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 preprocessNodes(mesh_file, out_dir, rank):
''' Preprocess nodal coordinates of a given mesh in Gmsh format.
: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 nodes
:rtype: int
'''
if rank == 0:
PETSc.Sys.Print(' Nodal coordinates (nodes.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessNodes(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read nodes
nodes, nNodes = readGmshNodes(mesh_file)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Build coordinates in PETGEM format where each row
# represent the xyz coordinates of the 4 tetrahedral element
numDimensions = 3
nodalOrder = 4
data = np.array((nodes[elemsN[:], :]), dtype=np.float)
data = data.reshape(nElems, numDimensions*nodalOrder)
# Delete unnecesary arrays
del nodes
del elemsN
# Get matrix dimensions
size = data.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], data)
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'nodes.dat'
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
return nNodes
def preprocessingNodalConnectivity(mesh_file, out_dir, rank):
''' Preprocess nodal connectivity of a given mesh in Gmsh format.
: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 tetrahedral elements
:rtype: int
'''
if rank == 0:
PETSc.Sys.Print(' Nodal connectivity (elemsN.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingNodalConnectivity(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Get matrix dimensions
size = elemsN.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsN)
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'meshConnectivity.dat'
# Write PETGEM nodes in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
return nElems
def preprocessingDataReceivers(mesh_file, receivers_file,
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 str receivers_file: receiver positions file name to be preprocess.
:param str out_dir: path for output.
:param int rank: MPI rank.
:return: None
'''
from scipy.spatial import Delaunay
if rank == 0:
PETSc.Sys.Print(' Receiver positions (receivers.dat)')
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingDataReceivers(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Check if receivers_file exist
success = checkFilePath(receivers_file)
if rank == 0:
if not success:
msg = (' preprocessingDataReceivers(): file ' + receivers_file +
' does not exist.')
raise ValueError(msg)
# Read receivers_file
receivers = np.loadtxt(receivers_file)
# Number of receivers
if receivers.ndim == 1:
nReceivers = 1
else:
dim = receivers.shape
nReceivers = dim[0]
# Read nodes
nodes, nNodes = readGmshNodes(mesh_file)
# Build Delaunay triangulation with nodes
tri = Delaunay(nodes)
# Delete unnecesary arrays
del nodes
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute dofs
dofs, _ = computeDofs(elemsN, nElems)
# Overwrite Delaunay structure with mesh_file connectivity
tri.simplices = elemsN.astype(np.int32)
# Delete unnecesary arrays
del elemsN
# Find out which tetrahedral element points are in
recvElems = tri.find_simplex(receivers)
# Determine if all receiver points were found
idx = np.where(recvElems < 0)[0]
# If idx is not empty, there are receivers outside the domain
if idx.size != 0:
PETSc.Sys.Print(' Some receivers are were not located')
PETSc.Sys.Print(' Following ID-receivers will not be taken ' +
'into account: ')
PETSc.Sys.Print(idx)
# Update number of receivers
nReceivers = nReceivers - len(idx)
if nReceivers == 0:
PETSc.Sys.Print(' No receiver has been found. Nothing to do.'
' Aborting')
exit(-1)
# Remove idx from receivers matrix
receivers = np.delete(receivers, idx, axis=0)
# Create new file with located points coordinates
# Build path to save the file
out_path = out_dir + 'receiversPETGEM.txt'
PETSc.Sys.Print(' Saving file with localized receiver positions ' +
'(receiversPETGEM.txt)')
np.savetxt(out_path, receivers, fmt='%1.8e')
# Allocate space for receives in PETGEM format
numDimensions = 3
nodalOrder = 4
edgeOrder = 6
allocate = numDimensions+nodalOrder*numDimensions+nodalOrder+edgeOrder
tmp = np.zeros((nReceivers, allocate), dtype=np.float)
# Fill tmp matrix with receiver positions, element coordinates and
# nodal indexes
for iReceiver in np.arange(nReceivers):
# If there is one receiver
if nReceivers == 1:
# Get receiver coordinates
coordiReceiver = receivers[0:]
# Get element coordinates (container element)
coordElement = tri.points[tri.simplices[recvElems, :]]
coordElement = coordElement.flatten()
# Get nodal indexes (container element)
nodesElement = tri.simplices[recvElems, :]
# Get element-dofs indices (container element)
dofsElement = dofs[recvElems, :]
# If there are more than one receivers
else:
# Get receiver coordinates
coordiReceiver = receivers[iReceiver, :]
# Get element coordinates (container element)
coordElement = tri.points[tri.simplices[recvElems[iReceiver], :]]
coordElement = coordElement.flatten()
# Get nodal indexes (container element)
nodesElement = tri.simplices[recvElems[iReceiver], :]
# Get element-dofs indices (container element)
dofsElement = dofs[recvElems[iReceiver], :]
# Insert data for iReceiver
tmp[iReceiver, 0:3] = coordiReceiver
tmp[iReceiver, 3:15] = coordElement
tmp[iReceiver, 15:19] = nodesElement
tmp[iReceiver, 19:] = dofsElement
# Delete unnecesary arrays
del tri
del dofs
# Get matrix dimensions
size = tmp.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], tmp)
# Delete unnecesary arrays
del tmp
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'receivers.dat'
# Write PETGEM receivers in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
return nReceivers
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 readPreprocessingParams(input_params, rank):
''' Read a preprocessing input, namely a preprocessing parameters file
name.
:params list input_params: user input parameters.
:param int rank: MPI rank.
:return: a modelling dictionary.
:rtype: dict of type modelling.
'''
num_params = checkNumberParamsPreprocessing(input_params)
# PETGEM parameters file in 3rd position in sys.argv
input_path = input_params[1]
# Check if file_name exist
success = checkFilePath(input_path)
if rank == 0:
if not success:
msg = (' readPreprocessingParams(): file ' + input_path +
' does not exist.')
raise ValueError(msg)
# Else, import file_name
DIR_NAME = path.dirname(input_path) # Split dir path
PARAMS_FILE_NAME = path.basename(input_path) # Split file path
sys.path.append(DIR_NAME) # Add dir path to system
# Remove extension if exist
remove_extension = False
if PARAMS_FILE_NAME.endswith('.py'):
PARAMS_FILE_NAME = PARAMS_FILE_NAME[:-3]
remove_extension = True
# Import params file as module (importlib)
import_success = False
try:
preprocessing_temp = import_module(PARAMS_FILE_NAME)
import_success = True
except:
pass
# Recover original file name
if remove_extension:
PARAMS_FILE_NAME = PARAMS_FILE_NAME + '.py'
if rank == 0:
if import_success:
PETSc.Sys.Print(' readPreprocessingParams(): file "' +
PARAMS_FILE_NAME +
'" has been successfully imported.')
else:
msg = (' readPreprocessingParams(): file "' + PARAMS_FILE_NAME +
'" has not been successfully imported.')
raise ValueError(msg)
# Check consistency
# Check dictionary content (This name must match with dictionary name
# in parameters file, namely, must be == 'preprocessing')
if rank == 0:
preprocessing = checkPreprocessingConsistency(rank,
preprocessing_temp.
preprocessing,
PARAMS_FILE_NAME)
# Print modelling content
if rank == 0:
printPreprocessingData(preprocessing, input_path)
return preprocessing
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 preprocessingFaces(nedelec_order, mesh_file, out_dir, rank):
''' Preprocess faces, face boundaries and its associated data structures
of a given mesh in Gmsh format.
: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
'''
# Check if mesh_file exist
success = checkFilePath(mesh_file)
if rank == 0:
if not success:
msg = (' preprocessingFaces(): file ' + mesh_file +
' does not exist.')
raise ValueError(msg)
# Read connectivity
elemsN, nElems = readGmshConnectivity(mesh_file)
# Compute faces
elemsF, facesN = computeFaces(elemsN, nElems, nedelec_order)
# Number of faces
size = facesN.shape
nFaces = size[0]
# Delete unnecesary arrays
del elemsN
# ---------- Export Faces connectivity ----------
if rank == 0:
PETSc.Sys.Print(' Faces connectivity (faces.dat)')
# Get matrix dimensions
size = elemsF.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], elemsF)
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'faces.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
# ---------- Export Faces connectivity ----------
if rank == 0:
PETSc.Sys.Print(' Faces-nodes connectivity (facesN.dat)')
# Build facesN connectivity for each element
nNodes_face = 3
nFaces_element = 4
# Allocate matrix with an additional position to store the total number of
# faces in the mesh
facesN_tmp = np.zeros((nElems, nNodes_face * nFaces_element + 1))
for iEle in np.arange(nElems):
facesElement = elemsF[iEle, :]
nodesFace = facesN[facesElement, :]
facesN_tmp[iEle, 0] = nFaces
facesN_tmp[iEle, 1:] = nodesFace.reshape(1,
nNodes_face * nFaces_element)
# Get matrix dimensions
size = facesN_tmp.shape
# Build PETSc structures
matrix = createSequentialDenseMatrixWithArray(size[0], size[1], facesN_tmp)
# Delete unnecesary arrays
del elemsF
del facesN
del facesN_tmp
# Verify if OUT_DIR exists
checkIfDirectoryExist(out_dir)
# Build path to save the file
out_path = out_dir + 'facesNodes.dat'
# Write PETGEM edges in PETSc format
writeParallelDenseMatrix(out_path, matrix, communicator=PETSc.COMM_SELF)
return nFaces
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