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 test_volume_quadrilateralR3(coordinates):
mesh = Mesh(MPI.comm_world, CellType.Type.quadrilateral,
numpy.array(coordinates, dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.init()
cell = Cell(mesh, 0)
assert cell.volume() == 1.0
def convert_and_create_facet_mesh_function(ifilename, ofilename):
# First convert the gmsh mesh
meshconvert.convert2xml(ifilename, ofilename)
# Now load the created mesh and initialise the required connectivity information
mesh = Mesh(ofilename)
mesh.order()
File(ofilename) << mesh
D = mesh.topology().dim()
mesh.init(D - 1, 0)
# read the data from the gmsh file once again
dim_count, vertices_used, tags = process_gmsh_elements(ifilename, D - 1)
# Get the facet-node connectivity information (reshape as a row of node indices per facet)
facets_as_nodes = mesh.topology()(D - 1, 0)().reshape(mesh.num_facets(), D)
# Create and initialise the mesh function
facet_mark_function = MeshFunction('uint', mesh, D - 1)
facet_mark_function.set_all(0)
# set the relevant values of the mesh function
facets_to_check = range(mesh.num_facets())
for i in range(len(tags)):
nodes = np.sort(np.array(vertices_used[2 * i:(2 * i + D)]))
value = tags[i][0]
if value != 0:
found = False
for j in range(len(facets_to_check)):
index = facets_to_check[j]
if np.array_equal(facets_as_nodes[index, :], nodes):
found = True
facets_to_check.pop(j)
# set the value of the mesh function
facet_mark_function[index] = value
break
if not found:
raise Exception("The facet (%d) was not found to mark: %s" %
(i, nodes))
# save the mesh function to file
fname = os.path.splitext(ofilename)[0]
mesh_function_file = File("%s_%s.xml" % (fname, "facet_regions"))
mesh_function_file << facet_mark_function
def convert_and_create_facet_mesh_function ( ifilename, ofilename ):
# First convert the gmsh mesh
meshconvert.convert2xml ( ifilename, ofilename )
# Now load the created mesh and initialise the required connectivity information
mesh = Mesh ( ofilename )
mesh.order()
File ( ofilename ) << mesh
D = mesh.topology().dim()
mesh.init(D-1, 0)
# read the data from the gmsh file once again
dim_count, vertices_used, tags = process_gmsh_elements( ifilename, D-1 )
# Get the facet-node connectivity information (reshape as a row of node indices per facet)
facets_as_nodes = mesh.topology()(D-1,0)().reshape ( mesh.num_facets(), D )
# Create and initialise the mesh function
facet_mark_function = MeshFunction ( 'uint', mesh, D-1 )
facet_mark_function.set_all( 0 )
# set the relevant values of the mesh function
facets_to_check = range( mesh.num_facets() )
for i in range(len(tags)):
nodes = np.sort(np.array(vertices_used[2*i:(2*i+D)]))
value = tags[i][0]
if value != 0:
found = False
for j in range(len(facets_to_check)):
index = facets_to_check[j]
if np.array_equal(facets_as_nodes[index,:], nodes):
found = True;
facets_to_check.pop(j)
# set the value of the mesh function
facet_mark_function[index] = value
break;
if not found:
raise Exception ( "The facet (%d) was not found to mark: %s" % (i, nodes) )
# save the mesh function to file
fname = os.path.splitext(ofilename)[0]
mesh_function_file = File("%s_%s.xml" % (fname, "facet_regions"))
mesh_function_file << facet_mark_function
def test_volume_quadrilateral_coplanarity_check_2(scaling):
with pytest.raises(RuntimeError) as error:
# Unit square cell scaled down by 'scaling' and the first
# vertex is distorted so that the vertices are clearly non
# coplanar
mesh = Mesh(
MPI.comm_world, CellType.Type.quadrilateral,
numpy.array([[1.0, 0.5, 0.6], [0.0, scaling, 0.0],
[0.0, 0.0, scaling], [0.0, 1.0, 1.0]],
dtype=numpy.float64),
numpy.array([[0, 1, 2, 3]], dtype=numpy.int32), [],
cpp.mesh.GhostMode.none)
mesh.init()
cell = Cell(mesh, 0)
cell.volume()
assert "are not coplanar" in str(error.value)
# Rossby radius.
LR=c/params["f"]
class InitialConditions(Expression):
def __init__(self):
pass
def eval(self, values, X):
r=(X[0]**2+X[1]**2)**0.5
if r>0.0001:
values[0]=-0.05*c*exp((r-r0)/LR)*X[0]/r*X[1]/r
values[1]= 0.05*c*exp((r-r0)/LR)*X[0]/r*X[0]/r
values[2]= 0.05*exp((r-r0)/LR)*X[0]/r
else:
values[0]=0.
values[1]=0.
values[2]=0.
def value_shape(self):
return (3,)
try:
mesh=Mesh("basin.xml")
except RuntimeError:
import sys
import os.path
mesh=Mesh(os.path.dirname(sys.argv[0]) + os.path.sep + "basin.xml")
mesh.order()
mesh.init()
# Rossby radius.
LR = c / params["f"]
class InitialConditions(Expression):
def eval(self, values, X):
r = (X[0]**2 + X[1]**2)**0.5
if r > 0.0001:
values[0] = -0.05 * c * exp((r - r0) / LR) * X[0] / r * X[1] / r
values[1] = 0.05 * c * exp((r - r0) / LR) * X[0] / r * X[0] / r
values[2] = 0.05 * exp((r - r0) / LR) * X[0] / r
else:
values[0] = 0.
values[1] = 0.
values[2] = 0.
def value_shape(self):
return (3, )
try:
mesh = Mesh("basin.xml")
except RuntimeError:
import sys
import os.path
mesh = Mesh(os.path.dirname(sys.argv[0]) + os.path.sep + "basin.xml")
mesh.order()
mesh.init()
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 test_convert_triangle(self): # Disabled because it fails, see FIXME below
# test no. 1
from dolfin import Mesh, MPI
if MPI.num_processes() != 1:
return
fname = os.path.join("data", "triangle")
dfname = fname+".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 96)
self.assertEqual(mesh.num_cells(), 159)
# Clean up
os.unlink(dfname)
# test no. 2
from dolfin import MPI, Mesh, MeshFunction, \
edges, Edge, faces, Face, \
SubsetIterator, facets, CellFunction
if MPI.num_processes() != 1:
return
fname = os.path.join("data", "test_Triangle_3")
dfname = fname+".xml"
dfname0 = fname+".attr0.xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
mesh.init()
mfun = MeshFunction('double', mesh, dfname0)
self.assertEqual(mesh.num_vertices(), 58)
self.assertEqual(mesh.num_cells(), 58)
# Create a size_t CellFunction and assign the values based on the
# converted Meshfunction
cf = CellFunction("size_t", mesh)
cf.array()[mfun.array()==10.0] = 0
cf.array()[mfun.array()==-10.0] = 1
# Meassure total area of cells with 1 and 2 marker
add = lambda x, y : x+y
area0 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 0)), 0.0)
area1 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 1)), 0.0)
total_area = reduce(add, (face.area() for face in faces(mesh)), 0.0)
# Check that all cells in the two domains are either above or below y=0
self.assertTrue(all(cell.midpoint().y()<0 for cell in SubsetIterator(cf, 0)))
self.assertTrue(all(cell.midpoint().y()>0 for cell in SubsetIterator(cf, 1)))
# Check that the areas add up
self.assertAlmostEqual(area0+area1, total_area)
# Measure the edge length of the two edge domains
edge_markers = mesh.domains().facet_domains()
self.assertTrue(edge_markers is not None)
length0 = reduce(add, (Edge(mesh, e.index()).length() \
for e in SubsetIterator(edge_markers, 0)), 0.0)
length1 = reduce(add, (Edge(mesh, e.index()).length() \
for e in SubsetIterator(edge_markers, 1)), 0.0)
# Total length of all edges and total length of boundary edges
total_length = reduce(add, (e.length() for e in edges(mesh)), 0.0)
boundary_length = reduce(add, (Edge(mesh, f.index()).length() \
for f in facets(mesh) if f.exterior()), 0.0)
# Check that the edges add up
self.assertAlmostEqual(length0+length1, total_length)
self.assertAlmostEqual(length1, boundary_length)
# Clean up
os.unlink(dfname)
os.unlink(dfname0)
def 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 test_convert_triangle(
self): # Disabled because it fails, see FIXME below
# test no. 1
from dolfin import Mesh, MPI
fname = os.path.join(os.path.dirname(__file__), "data", "triangle")
dfname = fname + ".xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
self.assertEqual(mesh.num_vertices(), 96)
self.assertEqual(mesh.num_cells(), 159)
# Clean up
os.unlink(dfname)
# test no. 2
from dolfin import MPI, Mesh, MeshFunction, \
edges, Edge, faces, Face, \
SubsetIterator, facets
fname = os.path.join(os.path.dirname(__file__), "data",
"test_Triangle_3")
dfname = fname + ".xml"
dfname0 = fname + ".attr0.xml"
# Read triangle file and convert to a dolfin xml mesh file
meshconvert.triangle2xml(fname, dfname)
# Read in dolfin mesh and check number of cells and vertices
mesh = Mesh(dfname)
mesh.init()
mfun = MeshFunction('double', mesh, dfname0)
self.assertEqual(mesh.num_vertices(), 58)
self.assertEqual(mesh.num_cells(), 58)
# Create a size_t MeshFunction and assign the values based on the
# converted Meshfunction
cf = MeshFunction("size_t", mesh, mesh.topology().dim())
cf.array()[mfun.array() == 10.0] = 0
cf.array()[mfun.array() == -10.0] = 1
# Meassure total area of cells with 1 and 2 marker
add = lambda x, y: x + y
area0 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 0)), 0.0)
area1 = reduce(add, (Face(mesh, cell.index()).area() \
for cell in SubsetIterator(cf, 1)), 0.0)
total_area = reduce(add, (face.area() for face in faces(mesh)), 0.0)
# Check that all cells in the two domains are either above or below y=0
self.assertTrue(
all(cell.midpoint().y() < 0 for cell in SubsetIterator(cf, 0)))
self.assertTrue(
all(cell.midpoint().y() > 0 for cell in SubsetIterator(cf, 1)))
# Check that the areas add up
self.assertAlmostEqual(area0 + area1, total_area)
# Measure the edge length of the two edge domains
#edge_markers = mesh.domains().facet_domains()
edge_markers = mesh.domains().markers(mesh.topology().dim() - 1)
self.assertTrue(edge_markers is not None)
#length0 = reduce(add, (Edge(mesh, e.index()).length() \
# for e in SubsetIterator(edge_markers, 0)), 0.0)
length0, length1 = 0.0, 0.0
for item in list(edge_markers.items()):
if item[1] == 0:
e = Edge(mesh, int(item[0]))
length0 += Edge(mesh, int(item[0])).length()
elif item[1] == 1:
length1 += Edge(mesh, int(item[0])).length()
# Total length of all edges and total length of boundary edges
total_length = reduce(add, (e.length() for e in edges(mesh)), 0.0)
boundary_length = reduce(add, (Edge(mesh, f.index()).length() \
for f in facets(mesh) if f.exterior()), 0.0)
# Check that the edges add up
self.assertAlmostEqual(length0 + length1, total_length)
self.assertAlmostEqual(length1, boundary_length)
# Clean up
os.unlink(dfname)
os.unlink(dfname0)
def test(path, type='mf'):
'''Evolve the tile in (n, n) pattern checking volume/surface properties'''
comm = mpi_comm_world()
h5 = HDF5File(comm, path, 'r')
tile = Mesh()
h5.read(tile, 'mesh', False)
init_container = lambda type, dim: (
MeshFunction('size_t', tile, dim, 0)
if type == 'mf' else MeshValueCollection('size_t', tile, dim))
for n in (2, 4):
data = {}
checks = {}
for dim, name in zip((2, 3), ('surfaces', 'volumes')):
# Get the collection
collection = init_container(type, dim)
h5.read(collection, name)
if type == 'mvc': collection = as_meshf(collection)
# Data to evolve
tile.init(dim, 0)
e2v = tile.topology()(dim, 0)
# Only want to evolve tag 1 (interfaces) for the facets.
data[(dim, 1)] = np.array(
[e2v(e.index()) for e in SubsetIterator(collection, 1)],
dtype='uintp')
if dim == 2:
check = lambda m, f: assemble(
FacetArea(m) * ds(domain=m,
subdomain_data=f,
subdomain_id=1) + avg(FacetArea(m)) *
dS(domain=m, subdomain_data=f, subdomain_id=1))
else:
check = lambda m, f: assemble(
CellVolume(m) * dx(
domain=m, subdomain_data=f, subdomain_id=1))
checks[
dim] = lambda m, f, t=tile, c=collection, n=n, check=check: abs(
check(m, f) - n**2 * check(t, c)) / (n**2 * check(t, c))
t = Timer('x')
mesh, mesh_data = TileMesh(tile, (n, n), mesh_data=data)
info('\tTiling took %g s. Ncells %d, nvertices %d, \n' %
(t.stop(), mesh.num_vertices(), mesh.num_cells()))
foos = mf_from_data(mesh, mesh_data)
# Mesh Functions
from_mf = np.array([checks[dim](mesh, foos[dim]) for dim in (2, 3)])
mvcs = mvc_from_data(mesh, mesh_data)
foos = as_meshf(mvcs)
# Mesh ValueCollections
from_mvc = np.array([checks[dim](mesh, foos[dim]) for dim in (2, 3)])
assert np.linalg.norm(from_mf - from_mvc) < 1E-13
# I ignore shared facets so there is bound to be some error in facets
# Volume should match well
print from_mf
def mesh_around_1d(mesh, size=1, scale=10, padding=0.05):
'''
From a 1d in xd (X > 1) mesh (in XML format) produce a Xd mesh where
the 1d structure is embedded. Mesh size close to strucure should
be size(given as multiple of hmin(), elsewhere scale * size. Padding
controls size of the bounding box.
'''
dot = mesh.find('.')
root, ext = mesh[:dot], mesh[dot:]
assert ext == '.xml' or ext == '.xml.gz', ext
mesh = Mesh(mesh)
gdim = mesh.geometry().dim()
assert gdim > 1 and mesh.topology().dim() == 1
x = mesh.coordinates()
mesh.init(1, 0)
# Compute fall back mesh size:
assert size > 0
size = mesh.hmin() * size
# Don't allow zero padding - collision of lines with bdry segfaults
# too ofter so we prevent it
assert padding > 0
# Finally scale better be positive
assert scale > 0
point = (lambda xi: tuple(xi) + (0, ))\
if gdim == 2 else (lambda xi: tuple(xi))
geo = '.'.join([root, 'geo'])
with open(geo, 'w') as outfile:
# Setup
outfile.write('SetFactory("OpenCASCADE");\n')
outfile.write('size = %g;\n' % size)
outfile.write('SIZE = %g;\n' % (size * scale))
# Points
fmt = 'Point(%d) = {%.16f, %.16f, %.16f, size};\n'
for i, xi in enumerate(x, 1):
outfile.write(fmt % ((i, ) + point(xi)))
# Lines
fmt = 'Line(%d) = {%d, %d};\n'
for i, cell in enumerate(cells(mesh), 1):
outfile.write(fmt % ((i, ) + tuple(cell.entities(0) + 1)))
# BBox
xmin, xmax = x.min(0), x.max(0)
padding = (xmax - xmin) * padding / 2.
xmin -= padding
xmax += padding
dx = xmax - xmin
if gdim == 2 or dx[-1] < 1E-14: # All points are on a plane
rect = 'Rectangle(1) = {%g, %g, %g, %g, %g};\n' % (
xmin[0], xmin[1], 0 if gdim == 2 else xmin[2], dx[0], dx[1])
outfile.write(rect)
bbox = 'Surface'
else:
box = 'Box(1) = {%g, %g, %g, %g, %g, %g};\n' % (
xmin[0], xmin[1], xmin[2], dx[0], dx[1], dx[2])
outfile.write(box)
bbox = 'Volume'
# Crack
for line in xrange(1, mesh.num_cells() + 1):
outfile.write('Line{%d} In %s{1};\n' % (line, bbox))
# Add Physical volume/surface
outfile.write('Physical %s(1) = {1};\n' % bbox)
# Add Physical surface/line
lines = ', '.join(
map(lambda v: '%d' % v, xrange(1,
mesh.num_cells() + 1)))
outfile.write('Physical Line(1) = {%s};\n' % lines)
return geo, gdim
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 scalar_laplacians(
mesh: df.Mesh,
markers: Optional[Dict[str, int]] = None,
ffun: Optional[MeshFunction] = None,
use_krylov_solver: bool = False,
krylov_solver_atol: Optional[float] = None,
krylov_solver_rtol: Optional[float] = None,
krylov_solver_max_its: Optional[int] = None,
verbose: bool = False,
strict: bool = False,
) -> Dict[str, df.Function]:
"""
Calculate the laplacians
Arguments
---------
mesh : dolfin.Mesh
A dolfin mesh
markers : dict (optional)
A dictionary with the markers for the
different bondaries defined in the facet function
or within the mesh itself.
The follwing markers must be provided:
'base', 'lv', 'epi, 'rv' (optional).
If the markers are not provided the following default
vales will be used: base = 10, rv = 20, lv = 30, epi = 40.
fiber_space : str
A string on the form {familiy}_{degree} which
determines for what space the fibers should be calculated for.
use_krylov_solver: bool
If True use Krylov solver, by default False
krylov_solver_atol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the absolute
residual. Default: 1e-15.
krylov_solver_rtol: float (optional)
If a Krylov solver is used, this option specifies a
convergence criterion in terms of the relative
residual. Default: 1e-10.
krylov_solver_max_its: int (optional)
If a Krylov solver is used, this option specifies the
maximum number of iterations to perform. Default: 10000.
verbose: bool
If true, print more info, by default False
strict: bool
If true raise RuntimeError if solutions does not sum to 1.0
"""
if not isinstance(mesh, df.Mesh):
raise TypeError("Expected a dolfin.Mesh as the mesh argument.")
# Init connectivities
mesh.init(2)
if ffun is None:
ffun = df.MeshFunction("size_t", mesh, 2, mesh.domains())
# Boundary markers, solutions and cases
cases, boundaries, markers = find_cases_and_boundaries(ffun, markers)
markers_str = "\n".join(
["{}: {}".format(k, v) for k, v in markers.items()])
df.info(("Compute scalar laplacian solutions with the markers: \n"
"{}").format(markers_str, ), )
check_boundaries_are_marked(
mesh=mesh,
ffun=ffun,
markers=markers,
boundaries=boundaries,
)
# Compte the apex to base solutons
num_vertices = mesh.num_vertices()
num_cells = mesh.num_cells()
if mesh.mpi_comm().size > 1:
num_vertices = mesh.mpi_comm().allreduce(num_vertices)
num_cells = mesh.mpi_comm().allreduce(num_cells)
df.info(" Num vertices: {0}".format(num_vertices))
df.info(" Num cells: {0}".format(num_cells))
if "mv" in cases and "av" in cases:
# Use Doste approach
pass
# Else use the Bayer approach
return bayer(
cases=cases,
mesh=mesh,
markers=markers,
ffun=ffun,
verbose=verbose,
use_krylov_solver=use_krylov_solver,
strict=strict,
krylov_solver_atol=krylov_solver_atol,
krylov_solver_rtol=krylov_solver_rtol,
krylov_solver_max_its=krylov_solver_max_its,
)
