def preprocessingNNZ(mesh_file, out_dir, rank):
''' Preprocess sparsity pattern (NNZ) for parallel matrix allocation
of a given mesh in Gmsh format. Here, dofs are defined for edge
finite element computations.
:param str mesh_file: mesh file name to be preprocess.
:param int rank: MPI rank.
:return: None
'''
if rank == 0:
PETSc.Sys.Print(' Sparsity pattern (nnz.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingNNZ(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute dofs
_, dofsNodes = computeDofs(elemsN, nElems)
nDofs = dofsNodes.shape[0]
# Since PETGEM parallelism is based on PETSc, computation of the matrix
# sparsity pattern is critical in sake of performance. Furthermore, PETGEM
# V1.0 is based on linear edge finite elements which produces six dofs per
# tetrahedral element. Hence, the tetrahedral valence is equal to 34. based
# on this information we build the NNZ vector.
# In order to avoid memory performance issues, add 40% to valence
valence = 50
nnz = np.full((nDofs), valence, dtype=np.int)
# Build PETSc structures
vector = createSequentialVectorWithArray(nnz)
# Delete unnecesary arrays
del nnz
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'nnz.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
return
def preprocessingConductivityModel(mesh_file, material_conductivities,
out_dir, rank):
''' Preprocess conductivity model associated to a given mesh in Gmsh
format. Here, dofs are defined for edge finite element computations.
:param str mesh_file: mesh file name to be preprocess.
:param ndarray material_conductivities: conductivity values
for each material in the mesh.
:param str out_dir: path for output.
:param int rank: MPI rank.
:return: None
'''
if rank == 0:
PETSc.Sys.Print(' Conductivity model (conductivityModel.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingConductivityModel(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsS, nElems = readGmshPhysicalGroups(mesh_file)
# Number of materials
nMaterials = elemsS.max()
# Ensure that material_conductivities (user input) is equal to those
# imported from the Gmsh file (user input)
if rank == 0:
if(not nMaterials == len(material_conductivities)-1):
PETSc.Sys.Print(' The number of materials in ' + mesh_file +
' is not consistent with ' +
'Material conductivities array. Aborting')
exit(-1)
# Build conductivity arrays
conductivityModel = np.zeros(nElems, dtype=np.float)
for iEle in np.arange(nElems):
conductivityModel[iEle] = material_conductivities[np.int(elemsS[iEle])]
# Build PETSc structures
vector = createSequentialVectorWithArray(conductivityModel)
# Delete unnecesary arrays
del conductivityModel
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'conductivityModel.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
return
def preprocessingDOF(mesh_file, out_dir, rank):
''' Preprocess degrees of freedom (DOF) and its associated data structures
of a given mesh in Gmsh format. Here, dofs are defined for edge
finite element computations.
:param str mesh_file: mesh file name to be preprocess.
:param str out_dir: path for output.
:param int rank: MPI rank.
:return: number of DOFS.
:rtype: int
'''
if rank == 0:
PETSc.Sys.Print(' Degrees of freedom (dofs.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingDOF(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute dofs
dofs, dofsNodes = computeDofs(elemsN, nElems)
nDofs = dofsNodes.shape[0]
# Compute faces
elemsF, facesN = computeFaces(elemsN, nElems)
# Compute boundary faces
boundaryFacesN = computeBoundaryFaces(elemsF, facesN)
# Delete unnecesary arrays
del elemsN
del elemsF
del facesN
# Compute boundary dofs
boundaryDofs = computeBoundaryDofs(dofsNodes, boundaryFacesN)
# Delete unnecesary arrays
del boundaryFacesN
# ---------- DOFS ----------
# Get matrix dimensions
size = dofs.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], dofs)
# Delete unnecesary arrays
del dofs
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'dofs.dat'
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------- DOFS TO NODES ----------
if rank == 0:
PETSc.Sys.Print(' Dofs connectivity (dofsNodes.dat)')
# Get matrix dimensions
size = dofsNodes.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], dofsNodes)
# Delete unnecesary arrays
del dofsNodes
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'dofsNodes.dat'
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------- BOUNDARY DOFs ----------
if rank == 0:
PETSc.Sys.Print(' Boundaries (boundaries.dat)')
# Build PETSc structures
vector = createSequentialVectorWithArray(boundaryDofs)
# Delete unnecesary arrays
del boundaryDofs
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'boundaries.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
return nDofs
def postProcessingFields(receivers, modelling, x, Iend_receivers,
Istart_receivers, edgeOrder, nodalOrder,
numDimensions, rank):
''' Compute the CSEM modelling output: primary electric field, secondary
electric field and total electric field on receivers position.
:param petsc matrix receivers: data receivers to compute electric fields
:param object_modelling model: CSEM modelling with physical parameters.
:param petsc vector x: solution vector
:param int Iend_receivers: last range for receivers
:param int Istart_receivers: init range for receivers
:param int edgeOrder: order of tetrahedral edge element
:param int nodalOrder: order of tetrahedral nodal element
:param int numDimensions: number of dimensions
:param int rank: MPI rank
:return: elapsedTimepostprocessing
:rtype: float
'''
# Start timer
Init_postprocessing = getTime()
# Number of receivers
nReceivers = receivers.getSize()[0]
nReceiversLocal = Iend_receivers-Istart_receivers
# Print number of receivers per MPI task
PETSc.Sys.Print(' Number of receivers:', nReceivers)
PETSc.Sys.syncPrint(' Rank: ', rank, ' is post-processing ',
nReceiversLocal, ' receivers')
PETSc.Sys.syncFlush()
# Read edges-connectivity for receivers
# Auxiliar arrays
dataRecv = np.zeros(edgeOrder, dtype=np.float)
edgesIdxRecv = np.zeros((nReceiversLocal, edgeOrder), dtype=PETSc.IntType)
idx = 0
for iRecv in np.arange(Istart_receivers, Iend_receivers):
# Get data of iRecv
temp = np.asarray(receivers.getRow(iRecv))
dataRecv[:] = np.real(temp[1, 19:25])
# Edge-indexes for iRecv
edgesIdxRecv[idx, :] = (dataRecv).astype(PETSc.IntType)
idx += 1
# Gather global solution of x to local vector
# Sequential vector for gather tasks
x_local = createSequentialVector(edgeOrder*nReceiversLocal,
communicator=None)
# Build Index set in PETSc format
IS_edges = PETSc.IS().createGeneral(edgesIdxRecv.flatten(),
comm=PETSc.COMM_WORLD)
# Build gather vector
gatherVector = PETSc.Scatter().create(x, IS_edges, x_local, None)
# Ghater values
gatherVector.scatter(x, x_local, PETSc.InsertMode.INSERT_VALUES,
PETSc.ScatterMode.FORWARD)
# Post-processing electric fields
# Create parallel structures
EpX = createParallelVector(nReceivers, communicator=None)
EpY = createParallelVector(nReceivers, communicator=None)
EpZ = createParallelVector(nReceivers, communicator=None)
EsX = createParallelVector(nReceivers, communicator=None)
EsY = createParallelVector(nReceivers, communicator=None)
EsZ = createParallelVector(nReceivers, communicator=None)
EtX = createParallelVector(nReceivers, communicator=None)
EtY = createParallelVector(nReceivers, communicator=None)
EtZ = createParallelVector(nReceivers, communicator=None)
EpDense = createParallelDenseMatrix(nReceivers, numDimensions,
communicator=None)
EsDense = createParallelDenseMatrix(nReceivers, numDimensions,
communicator=None)
EtDense = createParallelDenseMatrix(nReceivers, numDimensions,
communicator=None)
# Reshape auxiliar array
dataRecv = np.zeros(numDimensions+nodalOrder*numDimensions+nodalOrder,
dtype=np.float)
# Compute fields for all local receivers
idx = 0
for iRecv in np.arange(Istart_receivers, Iend_receivers):
# Get data of iRecv
temp = np.asarray(receivers.getRow(iRecv))
dataRecv[:] = np.real(temp[1, 0:19])
# Receivers coordinates
coordReceiver = dataRecv[0:3]
# Element coordinates
coordElement = dataRecv[3:15]
# Nodal-indexes
nodesElement = (dataRecv[15:19]).astype(PETSc.IntType)
# Compute fields
[EpRecv, EsRecv, EtRecv] = computeFieldsReceiver(modelling,
coordReceiver,
coordElement,
nodesElement,
x_local[idx *
edgeOrder:
(idx *
edgeOrder) +
edgeOrder],
edgeOrder,
numDimensions)
idx += 1
# Set primary field components
EpX.setValue(iRecv, EpRecv[0], addv=PETSc.InsertMode.INSERT_VALUES)
EpY.setValue(iRecv, EpRecv[1], addv=PETSc.InsertMode.INSERT_VALUES)
EpZ.setValue(iRecv, EpRecv[2], addv=PETSc.InsertMode.INSERT_VALUES)
EpDense.setValue(iRecv, 0, EpRecv[0],
addv=PETSc.InsertMode.INSERT_VALUES)
EpDense.setValue(iRecv, 1, EpRecv[1],
addv=PETSc.InsertMode.INSERT_VALUES)
EpDense.setValue(iRecv, 2, EpRecv[2],
addv=PETSc.InsertMode.INSERT_VALUES)
# Set secondary field components
EsX.setValue(iRecv, EsRecv[0],
addv=PETSc.InsertMode.INSERT_VALUES)
EsY.setValue(iRecv, EsRecv[1],
addv=PETSc.InsertMode.INSERT_VALUES)
EsZ.setValue(iRecv, EsRecv[2],
addv=PETSc.InsertMode.INSERT_VALUES)
EsDense.setValue(iRecv, 0, EsRecv[0],
addv=PETSc.InsertMode.INSERT_VALUES)
EsDense.setValue(iRecv, 1, EsRecv[1],
addv=PETSc.InsertMode.INSERT_VALUES)
EsDense.setValue(iRecv, 2, EsRecv[2],
addv=PETSc.InsertMode.INSERT_VALUES)
# Set total field components
EtX.setValue(iRecv, EtRecv[0], addv=PETSc.InsertMode.INSERT_VALUES)
EtY.setValue(iRecv, EtRecv[1], addv=PETSc.InsertMode.INSERT_VALUES)
EtZ.setValue(iRecv, EtRecv[2], addv=PETSc.InsertMode.INSERT_VALUES)
EtDense.setValue(iRecv, 0, EtRecv[0],
addv=PETSc.InsertMode.INSERT_VALUES)
EtDense.setValue(iRecv, 1, EtRecv[1],
addv=PETSc.InsertMode.INSERT_VALUES)
EtDense.setValue(iRecv, 2, EtRecv[2],
addv=PETSc.InsertMode.INSERT_VALUES)
# Start global vector assembly
EpX.assemblyBegin(), EpY.assemblyBegin(), EpZ.assemblyBegin()
EsX.assemblyBegin(), EsY.assemblyBegin(), EsZ.assemblyBegin()
EtX.assemblyBegin(), EtY.assemblyBegin(), EtZ.assemblyBegin()
EpDense.assemblyBegin(), EsDense.assemblyBegin(), EtDense.assemblyBegin()
# End global vector assembly
EpX.assemblyEnd(), EpY.assemblyEnd(), EpZ.assemblyEnd()
EsX.assemblyEnd(), EsY.assemblyEnd(), EsZ.assemblyEnd()
EtX.assemblyEnd(), EtY.assemblyEnd(), EtZ.assemblyEnd()
EpDense.assemblyEnd(), EsDense.assemblyEnd(), EtDense.assemblyEnd()
# Verify if directory exists
MASTER = 0
if rank == MASTER:
checkIfDirectoryExist(modelling['DIR_NAME'] + '/Output/Petsc')
checkIfDirectoryExist(modelling['DIR_NAME'] + '/Output/Ascii')
checkIfDirectoryExist(modelling['DIR_NAME'] + '/Output/Matlab')
# Print
PETSc.Sys.Print(' Saving output:')
# Export electric fields (petsc format)
printMessage(' Petsc format', rank)
# Save primary electric field
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EpX.dat',
EpX, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EpY.dat',
EpY, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EpZ.dat',
EpZ, communicator=None)
writeDenseMatrix(modelling['DIR_NAME'] + '/Output/Petsc/Ep.dat',
EpDense, communicator=None)
# Save secondary electric field
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EsX.dat',
EsX, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EsY.dat',
EsY, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EsZ.dat',
EsZ, communicator=None)
writeDenseMatrix(modelling['DIR_NAME'] + '/Output/Petsc/Es.dat',
EsDense, communicator=None)
# Save total electric field
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EtX.dat',
EtX, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EtY.dat',
EtY, communicator=None)
writePetscVector(modelling['DIR_NAME'] + '/Output/Petsc/EtZ.dat',
EtZ, communicator=None)
writeDenseMatrix(modelling['DIR_NAME'] + '/Output/Petsc/Et.dat',
EtDense, communicator=None)
# Export electric fields (Ascii and Matlab format)
if rank == MASTER:
# Export electric fields (Ascii format)
# Save primary electric field
printMessage(' Ascii format', rank)
dataEp = exportPetscToAscii(nReceivers,
modelling['DIR_NAME'] +
'/Output/Petsc/EpX.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EpY.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EpZ.dat',
modelling['DIR_NAME'] +
'/Output/Ascii/Ep.dat')
# Save secondary electric field
dataEs = exportPetscToAscii(nReceivers,
modelling['DIR_NAME'] +
'/Output/Petsc/EsX.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EsY.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EsZ.dat',
modelling['DIR_NAME'] +
'/Output/Ascii/Es.dat')
# Save total electric field
dataEt = exportPetscToAscii(nReceivers,
modelling['DIR_NAME'] +
'/Output/Petsc/EtX.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EtY.dat',
modelling['DIR_NAME'] +
'/Output/Petsc/EtZ.dat',
modelling['DIR_NAME'] +
'/Output/Ascii/Et.dat')
# Export electric fields (Matlab format)
printMessage(' Matlab format', rank)
# Save primary electric field
exportNumpytoMatlab(dataEp, modelling['DIR_NAME'] +
'/Output/Matlab/Ep.mat', electricField='Primary')
# Save secondary electric field
exportNumpytoMatlab(dataEs, modelling['DIR_NAME'] +
'/Output/Matlab/Es.mat', electricField='Secondary')
# Save total electric field
exportNumpytoMatlab(dataEt, modelling['DIR_NAME'] +
'/Output/Matlab/Et.mat', electricField='Total')
# Remove temporal files (petsc)
filesToDelete = [modelling['DIR_NAME'] + '/Output/Petsc/EpX.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EpY.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EpZ.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EsX.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EsY.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EsZ.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EtX.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EtY.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EtZ.dat',
modelling['DIR_NAME'] + '/Output/Petsc/EpX.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EpY.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EpZ.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EsX.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EsY.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EsZ.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EtX.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EtY.dat.info',
modelling['DIR_NAME'] + '/Output/Petsc/EtZ.dat.info']
for iFile in np.arange(len(filesToDelete)):
removeFile(filesToDelete[iFile])
# End timer
End_postprocessing = getTime()
# Elapsed time in assembly
elapsedTimepostprocessing = End_postprocessing-Init_postprocessing
return elapsedTimepostprocessing
def preprocessingNNZ(nedelec_order, mesh_file, out_dir, rank):
''' Preprocess sparsity pattern (NNZ) for parallel matrix allocation
of a given mesh in Gmsh format.
Since PETGEM parallelism is based on PETSc, computation of the matrix
sparsity pattern is critical in sake of performance. Furthermore, PETGEM
is based on tetrahedral edge finite elements of first, second and third
order which produces:
* 6 DOFs per element in first order discretizations
* 20 DOFs per element in second order discretizations
* 45 DOFs per element in third order discretizations
Hence, the tetrahedral valence is equal to:
* 34 in first order discretizations
* 134 in second order discretizations
* 363 in third order discretizations
:param int nedelec_order: nedelec element order.
:param str mesh_file: mesh file name to be preprocess.
:param int rank: MPI rank.
:return: None
'''
if rank == 0:
PETSc.Sys.Print(' Sparsity pattern (nnz.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingNNZ(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute number of edges
_, edgesNodes = computeEdges(elemsN, nElems, nedelec_order)
nEdges = edgesNodes.shape[0]
# Compute number of faces
elemsF, facesN = computeFaces(elemsN, nElems, nedelec_order)
nFaces = facesN.shape[0]
if nedelec_order == 1: # First order edge element
# Number of DOFs correspond to the number of edges in the mesh
nDofs = nEdges
# In order to avoid memory performance issues, add 20% to valence
valence = 41
elif nedelec_order == 2: # Second order edge element
# Number of DOFs
nDofs = nEdges * np.int(2) + nFaces * np.int(2)
# In order to avoid memory performance issues, add 20% to valence
valence = 161
elif nedelec_order == 3: # Third order edge element
# Number of DOFs
nDofs = nEdges * np.int(3) + nFaces * np.int(6) + nElems * np.int(3)
# In order to avoid memory performance issues, add 20% to valence
valence = 436
else:
raise ValueError('Edge element order=', nedelec_order,
' not supported.')
# Build nnz pattern for each row
nnz = np.full((nDofs), valence, dtype=np.int)
# Build PETSc structures
vector = createSequentialVectorWithArray(nnz)
# Delete unnecesary arrays
del nnz
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'nnz.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
return
def preprocessingEdges(nedelec_order, mesh_file, out_dir, rank):
''' Preprocess edges, edge boundaries and its associated data structures
of a given mesh in Gmsh format. For edge finite element of linear
order the edges are the dofs. For edge finite element of second order
the dofs are computed in runtime based on edges and faces on each
tetrahedral element.
:param int nedelec_order: nedelec element order.
:param str mesh_file: mesh file name to be preprocess.
:param str out_dir: path for output.
:param int rank: MPI rank.
:return: number of edges.
:rtype: int
'''
# ---------- Export Edges ----------
if rank == 0:
PETSc.Sys.Print(' Edges (edges.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingEdges(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute edges
elemsE, edgesNodes = computeEdges(elemsN, nElems, nedelec_order)
nEdges = edgesNodes.shape[0]
# Compute boundaries
boundaries, nDofs = computeBoundaries(elemsN, nElems, edgesNodes,
nedelec_order)
# ---------- Export Edges ----------
# Get matrix dimensions
size = elemsE.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsE)
# Delete unnecesary arrays
del elemsE
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'edges.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------- Export Edges to nodes ----------
if rank == 0:
PETSc.Sys.Print(' Edges connectivity (edgesNodes.dat)')
# Get matrix dimensions
size = edgesNodes.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], edgesNodes)
# Delete unnecesary arrays
del edgesNodes
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'edgesNodes.dat'
# Write PETGEM edgesNodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------- Export boundaries ----------
if rank == 0:
PETSc.Sys.Print(' Boundaries (boundaries.dat)')
# Build PETSc structures
vector = createSequentialVectorWithArray(boundaries)
# Delete unnecesary arrays
del boundaries
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'boundaries.dat'
# Write PETGEM nodes in PETSc format
writePetscVector(out_path, vector, communicator=PETSc.COMM_SELF)
return nEdges, nDofs