh_facet_global_index) in enumerate(allgathered__mesh_facets_global_indices_in_submesh):
mesh_to_submesh_facets_global_indices[mesh_facet_global_index] = submesh_facet_global_index
submesh_facets_local_to_global_indices = dict()
for (submesh_facet_local_index, mesh_facet_local_index) in submesh_to_mesh_facets_local_indices.items():
submesh_facets_local_to_global_indices[submesh_facet_local_index] = mesh_to_submesh_facets_global_indices[mesh_facets_local_to_global_indices[mesh_facet_local_index]]
# == 4. Assign shared vertices == #
shared_entities_dimensions = {
"vertex": 0,
"facet": submesh.topology().dim() - 1,
"cell": submesh.topology().dim()
}
shared_entities_class = {
"vertex": Vertex,
"facet": Facet,
"cell": Cell
}
shared_entities_iterator = {
"vertex": vertices,
"facet": facets,
"cell": cells
}
shared_entities_submesh_global_index_getter = {
"vertex": lambda entity: entity.global_index(),
"facet": lambda entity: submesh_facets_local_to_global_indices[entity.index()],
"cell": lambda entity: entity.global_index()
}
for entity_type in ["vertex", "facet", "cell"]: # do not use .keys() because the order is important
dim = shared_entities_dimensions[entity_type]
class_ = shared_entities_class[entity_type]
iterator = shared_entities_iterator[entity_type]
submesh_global_index_getter = shared_entities_submesh_global_index_getter[entity_type]
# Get shared entities from mesh. A subset of these will end being shared entities also the submesh
# (thanks to the fact that we do not redistribute cells from one processor to another)
if mpi_comm.size > 1: # some entities may not be initialized in serial, since they are not needed
assert mesh.topology().have_shared_entities(dim), "Mesh shared entities have not been initialized for dimension " + str(dim)
if mesh.topology().have_shared_entities(dim): # always true in parallel (when really needed)
# However, it may happen that an entity which has been selected is not shared anymore because only one of
# the sharing processes has it in the submesh. For instance, consider the case
# of two cells across the interface (located on a facet f) between two processors. It may happen that
# only one of the two cells is selected: the facet f and its vertices are not shared anymore!
# For this reason, we create a new dict from global entity index to processors sharing them. Thus ...
# ... first of all get global indices corresponding to local entities
if entity_type in ["vertex", "cell"]:
assert submesh.topology().have_global_indices(dim), "Submesh global indices have not been initialized for dimension " + str(dim)
submesh_local_entities_global_index = list()
submesh_local_entities_global_to_local_index = dict()
for entity in iterator(submesh):
local_entity_index = entity.index()
global_entity_index = submesh_global_index_getter(entity)
submesh_local_entities_global_index.append(global_entity_index)
submesh_local_entities_global_to_local_index[global_entity_index] = local_entity_index
# ... then gather all global indices from all processors
gathered__submesh_local_entities_global_index = list() # over processor id
for r in range(mpi_comm.size):
gathered__submesh_local_entities_global_index.append(mpi_comm.bcast(submesh_local_entities_global_index, root=r))
# ... then create dict from global index to processors sharing it
submesh_shared_entities__global = dict()
for r in range(mpi_comm.size):
for global_entity_index in gathered__submesh_local_entities_global_index[r]:
if global_entity_index not in submesh_shared_entities__global:
submesh_shared_entities__global[global_entity_index] = list()
submesh_shared_entities__global[global_entity_index].append(r)
# ... and finally popuplate shared entities dict, which is the same as the dict above except that
# the current processor rank is removed and a local indexing is used
submesh_shared_entities = dict() # from local index to list of integers
for (global_entity_index, processors) in submesh_shared_entities__global.items():
if (
mpi_comm.rank in processors # only local entities
and
len(processors) > 1 # it was still shared after submesh extraction
):
other_processors_list = list(processors)
other_processors_list.remove(mpi_comm.rank)
other_processors = array(other_processors_list, dtype=uintp)
submesh_shared_entities[submesh_local_entities_global_to_local_index[global_entity_index]] = other_processors
# Need an extension module to populate shared_entities because in python each call to shared_entities
# returns a temporary.
if has_pybind11():
cpp_code = """
#include <Eigen/Core>
#include <pybind11/pybind11.h>
#include <pybind11/eigen.h>
#include <dolfin/mesh/Mesh.h>
using OtherProcesses = Eigen::Ref<const Eigen::Matrix<std::size_t, Eigen::Dynamic, 1>>;
void set_shared_entities(std::shared_ptr<dolfin::Mesh> submesh, std::size_t idx, const OtherProcesses other_processes, std::size_t dim)
{
std::set<unsigned int> set_other_processes;
for (std::size_t i(0); i < other_processes.size(); i++)
set_other_processes.insert(other_processes[i]);
submesh->topology().shared_entities(dim)[idx] = set_other_processes;
}
PYBIND11_MODULE(SIGNATURE, m)
{
m.def("set_shared_entities", &set_shared_entities);
}
"""
set_shared_entities = compile_cpp_code(cpp_code).set_shared_entities
else:
cpp_code = """
void set_shared_entities(Mesh & submesh, std::size_t idx, const Array<std::size_t>& other_processes, std::size_t dim)
{
std::set<unsigned int> set_other_processes;
for (std::size_t i(0); i < other_processes.size(); i++)
set_other_processes.insert(other_processes[i]);
submesh.topology().shared_entities(dim)[idx] = set_other_processes;
}
"""
set_shared_entities = compile_extension_module(cpp_code).set_shared_entities
for (submesh_entity_local_index, other_processors) in submesh_shared_entities.items():
set_shared_entities(submesh, submesh_entity_local_index, other_processors, dim)
log(DEBUG, "Local indices of shared entities for dimension " + str(dim) + ": " + str(list(submesh.topology().shared_entities(0).keys())))
log(DEBUG, "Global indices of shared entities for dimension " + str(dim) + ": " + str([class_(submesh, local_index).global_index() for local_index in submesh.topology().shared_entities(dim).keys()]))
# == 5. Also initialize submesh facets global indices, now that shared facets have been computed == #
initialize_global_indices(submesh, submesh.topology().dim() - 1) # note that DOLFIN might change the numbering when compared to the one at 3bis
# == 6. Restore backup_first_marker_id and return == #
if backup_first_marker_id is not None:
markers.array()[0] = backup_first_marker_id
return submesh
def gmsh2xml(ifilename, handler):
"""Convert between .gmsh v2.0 format (http://www.geuz.org/gmsh/) and .xml,
parser implemented as a state machine:
0 = read 'MeshFormat'
1 = read mesh format data
2 = read 'EndMeshFormat'
3 = read 'Nodes'
4 = read number of vertices
5 = read vertices
6 = read 'EndNodes'
7 = read 'Elements'
8 = read number of cells
9 = read cells
10 = done
Afterwards, extract physical region numbers if they are defined in
the mesh file as a mesh function.
"""
print("Converting from Gmsh format (.msh, .gmsh) to DOLFIN XML format")
# The dimension of the gmsh element types supported here as well as the dolfin cell types for each dimension
gmsh_dim = {15: 0, 1: 1, 2: 2, 4: 3}
cell_type_for_dim = {1: "interval", 2: "triangle", 3: "tetrahedron" }
# the gmsh element types supported for conversion
supported_gmsh_element_types = [1, 2, 4, 15]
# Open files
ifile = open(ifilename, "r")
# Scan file for cell type
cell_type = None
highest_dim = 0
line = ifile.readline()
while line:
# Remove newline
line = line.rstrip("\n\r")
# Read dimension
if line.find("$Elements") == 0:
line = ifile.readline()
num_elements = int(line)
if num_elements == 0:
_error("No elements found in gmsh file.")
line = ifile.readline()
# Now iterate through elements to find largest dimension. Gmsh
# format might include elements of lower dimensions in the element list.
# We also need to count number of elements of correct dimensions.
# Also determine which vertices are not used.
dim_count = {0: 0, 1: 0, 2: 0, 3: 0}
vertices_used_for_dim = {0: [], 1: [], 2: [], 3: []}
# Array used to store gmsh tags for 1D (type 1/line), 2D (type 2/triangular) elements and 3D (type 4/tet) elements
tags_for_dim = {0: [], 1: [], 2: [], 3: []}
while line.find("$EndElements") == -1:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
if highest_dim < dim:
highest_dim = dim
node_num_list = [int(node) for node in element[3 + num_tags:]]
vertices_used_for_dim[dim].extend(node_num_list)
if num_tags > 0:
tags_for_dim[dim].append(tuple(int(tag) for tag in element[3:3+num_tags]))
dim_count[dim] += 1
else:
#TODO: output a warning here. "gmsh element type %d not supported" % elem_type
pass
line = ifile.readline()
else:
# Read next line
line = ifile.readline()
# Check that we got the cell type and set num_cells_counted
if highest_dim == 0:
_error("Unable to find cells of supported type.")
num_cells_counted = dim_count[highest_dim]
vertex_set = set(vertices_used_for_dim[highest_dim])
vertices_used_for_dim[highest_dim] = None
vertex_dict = {}
for n,v in enumerate(vertex_set):
vertex_dict[v] = n
# Step to beginning of file
ifile.seek(0)
# Set mesh type
handler.set_mesh_type(cell_type_for_dim[highest_dim], highest_dim)
# Initialise node list (gmsh does not export all vertexes in order)
nodelist = {}
# Current state
state = 0
# Write data
num_vertices_read = 0
num_cells_read = 0
# Only import the dolfin objects if facet markings exist
process_facets = False
if len(tags_for_dim[highest_dim-1]) > 0:
# first construct the mesh
try:
from dolfin import MeshEditor, Mesh
except ImportError:
_error("DOLFIN must be installed to handle Gmsh boundary regions")
mesh = Mesh()
mesh_editor = MeshEditor ()
mesh_editor.open( mesh, highest_dim, highest_dim )
process_facets = True
else:
# TODO: Output a warning or an error here
me = None
while state != 10:
# Read next line
line = ifile.readline()
if not line: break
# Skip comments
if line[0] == '#':
continue
# Remove newline
line = line.rstrip("\n\r")
if state == 0:
if line == "$MeshFormat":
state = 1
elif state == 1:
(version, file_type, data_size) = line.split()
state = 2
elif state == 2:
if line == "$EndMeshFormat":
state = 3
elif state == 3:
if line == "$Nodes":
state = 4
elif state == 4:
num_vertices = len(vertex_dict)
handler.start_vertices(num_vertices)
if process_facets:
mesh_editor.init_vertices_global(num_vertices, num_vertices)
state = 5
elif state == 5:
(node_no, x, y, z) = line.split()
node_no = int(node_no)
x,y,z = [float(xx) for xx in (x,y,z)]
if node_no in vertex_dict:
node_no = vertex_dict[node_no]
else:
continue
nodelist[int(node_no)] = num_vertices_read
handler.add_vertex(num_vertices_read, [x, y, z])
if process_facets:
if highest_dim == 1:
coords = numpy.array([x])
elif highest_dim == 2:
coords = numpy.array([x, y])
elif highest_dim == 3:
coords = numpy.array([x, y, z])
mesh_editor.add_vertex(num_vertices_read, coords)
num_vertices_read +=1
if num_vertices == num_vertices_read:
handler.end_vertices()
state = 6
elif state == 6:
if line == "$EndNodes":
state = 7
elif state == 7:
if line == "$Elements":
state = 8
elif state == 8:
handler.start_cells(num_cells_counted)
if process_facets:
mesh_editor.init_cells_global(num_cells_counted, num_cells_counted)
state = 9
elif state == 9:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
else:
dim = 0
if dim == highest_dim:
node_num_list = [vertex_dict[int(node)] for node in element[3 + num_tags:]]
for node in node_num_list:
if not node in nodelist:
_error("Vertex %d of %s %d not previously defined." %
(node, cell_type_for_dim[dim], num_cells_read))
cell_nodes = [nodelist[n] for n in node_num_list]
handler.add_cell(num_cells_read, cell_nodes)
if process_facets:
cell_nodes = numpy.array([nodelist[n] for n in node_num_list], dtype=numpy.uintp)
mesh_editor.add_cell(num_cells_read, cell_nodes)
num_cells_read +=1
if num_cells_counted == num_cells_read:
handler.end_cells()
if process_facets:
mesh_editor.close()
state = 10
elif state == 10:
break
# Write mesh function based on the Physical Regions defined by
# gmsh, but only if they are not all zero. All zero physical
# regions indicate that no physical regions were defined.
if highest_dim not in [1,2,3]:
_error("Gmsh tags not supported for dimension %i. Probably a bug" % dim)
tags = tags_for_dim[highest_dim]
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
handler.start_meshfunction("physical_region", dim, num_cells_counted)
for i, physical_region in enumerate(physical_regions):
handler.add_entity_meshfunction(i, physical_region)
handler.end_meshfunction()
# Now process the facet markers
tags = tags_for_dim[highest_dim-1]
if (len(tags) > 0) and (mesh is not None):
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
mesh.init(highest_dim-1,0)
# Get the facet-node connectivity information (reshape as a row of node indices per facet)
if highest_dim==1:
# for 1d meshes the mesh topology returns the vertex to vertex map, which isn't what we want
# as facets are vertices
facets_as_nodes = numpy.array([[i] for i in range(mesh.num_facets())])
else:
facets_as_nodes = mesh.topology()(highest_dim-1,0)().reshape ( mesh.num_facets(), highest_dim )
# Build the reverse map
nodes_as_facets = {}
for facet in range(mesh.num_facets()):
nodes_as_facets[tuple(facets_as_nodes[facet,:])] = facet
data = [int(0*k) for k in range(mesh.num_facets()) ]
for i, physical_region in enumerate(physical_regions):
nodes = [n-1 for n in vertices_used_for_dim[highest_dim-1][highest_dim*i:(highest_dim*i+highest_dim)]]
nodes.sort()
if physical_region != 0:
try:
index = nodes_as_facets[tuple(nodes)]
data[index] = physical_region
except IndexError:
raise Exception ( "The facet (%d) was not found to mark: %s" % (i, nodes) )
# Create and initialise the mesh function
handler.start_meshfunction("facet_region", highest_dim-1, mesh.num_facets() )
for index, physical_region in enumerate ( data ):
handler.add_entity_meshfunction(index, physical_region)
handler.end_meshfunction()
# Check that we got all data
if state == 10:
print("Conversion done")
else:
_error("Missing data, unable to convert \n\ Did you use version 2.0 of the gmsh file format?")
# Close files
ifile.close()
def iterkeys(self): # real signature unknown; restored from __doc__
""" D.iterkeys() -> an iterator over the keys of D """
for k in self._entity_values.iterkeys():
# @todo - how do we get the entity back rather than our handle???
yield MeshEntity(self._mesh, *k)
def itervalues(self): # real signature unknown; restored from __doc__
""" D.itervalues() -> an iterator over the values of D """
for v in self._entity_values.itervalues():
# @todo - how do we get the entity back rather than our handle???
yield v
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2) # topo_dim = 2, geom dim = 2
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)
def fit2d(x0, y0, points, cells, lmbda, degree=1, solver="sparse"):
# Convert points, cells to dolfin mesh
editor = MeshEditor()
mesh = Mesh()
# topological and geometrical dimension 2
editor.open(mesh, "triangle", 2, 2, 1)
editor.init_vertices(len(points))
editor.init_cells(len(cells))
for k, point in enumerate(points):
editor.add_vertex(k, point[:2])
for k, cell in enumerate(cells.astype(numpy.uintp)):
editor.add_cell(k, cell)
editor.close()
V = FunctionSpace(mesh, "CG", degree)
return fit(x0, y0, V, lmbda, solver=solver)
def gmsh_to_dolfin_mesh(ifilename, handler):
"""Convert between .gmsh v2.0 format (http://www.geuz.org/gmsh/) and .xml,
parser implemented as a state machine:
0 = read 'MeshFormat'
1 = read mesh format data
2 = read 'EndMeshFormat'
3 = read 'Nodes'
4 = read number of vertices
5 = read vertices
6 = read 'EndNodes'
7 = read 'Elements'
8 = read number of cells
9 = read cells
10 = done
Afterwards, extract physical region numbers if they are defined in
the mesh file as a mesh function.
"""
print "Converting from Gmsh format (.msh, .gmsh) to DOLFIN XML format"
# The dimension of the gmsh element types supported here as well as the dolfin cell types for each dimension
gmsh_dim = {1: 1, 2: 2, 4: 3}
gmsh_cell_type = {1: "interval", 2: "triangle", 3: "tetrahedron"}
# the gmsh element types supported for conversion
supported_gmsh_element_types = [1, 2, 4]
# Open files
ifile = open(ifilename, "r")
# Scan file for cell type
cell_type = None
highest_dim = 0
line = ifile.readline()
while line:
# Remove newline
if line[-1] == "\n":
line = line[:-1]
# Read dimension
if line.find("$Elements") == 0:
line = ifile.readline()
num_elements = int(line)
num_cells_counted = 0
if num_elements == 0:
_error("No elements found in gmsh file.")
line = ifile.readline()
# Now iterate through elements to find largest dimension. Gmsh
# format might include elements of lower dimensions in the element list.
# We also need to count number of elements of correct dimensions.
# Also determine which vertices are not used.
dim_count = {1: 0, 2: 0, 3: 0}
vertices_used = {1: [], 2: [], 3: []}
# Array used to store gmsh tags for 1D (type 1/line), 2D (type 2/triangular) elements and 3D (type 4/tet) elements
tags_for_dim = {1: [], 2: [], 3: []}
while line.find("$EndElements") == -1:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
if highest_dim < dim:
highest_dim = dim
node_num_list = [
int(node) for node in element[3 + num_tags:]
]
vertices_used[dim].extend(node_num_list)
if num_tags > 0:
tags_for_dim[dim].append(
tuple(int(tag) for tag in element[3:3 + num_tags]))
dim_count[dim] += 1
else:
#TODO: output a warning here. "gmsh element type %d not supported" % elem_type
pass
line = ifile.readline()
else:
# Read next line
line = ifile.readline()
# Check that we got the cell type and set num_cells_counted
if highest_dim == 0:
_error("Unable to find cells of supported type.")
num_cells_counted = dim_count[highest_dim]
vertex_set = set(vertices_used[highest_dim])
vertices_used[highest_dim] = None
vertex_dict = {}
for n, v in enumerate(vertex_set):
vertex_dict[v] = n
# Step to beginning of file
ifile.seek(0)
# Set mesh type
handler.set_mesh_type(gmsh_cell_type[highest_dim], highest_dim)
# Initialise node list (gmsh does not export all vertexes in order)
nodelist = {}
# Current state
state = 0
# Write data
num_vertices_read = 0
num_cells_read = 0
# Now handle the facet markings
if len(tags_for_dim[highest_dim - 1]) > 0:
# first construct the mesh
from dolfin import MeshEditor, Mesh
mesh = Mesh()
me = MeshEditor()
me.open(mesh, highest_dim, highest_dim)
else:
me = None
while state != 10:
# Read next line
line = ifile.readline()
if not line: break
# Skip comments
if line[0] == '#':
continue
# Remove newline
if line[-1] == "\n":
line = line[:-1]
if state == 0:
if line == "$MeshFormat":
state = 1
elif state == 1:
(version, file_type, data_size) = line.split()
state = 2
elif state == 2:
if line == "$EndMeshFormat":
state = 3
elif state == 3:
if line == "$Nodes":
state = 4
elif state == 4:
num_vertices = len(vertex_dict)
handler.start_vertices(num_vertices)
if me is not None:
me.init_vertices(num_vertices)
state = 5
elif state == 5:
(node_no, x, y, z) = line.split()
node_no = int(node_no)
x, y, z = [float(xx) for xx in (x, y, z)]
if vertex_dict.has_key(node_no):
node_no = vertex_dict[node_no]
else:
continue
nodelist[int(node_no)] = num_vertices_read
handler.add_vertex(num_vertices_read, [x, y, z])
if me is not None:
if highest_dim == 1:
me.add_vertex(num_vertices_read, x)
elif highest_dim == 2:
me.add_vertex(num_vertices_read, x, y)
elif highest_dim == 3:
me.add_vertex(num_vertices_read, x, y, z)
num_vertices_read += 1
if num_vertices == num_vertices_read:
handler.end_vertices()
state = 6
elif state == 6:
if line == "$EndNodes":
state = 7
elif state == 7:
if line == "$Elements":
state = 8
elif state == 8:
handler.start_cells(num_cells_counted)
if me is not None:
me.init_cells(num_cells_counted)
state = 9
elif state == 9:
element = line.split()
elem_type = int(element[1])
num_tags = int(element[2])
if elem_type in supported_gmsh_element_types:
dim = gmsh_dim[elem_type]
else:
dim = 0
if dim == highest_dim:
node_num_list = [
vertex_dict[int(node)] for node in element[3 + num_tags:]
]
for node in node_num_list:
if not node in nodelist:
_error("Vertex %d of %s %d not previously defined." %
(node, gmsh_cell_type[dim], num_cells_read))
cell_nodes = [nodelist[n] for n in node_num_list]
handler.add_cell(num_cells_read, cell_nodes)
if me is not None:
me.add_cell(num_cells_read, *cell_nodes)
num_cells_read += 1
if num_cells_counted == num_cells_read:
handler.end_cells()
if me is not None:
me.close()
state = 10
elif state == 10:
break
# Write mesh function based on the Physical Regions defined by
# gmsh, but only if they are not all zero. All zero physical
# regions indicate that no physical regions were defined.
if highest_dim not in [1, 2, 3]:
_error("Gmsh tags not supported for dimension %i. Probably a bug" %
dim)
tags = tags_for_dim[highest_dim]
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
handler.start_meshfunction("physical_region", dim, num_cells_counted)
for i, physical_region in enumerate(physical_regions):
handler.add_entity_meshfunction(i, physical_region)
handler.end_meshfunction()
# Now process the facet markers
tags = tags_for_dim[highest_dim - 1]
if len(tags) > 0:
print tags
print vertices_used[highest_dim - 1]
physical_regions = tuple(tag[0] for tag in tags)
if not all(tag == 0 for tag in physical_regions):
mesh.init(highest_dim - 1, 0)
# Get the facet-node connectivity information (reshape as a row of node indices per facet)
facets_as_nodes = mesh.topology()(highest_dim - 1, 0)().reshape(
mesh.num_facets(), highest_dim)
# from dolfin import MeshFunction
# # Create and initialise the mesh function
# facet_mark_function = MeshFunction ( 'uint', mesh, highest_dim-1 )
# facet_mark_function.set_all( 0 )
handler.start_meshfunction("facet_region", highest_dim - 1,
mesh.num_facets())
facets_to_check = range(mesh.num_facets())
data = [int(0 * k) for k in range(len(facets_to_check))]
for i, physical_region in enumerate(physical_regions):
nodes = [
n - 1
for n in vertices_used[highest_dim -
1][2 * i:(2 * i + highest_dim)]
]
nodes.sort()
if physical_region != 0:
found = False
for j in range(len(facets_to_check)):
index = facets_to_check[j]
if all(facets_as_nodes[index, k] == nodes[k]
for k in range(len(nodes))):
found = True
facets_to_check.pop(j)
# set the value of the mesh function
# facet_mark_function[index] = physical_region
data[index] = physical_region
break
if not found:
raise Exception(
"The facet (%d) was not found to mark: %s" %
(i, nodes))
# fname = os.path.splitext('tmp.xml')[0]
# mesh_function_file = File("%s_%s.xml" % (fname, "facet_region"))
# mesh_function_file << facet_mark_function
for index, physical_region in enumerate(data):
handler.add_entity_meshfunction(index, physical_region)
handler.end_meshfunction()
mf = MeshFunction('uint', mesh, 'tmp_facet_region.xml')
plot(mf, interactive=True)
# Check that we got all data
if state == 10:
print "Conversion done"
else:
_error(
"Missing data, unable to convert \n\ Did you use version 2.0 of the gmsh file format?"
)
# Close files
ifile.close()
def _fit_dolfin(x0,
y0,
points,
cells,
lmbda: float,
degree: int = 1,
solver: str = "lsqr"):
from dolfin import (
BoundingBoxTree,
Cell,
EigenMatrix,
FacetNormal,
Function,
FunctionSpace,
Mesh,
MeshEditor,
Point,
TestFunction,
TrialFunction,
assemble,
dot,
ds,
dx,
grad,
)
def _assemble_eigen(form):
L = EigenMatrix()
assemble(form, tensor=L)
return L
def _build_eval_matrix(V, points):
"""Build the sparse m-by-n matrix that maps a coefficient set for a function in
V to the values of that function at m given points."""
# See <https://www.allanswered.com/post/lkbkm/#zxqgk>
mesh = V.mesh()
bbt = BoundingBoxTree()
bbt.build(mesh)
dofmap = V.dofmap()
el = V.element()
sdim = el.space_dimension()
rows = []
cols = []
data = []
for i, x in enumerate(points):
cell_id = bbt.compute_first_entity_collision(Point(*x))
cell = Cell(mesh, cell_id)
coordinate_dofs = cell.get_vertex_coordinates()
rows.append(np.full(sdim, i))
cols.append(dofmap.cell_dofs(cell_id))
v = el.evaluate_basis_all(x, coordinate_dofs, cell_id)
data.append(v)
rows = np.concatenate(rows)
cols = np.concatenate(cols)
data = np.concatenate(data)
m = len(points)
n = V.dim()
matrix = sparse.csr_matrix((data, (rows, cols)), shape=(m, n))
return matrix
editor = MeshEditor()
mesh = Mesh()
# Convert points, cells to dolfin mesh
if cells.shape[1] == 2:
editor.open(mesh, "interval", 1, 1, 1)
else:
# can only handle triangles for now
assert cells.shape[1] == 3
# topological and geometrical dimension 2
editor.open(mesh, "triangle", 2, 2, 1)
editor.init_vertices(len(points))
editor.init_cells(len(cells))
for k, point in enumerate(points):
editor.add_vertex(k, point)
for k, cell in enumerate(cells.astype(np.uintp)):
editor.add_cell(k, cell)
editor.close()
V = FunctionSpace(mesh, "CG", degree)
u = TrialFunction(V)
v = TestFunction(V)
mesh = V.mesh()
n = FacetNormal(mesh)
# omega = assemble(1 * dx(mesh))
A = _assemble_eigen(dot(grad(u), grad(v)) * dx -
dot(n, grad(u)) * v * ds).sparray()
A *= lmbda
E = _build_eval_matrix(V, x0)
# mass matrix
M = _assemble_eigen(u * v * dx).sparray()
x = _solve(A, M, E, y0, solver)
u = Function(V)
u.vector().set_local(x)
return u
def get_reference_element(dim=2):
nodes, cell = get_reference_coordinates(dim)
cells = np.atleast_2d(np.arange(
dim + 1, dtype=np.uintp)) # connection of nodes (defines element)
# this piece of code creates a mesh containing one element only
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, cell, dim, dim)
editor.init_vertices(dim + 1)
editor.init_cells(1)
for i, n in enumerate(nodes):
p = Point(n)
editor.add_vertex(i, p)
for i, n in enumerate(cells):
editor.add_cell(i, n)
editor.close()
return mesh
def setUp(self, *args, **kwargs):
self.mesh = Mesh()
editor = MeshEditor()
editor.open(self.mesh, 2, 2) # topo_dim = 2, geom dim = 2
editor.init_vertices(6)
editor.init_cells(2)
vertex_0 = Vertex(self.mesh, 0)
vertex_1 = Vertex(self.mesh, 1)
vertex_2 = Vertex(self.mesh, 2)
vertex_3 = Vertex(self.mesh, 3)
vertex_4 = Vertex(self.mesh, 4)
vertex_5 = Vertex(self.mesh, 5)
editor.add_cell(0,1,2,3)
editor.add_cell(1,0,2,3)
editor.close()
def IcosahedralSphereMesh(level, layers):
from dolfin import Mesh, MeshEditor, File
# generate vertices and cells
(vertices, cells) = generate_icoshedral_sphere_mesh( level, layers)
# init mesh and mesh editor helper
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3);
# add vertices to mesh
nVert = len(vertices)
editor.init_vertices(nVert)
verts = vertices.items()
#verts = sorted(verts, key=lambda key: key[1])
for v in verts:
editor.add_vertex(v[1], v[0][0], v[0][1], v[0][2])
ncells = len(cells)
editor.init_cells(ncells)
id = 0
for c in cells:
editor.add_cell(id, c[0], c[1], c[2], c[3])
id += 1
# done: create and return mesh object
editor.close()
return mesh
def create_dolfin_mesh(points, cells):
# https://bitbucket.org/fenics-project/dolfin/issues/845/initialize-mesh-from-vertices
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh, "triangle", 2, 2)
editor.init_vertices(points.shape[0])
editor.init_cells(cells.shape[0])
for k, point in enumerate(points):
editor.add_vertex(k, point)
for k, cell in enumerate(cells):
editor.add_cell(k, cell)
editor.close()
return mesh
def fluent2xml(ifilename, ofilename):
"""Converting from ANSYS Fluent format (.msh) to FEniCS xml format
The fluent mesh (the .msh file) is basically stored as a list of vertices, and then a
list of faces for each zone of the mesh, the interior and the boundaries."""
# Use regular expressions to identify sections and tokens found in a fluent file
re_dimline = re.compile(r"\(2\s(\d)\)")
re_comment = re.compile(r"\(0\s.*")
re_zone_init = re.compile(r"\(10\s\(0\s(\w+)\s(\w+)\s(\d+)\s(\d+)\)\)")
re_zone = re.compile(r"\(10\s\((\w+)\s(\w+)\s(\w+)\s(\d+)\s(\d)\)(\(|)")
re_face_init = re.compile(r"\(13(\s*)\(0\s+(\w+)\s+(\w+)\s+(0|0 0)\)\)")
re_face = re.compile(
r"\(13(\s*)\((\w+)\s+(\w+)\s+(\w+)\s+(\w+)\s+(\w+)\)(\s*)(\(|)")
re_periodic = re.compile(r"\(18.*\((\w+)\s+(\w+)\s+(\w+)\s+(\w+)\).*\(")
re_pfaces = re.compile(r"((^\s)|)(\w+)(\s*)(\w+)")
re_cells_init = re.compile(
r"\(12(\s*)\(0(\s+)(\w+)(\s+)(\w+)(\s+)(0|0 0)\)\)")
re_cells = re.compile(r"\(12.*\((\w+)\s+(\w+)\s+(\w+)\s+(\d+)\s+(\d+)\)\)")
re_cells2 = re.compile(
r"\(12(\s*)\((\w+)\s+(\w+)\s+(\w+)\s+(\w+)\s+(\w+)\)(\s*)(\(|)")
re_zones = re.compile(
r"\((45|39)\s+\((\d+)\s+(\S+)\s+(\S+).*\)\((.*|[0-9]+[\.]*[0-9]*)\)\)")
re_parthesis = re.compile(r"(^\s*\)(\s*)|^\s*\)\)(\s*)|^\s*\(\s*)")
# Declare som maps that will be built when reading in the lists of vertices and faces:
cell_map = {} # Maps cell id with vertices
boundary_cells = {
} # List of cells attached to a boundary facet. Key is zone id
zones = {} # zone information (not really used yet)
def read_periodic(ifile, periodic_dx):
"""Scan past periodic section. Periodicity is computed by FEniCS."""
while 1:
line = ifile.readline()
a = re.search(re_pfaces, line)
if a:
continue
break
def read_zone_vertices(dim, Nmin, Nmax, ifile, editor):
"""Scan ifile for vertices and add to mesh_editor."""
# First line could be either just "(" or a regular vertex.
# Check for initial paranthesis. If paranthesis then read a new line, else reset
pos = ifile.tell()
line = ifile.readline()
if not re.search(re_parthesis, line):
ifile.seek(pos) # reset
# read Nmax-Nmin vertices
for i in range(Nmin, Nmax + 1):
line = ifile.readline()
vertex = [eval(x) for x in line.split()]
if dim == 2:
editor.add_vertex(i - Nmin, vertex[0], vertex[1])
else:
editor.add_vertex(i - Nmin, vertex[0], vertex[1], vertex[2])
def read_faces(zone_id, Nmin, Nmax, bc_type, face, ifile):
"""Read all faces and create cell_map + boundary maps."""
pos = ifile.tell() # current position
line = ifile.readline()
if not re.search(
re_parthesis, line
): # check for initial paranthesis. If paranthesis then read a new line, else reset
ifile.seek(pos)
# read Nmax-Nmin faces
for i in range(Nmin, Nmax + 1):
line = ifile.readline()
ln = line.split()
if face == 0:
nd = int(ln[0], 16) # Number of vertices
nds = [int(x, 16) for x in ln[1:(nd + 1)]]
cells = [int(x, 16) for x in ln[(nd + 1):]]
else:
nd = face
nds = [int(x, 16) for x in ln[:nd]]
cells = [int(x, 16) for x in ln[nd:]]
if min(cells) == 0: # A boundary zone
if zone_id in boundary_cells:
boundary_cells[zone_id][max(cells)] = array(nds)
else:
boundary_cells[zone_id] = {max(cells): array(nds)}
for c in cells:
if c > 0:
if not c in cell_map:
cell_map[c] = copy(nds)
else:
cell_map[c] = list(Set(cell_map[c] + nds))
def scan_fluent_mesh(ifile, mesh, editor):
"""Scan fluent mesh and generate maps."""
dim = 0
one = 0
while 1:
line = ifile.readline()
if len(line) == 0:
print 'Finished reading file\n'
break
if dim == 0: # Dimension usually comes first
a = re.search(re_dimline, line)
if a:
print 'Reading dimensions\n'
dim = int(a.group(1))
editor.open(mesh, dim, dim)
continue
if one == 0: # The total number of vertices
a = re.search(re_zone_init, line)
if a:
print 'Reading zone info\n'
one, num_vertices, dummy1, dummy2 = int(a.group(1)), \
int(a.group(2), 16), int(a.group(3), 16), int(a.group(4))
editor.init_vertices(num_vertices)
continue
a = re.search(re_zone, line) # Vertices
if a:
zone_id, first_id, last_id = int(a.group(1), 16), \
int(a.group(2), 16), int(a.group(3), 16)
print 'Reading ', last_id - first_id + 1, ' vertices in zone ', zone_id + 1, '\n'
read_zone_vertices(dim, first_id, last_id, ifile, editor)
continue
a = re.search(re_zones, line) # Zone info
if a:
print 'Reading zone info ', line
dummy, zone_id, zone_type, zone_name, radius = \
int(a.group(1)), int(a.group(2)), a.group(3), \
a.group(4), a.group(5)
zones[zone_id] = [zone_type, zone_name, radius]
continue
a = re.search(re_cells_init,
line) # Get total number of cells/elements
if a:
print 'Reading cell info ', line
first_id, tot_num_cells = int(a.group(3),
16), int(a.group(5), 16)
editor.init_cells(tot_num_cells)
continue
a = re.search(re_cells, line) # Get the cell info.
if a:
zone_id, first_id, last_id, bc_type, element_type = \
int(a.group(1)), int(a.group(2), 16), int(a.group(3), 16), \
int(a.group(4), 16), int(a.group(5), 16)
print 'Found ', last_id - first_id + 1, ' cells in zone ', zone_id, '\n'
if last_id == 0:
raise TypeError("Zero elements!")
continue
a = re.search(re_cells2, line) # Get the cell info.
if a:
raise TypeError(
"Wrong cell type. Can only handle one single cell type")
a = re.search(re_face_init, line)
if a:
print 'Reading total number of faces\n', line
continue
a = re.search(re_face, line)
if a:
print 'Reading faces ', line
zone_id, first_id, last_id, bc_type, face_type = \
int(a.group(2), 16), int(a.group(3), 16), int(a.group(4), 16), \
int(a.group(5), 16), int(a.group(6), 16)
read_faces(zone_id, first_id, last_id, bc_type, face_type,
ifile)
continue
a = re.search(re_periodic, line)
if a:
print 'Scanning past periodic connectivity\n', line
read_periodic(ifile, periodic_dx)
continue
if any([re.search(st, line) for st in (re_parthesis, re_comment)]) or \
not line.strip():
continue
# Should not make it here
raise IOError('Something went wrong reading fluent mesh.')
def write_fenics_file(ofile, mesh, editor):
dim = mesh.geometry().dim()
for i in range(1, len(cell_map) + 1):
if dim == 2:
editor.add_cell(i - 1, cell_map[i][0] - 1, cell_map[i][1] - 1,
cell_map[i][2] - 1)
else:
editor.add_cell(i - 1, cell_map[i][0] - 1, cell_map[i][1] - 1,
cell_map[i][2] - 1, cell_map[i][3] - 1)
mesh.order()
# Set MeshValueCollections from info in boundary_cell
#mvc = mesh.domains().markers(dim-1)
md = mesh.domains()
for zone, cells in boundary_cells.iteritems():
for cell, nds in cells.iteritems():
dolfin_cell = Cell(mesh, cell - 1)
vertices_of_cell = dolfin_cell.entities(0)
vertices_of_face = nds - 1
for jj, ff in enumerate(facets(dolfin_cell)):
facet_vertices = ff.entities(0)
if all(map(lambda x: x in vertices_of_face,
facet_vertices)):
local_index = jj
break
#mvc.set_value(cell-1, local_index, zone)
md.set_marker((ff.index(), zone), dim - 1)
ofile << mesh
from dolfin import plot
plot(mesh, interactive=True)
print 'Finished writing FEniCS mesh\n'
ifile = open(ifilename, "r")
ofile = File(ofilename)
mesh = Mesh()
editor = MeshEditor()
scan_fluent_mesh(ifile, mesh, editor)
write_fenics_file(ofile, mesh, editor)
ifile.close()
def convert(ifilename, handler):
""" Convert from Abaqus.
The Abaqus format first defines a node block, then there should be a number
of elements containing these nodes.
"""
# Dictionary of nodes (maps node id to coordinates)
nodes = {}
# Dictionary of elements (maps cell id to list of cell nodes)
elems = {}
# Lists of nodes for given name (key)
node_sets = {}
# Lists of cells for given name (key)
cell_sets = {}
# Lists of surfaces for given name (key) in the format:
# {'SS1': [set(['SS1_S1', 'S1']), set(['SS1_S4', 'S4'])]},
# where SS1 is the name of the surface, SS1_S1 is the name of the
# cell list whose first face is to be selected, ...
surface_sets = {}
# Open file Abaqus file
csv_file = csv.reader(open(ifilename, 'rb'), delimiter=',', skipinitialspace=True)
node_set_name = None
generate = None
# Set intial state state
state = State.Init
# Read data from input file
for l in csv_file:
# Sanity check
if (len(l) == 0): print "Ooops, zero length."
if l[0].startswith('**'): # Pass over comments
continue
elif l[0].startswith('*'): # Have a keyword
state = State.Unknown
if l[0].lower() == "*heading":
state = State.ReadHeading
elif l[0].lower() == "*part":
part_name = _read_part_name(l)
elif l[0].lower() == "*end part":
state = State.Invalid
elif l[0].lower() == "*node":
node_set_name = _create_node_list_entry(node_sets, l)
state = State.ReadNodes
elif l[0].lower() == "*element":
cell_type, cell_set_name = _read_element_keywords(cell_sets, l)
state = State.ReadCells
elif l[0].lower() == "*nset":
node_set_name, generate = _read_nset_keywords(node_sets, l)
state = State.ReadNodeSet
elif l[0].lower() == "*elset":
cell_set_name, generate = _read_elset_keywords(cell_sets, l)
if generate:
print "WARNING: generation of *elsets not tested."
state = State.ReadCellSet
elif l[0].lower() == "*surface":
surface_set_name, generate = _read_surface_keywords(surface_sets, l)
state = State.ReadSurfaceSet
else:
print "WARNING: unrecognised Abaqus input keyword:", l[0]
state = State.Unknown
else:
if state == State.ReadHeading:
model_name = _read_heading(l)
elif state == State.ReadNodes:
node_id = int(l[0]) - 1
coords = [float(c) for c in l[1:]]
nodes[node_id] = coords
if node_set_name is not None:
node_sets[node_set_name].add(node_id)
elif state == State.ReadCells:
cell_id = int(l[0]) - 1
cell_connectivity = [int(v) - 1 for v in l[1:]]
elems[cell_id] = cell_connectivity
if cell_set_name is not None:
cell_sets[cell_set_name].add(cell_id)
elif state == State.ReadNodeSet:
try:
if generate:
n0, n1, increment = l
node_range = range(int(n0) - 1, int(n1) - 1, int(increment))
node_range.append(int(n1) - 1)
node_sets[node_set_name].update(node_range)
else:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
node_range = [int(n) - 1 for n in l]
node_sets[node_set_name].update(node_range)
except:
print "WARNING: Non-integer node sets not yet supported."
elif state == State.ReadCellSet:
try:
if generate:
n0, n1, increment = l
cell_range = range(int(n0) - 1, int(n1) - 1, int(increment))
cell_range.append(int(n1) - 1)
cell_sets[cell_set_name].update(cell_range)
else:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
cell_range = [int(n) - 1 for n in l]
cell_sets[cell_set_name].update(cell_range)
except:
print "WARNING: Non-integer element sets not yet supported."
elif state == State.ReadSurfaceSet:
# Strip empty term at end of list, if present
if l[-1] == '': l.pop(-1)
surface_sets[surface_set_name].update([tuple(l)])
elif state == State.Invalid: # part
raise StandardError("Inavlid Abaqus parser state..")
# Close CSV object
del csv_file
# Write data to XML file
# Note that vertices/cells must be consecutively numbered, which
# isn't necessarily the case in Abaqus. Therefore we enumerate and
# translate original IDs to sequence indexes if gaps are present.
# FIXME
handler.set_mesh_type("tetrahedron", 3)
process_facets = len(surface_sets) > 0
if process_facets:
try:
from dolfin import MeshEditor, Mesh
except ImportError:
_error("DOLFIN must be installed to handle Abaqus boundary regions")
mesh = Mesh()
mesh_editor = MeshEditor()
mesh_editor.open(mesh, 3, 3)
node_ids_order = {}
# Check for gaps in vertex numbering
node_ids = nodes.keys()
if len(node_ids) > 0:
vertex_gap = (min(node_ids) != 0 or max(node_ids) != len(node_ids) - 1)
for x, y in enumerate(node_ids):
node_ids_order[y]= x # Maps Abaqus IDs to Dolfin IDs
else:
vertex_gap = True
# Check for gaps in cell numbering
elemids = elems.keys()
if len(elemids) > 0:
cell_gap = (min(elemids) != 0 or max(elemids) != len(elemids) - 1)
else:
cell_gap = True
# Write vertices to XML file
handler.start_vertices(len(nodes))
if process_facets:
mesh_editor.init_vertices (len(nodes))
if not vertex_gap:
for v_id, v_coords in nodes.items():
handler.add_vertex(v_id, v_coords)
if process_facets:
mesh_editor.add_vertex(v_id, np.array(v_coords, dtype=np.float_))
else:
for idx, (v_id, v_coords) in enumerate(nodes.items()):
handler.add_vertex(idx, v_coords)
if process_facets:
mesh_editor.add_vertex(idx, np.array(v_coords, dtype=np.float_))
handler.end_vertices()
# Write cells to XML file
handler.start_cells(len(elems))
if process_facets:
mesh_editor.init_cells(len(elems))
if not vertex_gap and not cell_gap:
for c_index, c_data in elems.items():
for v_id in c_data:
if not (0 <= v_id < len(nodes)):
handler.error("Element %s references non-existent node %s" % (c_index, v_id))
handler.add_cell(c_index, c_data)
if process_facets:
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
mesh_editor.add_cell(c_index, np.array(c_data_tmp, dtype=np.uintp))
elif not vertex_gap and cell_gap:
for idx, (c_index, c_data) in enumerate(elems.items()):
for v_id in c_data:
if not (0 <= v_id < len(nodes)):
handler.error("Element %s references non-existent node %s" % (c_index, v_id))
handler.add_cell(idx, c_data)
if process_facets:
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
mesh_editor.add_cell(idx, np.array(c_data_tmp, dtype=np.uintp))
else:
for idx, (c_id, c_data) in enumerate(elems.items()):
c_nodes = []
for v_id in c_data:
try: c_nodes.append(node_ids_order[v_id])
except ValueError:
handler.error("Element %s references non-existent node %s" % (c_id, v_id))
handler.add_cell(idx, c_nodes)
if process_facets:
c_nodes.sort()
mesh_editor.add_cell(idx, np.array(c_nodes, dtype=np.uintp))
handler.end_cells()
# Write MeshValueCollections to XML file
handler.start_domains()
# Build a abaqus node ID -> dolfin cell ID map (which is not unique but that is irrelevant here)
# and its local entity.
if len(node_sets.items()) > 0:
node_cell_map = {}
for c_dolfin_index, (c_index, c_data) in enumerate(elems.items()):
c_data_tmp = np.array(c_data)
c_data_tmp.sort()
for local_entity, n_index in enumerate(c_data_tmp):
node_cell_map[n_index] = (c_dolfin_index, local_entity)
# Write vertex/node sets
dim = 0
for value, (name, node_set) in enumerate(node_sets.items()):
handler.start_mesh_value_collection(name, dim, len(node_set), "uint")
for node in node_set:
try:
cell, local_entity = node_cell_map[node]
handler.add_entity_mesh_value_collection(dim, cell, value, local_entity=local_entity)
except KeyError:
print "Warning: Boundary references non-existent node %s" % node
handler.end_mesh_value_collection()
# Write cell/element sets
dim = 3
for name, s in cell_sets.items():
handler.start_mesh_value_collection(name, dim, len(s), "uint")
for cell in s:
handler.add_entity_mesh_value_collection(dim, cell, 0)
handler.end_mesh_value_collection()
# Write surface sets
if process_facets:
dim = 2
nodes_facet_map = _nodes_facet_map(mesh)
data = [int(0)] * mesh.num_facets()
S1 = [0, 1, 2]
S2 = [0, 3, 1]
S3 = [1, 3, 2]
S4 = [2, 3, 0]
node_selector = {'S1': S1,
'S2': S2,
'S3': S3,
'S4': S4,
}
for index, (name, s) in enumerate(surface_sets.items()):
cell_face_list = []
for cell_set_name, face_index in s:
cell_face_list += [(cell, face_index) for cell in cell_sets[cell_set_name]]
for cell, face in cell_face_list:
cell_nodes = elems[cell]
# Extract the face nodes
face_nodes = [cell_nodes[i] for i in node_selector[face]]
dolfin_face_nodes = [node_ids_order[n] for n in face_nodes]
dolfin_face_nodes.sort()
# Convert the face_nodes to dolfin IDs
face_id = nodes_facet_map[tuple(dolfin_face_nodes)]
data[face_id] = index + 1
# Create and initialise the mesh function
handler.start_meshfunction("facet_region", dim, mesh.num_facets() )
for index, physical_region in enumerate (data):
handler.add_entity_meshfunction(index, physical_region)
handler.end_meshfunction()
handler.end_domains()
def _main():
args = _parse_cmd_arguments()
content = np.load(args.infile)
data = content.item()["data"]
n = content.item()["n"]
# # plot statistics
# axes0 = problem.get_ellipse_axes(alpha0).T.flatten()
# plt.plot(axes0, label='axes lengths before')
# axes1 = problem.get_ellipse_axes(out.x).T.flatten()
# plt.plot(axes1, label='axes lengths opt')
# plt.legend()
# plt.grid()
# Plot unperturbed MacAdam
# colorio.plot_luo_rigg(
# ellipse_scaling=1,
colorio.save_macadam("macadam-native.png",
ellipse_scaling=10,
plot_rgb_triangle=False,
n=n)
points, cells = meshzoo.triangle(corners=np.array([[0.0, 0.0, 0.0],
[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0]]),
n=n)
# https://bitbucket.org/fenics-project/dolfin/issues/845/initialize-mesh-from-vertices
editor = MeshEditor()
mesh = Mesh()
editor.open(mesh, "triangle", 2, 2)
editor.init_vertices(points.shape[0])
editor.init_cells(cells.shape[0])
for k, point in enumerate(points):
editor.add_vertex(k, point[:2])
for k, cell in enumerate(cells):
editor.add_cell(k, cell)
editor.close()
V = FunctionSpace(mesh, "CG", 1)
def get_u(alpha):
n = V.dim()
ax = alpha[:n]
ay = alpha[n:]
ux = Function(V)
ux.vector().set_local(ax)
ux.vector().apply("")
uy = Function(V)
uy.vector().set_local(ay)
uy.vector().apply("")
return ux, uy
# Plot perturbed MacAdam
def transform(XY, data=data):
is_solo = len(XY.shape) == 1
if is_solo:
XY = np.array([XY]).T
# print(XY)
ux, uy = get_u(data)
out = np.array([[ux(x, y) for x, y in XY.T],
[uy(x, y) for x, y in XY.T]])
if is_solo:
out = out[..., 0]
return out
# colorio.plot_luo_rigg(
# ellipse_scaling=1,
plt.figure()
colorio.plot_macadam(
ellipse_scaling=10,
# xy_to_2d=problem.pade2d.eval,
xy_to_2d=transform,
plot_rgb_triangle=False,
mesh_resolution=n,
)
# plt.xlim(-0.2, 0.9)
# plt.ylim(+0.0, 0.7)
plt.savefig(f"macadam-{n:03d}.png")
return
def build_mesh_old(cells, vertices):
"""Assemble a mesh object from cells and vertices."""
mesh = Mesh()
editor = MeshEditor()
dim = len(vertices[0])
if dim == 2:
editor.open(mesh, 'triangle', 2, 2)
else:
editor.open(mesh, 'tetrahedron', 3, 3)
editor.init_vertices(len(vertices))
editor.init_cells(len(cells))
for i, v in enumerate(vertices):
editor.add_vertex(i, *v)
for i, c in enumerate(cells):
editor.add_cell(i, *c)
editor.close()
return mesh
def build_interval_mesh(vertices, cells):
'''Mesh of 1d topology in n-dims.'''
imesh = Mesh()
editor = MeshEditor()
editor.open(imesh, 1, vertices.shape[1])
editor.init_vertices(len(vertices))
editor.init_cells(len(cells))
# Add vertices
for vertex_index, v in enumerate(vertices):
editor.add_vertex(vertex_index, v)
# Add cells
for cell_index, (v0, v1) in enumerate(cells):
editor.add_cell(cell_index, v0, v1)
editor.close()
return imesh
def get(self):
"""Just one cell."""
topx, topy = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(3)
editor.init_cells(1)
editor.add_vertex(0, 0, 0)
editor.add_vertex(1, 1, 0)
editor.add_vertex(2, topx, topy)
editor.add_cell(0, 0, 1, 2)
editor.close()
return mesh
def _create_dolfin_mesh(points, cells):
editor = MeshEditor()
mesh = Mesh()
# topological and geometrical dimension 2
editor.open(mesh, "triangle", 2, 2, 1)
editor.init_vertices(len(points))
editor.init_cells(len(cells))
for k, point in enumerate(points):
editor.add_vertex(k, point[:2])
for k, cell in enumerate(cells.astype(numpy.uintp)):
editor.add_cell(k, cell)
editor.close()
return mesh
def get(self):
"""Build vertices from polar coordinates."""
angle, dist = self.values
if len(angle) < 3:
angle = np.array(range(int(angle[0]))) * 360.0 / angle[0]
while len(dist) < len(angle):
dist = dist * 2
dist = np.array(dist)
sides = len(angle)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(sides + 1)
editor.init_cells(sides)
editor.add_vertex(0, 0, 0)
for i in range(1, sides + 1):
editor.add_vertex(i, dist[i - 1] * cos(angle[i - 1] / 180.0 * pi),
dist[i - 1] * sin(angle[i - 1] / 180.0 * pi))
for i in range(sides - 1):
editor.add_cell(i, 0, i + 1, i + 2)
editor.add_cell(sides - 1, 0, sides, 1)
editor.close()
return mesh
def import_from_gmsh(fname):
"Convert from gmsh to dolfin"
# read with meshio
msh = meshio.read(fname)
# create a DOLFIN mesh (assuming 2d)
gdim, tdim = 2, 2
mm = Mesh()
editor = MeshEditor()
editor.open(mm, "triangle", gdim, tdim)
npt = msh.points.shape[0]
nc = msh.get_cells_type("triangle").shape[0]
editor.init_vertices_global(npt, npt)
editor.init_cells_global(nc, nc)
for i, p in enumerate(msh.points):
editor.add_vertex(i, p[:2])
for i, c in enumerate(msh.get_cells_type("triangle")):
editor.add_cell(i, c)
editor.close()
# domains
md = mm.domains()
md.init(tdim)
markers = {}
if 'gmsh:physical' not in msh.cell_data_dict:
# no markers at all
return mm, markers
phy = msh.cell_data_dict['gmsh:physical']
if 'triangle' in phy:
for eid, val in enumerate(phy['triangle']):
md.set_marker((eid, val), 2)
if 'line' in phy:
mm.init(0, 1)
p2e = mm.topology()(0, 1)
for l, k in zip(msh.get_cells_type("line"), phy['line']):
e = set(p2e(l[0])).intersection(p2e(l[1])).pop()
md.set_marker((e, k), 1)
if 'vertex' in phy:
for eid, val in zip(msh.get_cells_type("vertex"), phy['vertex']):
md.set_marker((eid[0], val), 0)
# names
markers = tuple(
{n: v.item()
for n, (v, d) in msh.field_data.items() if d == dim}
for dim in range(tdim + 1))
return mm, markers
def get(self):
"""One triangle per side in smaller, two triangles in larger."""
sides, R = self.pad(self.values)
mesh = Mesh()
large = [np.array((cos(2 * pi * i / sides), sin(2 * pi * i / sides)))
for i in range(1, sides+1)]
small = np.array([v * R for v in large])
# centers of edges in large polygon
center = np.array([(v + w) / 2
for v, w in zip(large, large[1:] + [large[0]])])
large = np.array(large)
editor = MeshEditor()
editor.open(mesh, 2, 2)
editor.init_vertices(3 * sides)
editor.init_cells(3 * sides)
for i in range(sides):
editor.add_vertex(3 * i, *large[i])
editor.add_vertex(3 * i + 1, *small[i])
editor.add_vertex(3 * i + 2, *center[i])
for i, j in zip(range(sides), range(1, sides) + [0]):
editor.add_cell(3*i, 3*i, 3*i+1, 3*i+2)
editor.add_cell(3*i+1, 3*i+1, 3*i+2, 3*j+1)
editor.add_cell(3*i+2, 3*i+2, 3*j+1, 3*j)
editor.close()
return mesh
def test_readme_images():
from dolfin import (
MeshEditor, Mesh, FunctionSpace, assemble, EigenMatrix, dot, grad, dx,
TrialFunction, TestFunction
)
import meshzoo
points, cells = meshzoo.rectangle(-1.0, 1.0, -1.0, 1.0, 20, 20)
# Convert points, cells to dolfin mesh
editor = MeshEditor()
mesh = Mesh()
# topological and geometrical dimension 2
editor.open(mesh, 'triangle', 2, 2, 1)
editor.init_vertices(len(points))
editor.init_cells(len(cells))
for k, point in enumerate(points):
editor.add_vertex(k, point[:2])
for k, cell in enumerate(cells.astype(numpy.uintp)):
editor.add_cell(k, cell)
editor.close()
V = FunctionSpace(mesh, 'CG', 1)
u = TrialFunction(V)
v = TestFunction(V)
L = EigenMatrix()
assemble(dot(grad(u), grad(v)) * dx, tensor=L)
A = L.sparray()
# M = A.T.dot(A)
M = A
with tempfile.TemporaryDirectory() as temp_dir:
filepath = os.path.join(temp_dir, 'test.png')
betterspy.write_png(filepath, M, border_width=2)
# betterspy.write_png(
# 'ATA.png', M, border_width=2,
# colormap='viridis'
# )
return
def get(self):
"""Eight cells."""
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3)
editor.init_vertices(7)
editor.init_cells(8)
editor.add_vertex(0, 1, 0, 0)
editor.add_vertex(1, 0, 1, 0)
editor.add_vertex(2, 0, 0, 1)
editor.add_vertex(3, -1, 0, 0)
editor.add_vertex(4, 0, -1, 0)
editor.add_vertex(5, 0, 0, -1)
editor.add_vertex(6, 0, 0, 0)
editor.add_cell(0, 6, 0, 1, 2)
editor.add_cell(1, 6, 0, 1, 5)
editor.add_cell(2, 6, 0, 4, 2)
editor.add_cell(3, 6, 0, 4, 5)
editor.add_cell(4, 6, 3, 1, 2)
editor.add_cell(5, 6, 3, 1, 5)
editor.add_cell(6, 6, 3, 4, 2)
editor.add_cell(7, 6, 3, 4, 5)
editor.close()
return mesh
def make_mesh(vertices, cells, cell_type):
'''Mesh from data by MeshEditor'''
gdim = cell_type.geometric_dimension()
assert vertices.shape[1] == gdim
tdim = cell_type.topological_dimension()
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, str(cell_type), tdim, gdim)
editor.init_vertices(len(vertices))
editor.init_cells(len(cells))
for vi, x in enumerate(vertices):
editor.add_vertex(vi, x)
for ci, c in enumerate(cells):
editor.add_cell(ci, *c)
editor.close()
return mesh
def get(self):
"""Single cell."""
a, b, c, d, e = self.pad(self.values)
mesh = Mesh()
editor = MeshEditor()
editor.open(mesh, 3, 3) # dimension
editor.init_vertices(4)
editor.init_cells(1)
editor.add_vertex(0, 0, 0, 0)
editor.add_vertex(1, 1, 0, 0)
editor.add_vertex(2, a, b, 0)
editor.add_vertex(3, c, d, e)
editor.add_cell(0, 0, 1, 2, 3)
editor.close()
return mesh
def build_interval_mesh(vertices, cells):
'''Mesh of 1d topology in n-dims.'''
imesh = Mesh()
editor = MeshEditor()
editor.open(imesh, 1, vertices.shape[1])
editor.init_vertices(len(vertices))
editor.init_cells(len(cells))
# Add vertices
for vertex_index, v in enumerate(vertices):
editor.add_vertex(vertex_index, v)
# Add cells
for cell_index, (v0, v1) in enumerate(cells):
editor.add_cell(cell_index, v0, v1)
editor.close()
return imesh
