# Copyright (C) 2022 Jørgen S. Dokken
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier: LGPL-3.0-or-later
"""Tools to extract data from Gmsh models."""
import typing
from mpi4py import MPI as _MPI
import numpy as np
import numpy.typing as npt
import basix
import basix.ufl
import ufl
from dolfinx import cpp as _cpp
from dolfinx import default_real_type
from dolfinx.cpp.graph import AdjacencyList_int32
from dolfinx.io.utils import distribute_entity_data
from dolfinx.mesh import CellType, Mesh, create_mesh, meshtags, meshtags_from_entities
__all__ = [
"cell_perm_array",
"ufl_mesh",
"extract_topology_and_markers",
"extract_geometry",
"model_to_mesh",
"read_from_msh",
]
# Map from Gmsh cell type identifier (integer) to DOLFINx cell type and
# degree https://gmsh.info//doc/texinfo/gmsh.html#MSH-file-format
_gmsh_to_cells = {
1: ("interval", 1),
2: ("triangle", 1),
3: ("quadrilateral", 1),
4: ("tetrahedron", 1),
5: ("hexahedron", 1),
8: ("interval", 2),
9: ("triangle", 2),
10: ("quadrilateral", 2),
11: ("tetrahedron", 2),
12: ("hexahedron", 2),
15: ("point", 0),
21: ("triangle", 3),
26: ("interval", 3),
29: ("tetrahedron", 3),
36: ("quadrilateral", 3),
92: ("hexahedron", 3),
}
[docs]
def ufl_mesh(gmsh_cell: int, gdim: int, dtype: npt.DTypeLike) -> ufl.Mesh:
"""Create a UFL mesh from a Gmsh cell identifier and geometric dimension.
See https://gmsh.info//doc/texinfo/gmsh.html#MSH-file-format.
Args:
gmsh_cell: Gmsh cell identifier.
gdim: Geometric dimension of the mesh.
Returns:
UFL Mesh using Lagrange elements (equispaced) of the
corresponding DOLFINx cell.
"""
try:
shape, degree = _gmsh_to_cells[gmsh_cell]
except KeyError as e:
print(f"Unknown cell type {gmsh_cell}.")
raise e
cell = ufl.Cell(shape)
element = basix.ufl.element(
basix.ElementFamily.P,
cell.cellname(),
degree,
basix.LagrangeVariant.equispaced,
shape=(gdim,),
dtype=dtype, # type: ignore[arg-type]
)
return ufl.Mesh(element)
[docs]
def cell_perm_array(cell_type: CellType, num_nodes: int) -> list[int]:
"""The permutation array for permuting Gmsh ordering to DOLFINx ordering.
Args:
cell_type: DOLFINx cell type.
num_nodes: Number of nodes in the cell.
Returns:
An array ``p`` such that ``a_dolfinx[i] = a_gmsh[p[i]]``.
"""
return _cpp.io.perm_gmsh(cell_type, num_nodes)
[docs]
def extract_topology_and_markers(model, name: typing.Optional[str] = None):
"""Extract all entities tagged with a physical marker in the gmsh model.
Returns a nested dictionary where the first key is the gmsh MSH
element type integer. Each element type present in the model
contains the cell topology of the elements and corresponding
markers.
Args:
model: Gmsh model.
name: Name of the gmsh model. If not set the current
model will be used.
Returns:
A nested dictionary where each key corresponds to a gmsh cell
type. Each cell type found in the mesh has a 2D array containing
the topology of the marked cell and a list with the
corresponding markers.
"""
if name is not None:
model.setCurrent(name)
# Get the physical groups from gmsh in the form [(dim1, tag1),
# (dim1, tag2), (dim2, tag3),...]
phys_grps = model.getPhysicalGroups()
topologies: dict[int, dict[str, npt.NDArray[typing.Any]]] = {}
for dim, tag in phys_grps:
# Get the entities of dimension `dim`, dim=0 -> Points, dim=1 -
# >Lines, dim=2 -> Triangles/Quadrilaterals, etc.
entities = model.getEntitiesForPhysicalGroup(dim, tag)
for entity in entities:
# Get cell type, list of cells with given tag and topology
# of tagged cells NOTE: Assumes that each entity only have
# one cell-type,
# i.e. facets of prisms and pyramid meshes are not supported
(entity_types, entity_tags, entity_topologies) = model.mesh.getElements(dim, tag=entity)
assert len(entity_types) == 1
# Determine number of local nodes per element to create the
# topology of the elements
properties = model.mesh.getElementProperties(entity_types[0])
name, dim, _, num_nodes, _, _ = properties
# Array of shape (num_elements,num_nodes_per_element)
# containing the topology of the elements on this entity.
# NOTE: Gmsh indexing starts with one, we therefore subtract
# 1 from each node to use zero-based numbering
topology = entity_topologies[0].reshape(-1, num_nodes) - 1
# Create marker array of length of number of tagged cells
marker = np.full_like(entity_tags[0], tag)
# Group element topology and markers of the same entity type
entity_type = entity_types[0]
if entity_type in topologies.keys():
topologies[entity_type]["topology"] = np.concatenate(
(topologies[entity_type]["topology"], topology), axis=0
)
topologies[entity_type]["cell_data"] = np.hstack(
[topologies[entity_type]["cell_data"], marker]
)
else:
topologies[entity_type] = {"topology": topology, "cell_data": marker}
return topologies
[docs]
def model_to_mesh(
model,
comm: _MPI.Comm,
rank: int,
gdim: int = 3,
partitioner: typing.Optional[
typing.Callable[[_MPI.Comm, int, int, AdjacencyList_int32], AdjacencyList_int32]
] = None,
dtype=default_real_type,
) -> tuple[Mesh, _cpp.mesh.MeshTags_int32, _cpp.mesh.MeshTags_int32]:
"""Create a Mesh from a Gmsh model.
Creates a :class:`dolfinx.mesh.Mesh` from the physical entities of
the highest topological dimension in the Gmsh model. In parallel,
the gmsh model is processed on one MPI rank, and the
:class:`dolfinx.mesh.Mesh` is distributed across ranks.
Args:
model: Gmsh model.
comm: MPI communicator to use for mesh creation.
rank: MPI rank that the Gmsh model is initialized on.
gdim: Geometrical dimension of the mesh.
partitioner: Function that computes the parallel
distribution of cells across MPI ranks.
Returns:
A triplet ``(mesh, cell_tags, facet_tags)``, where cell_tags
hold markers for the cells and facet tags holds markers for
facets (if tags are found in Gmsh model).
Note:
For performance, this function should only be called once for
large problems. For re-use, it is recommended to save the mesh
and corresponding tags using :class:`dolfinxio.XDMFFile` after
creation for efficient access.
"""
if comm.rank == rank:
assert model is not None, "Gmsh model is None on rank responsible for mesh creation."
# Get mesh geometry and mesh topology for each element
x = extract_geometry(model)
topologies = extract_topology_and_markers(model)
# Extract Gmsh cell id, dimension of cell and number of nodes to
# cell for each
num_cell_types = len(topologies.keys())
cell_information = dict()
cell_dimensions = np.zeros(num_cell_types, dtype=np.int32)
for i, element in enumerate(topologies.keys()):
_, dim, _, num_nodes, _, _ = model.mesh.getElementProperties(element)
cell_information[i] = {"id": element, "dim": dim, "num_nodes": num_nodes}
cell_dimensions[i] = dim
# Sort elements by ascending dimension
perm_sort = np.argsort(cell_dimensions)
# Broadcast cell type data and geometric dimension
cell_id = cell_information[perm_sort[-1]]["id"]
tdim = cell_information[perm_sort[-1]]["dim"]
num_nodes = cell_information[perm_sort[-1]]["num_nodes"]
cell_id, num_nodes = comm.bcast([cell_id, num_nodes], root=rank)
# Check for facet data and broadcast relevant info if True
has_facet_data = False
if tdim - 1 in cell_dimensions:
has_facet_data = True
has_facet_data = comm.bcast(has_facet_data, root=rank)
if has_facet_data:
num_facet_nodes = comm.bcast(cell_information[perm_sort[-2]]["num_nodes"], root=rank)
gmsh_facet_id = cell_information[perm_sort[-2]]["id"]
marked_facets = np.asarray(topologies[gmsh_facet_id]["topology"], dtype=np.int64)
facet_values = np.asarray(topologies[gmsh_facet_id]["cell_data"], dtype=np.int32)
cells = np.asarray(topologies[cell_id]["topology"], dtype=np.int64)
cell_values = np.asarray(topologies[cell_id]["cell_data"], dtype=np.int32)
else:
cell_id, num_nodes = comm.bcast([None, None], root=rank)
cells, x = np.empty([0, num_nodes], dtype=np.int32), np.empty([0, gdim], dtype=dtype)
cell_values = np.empty((0,), dtype=np.int32)
has_facet_data = comm.bcast(None, root=rank)
if has_facet_data:
num_facet_nodes = comm.bcast(None, root=rank)
marked_facets = np.empty((0, num_facet_nodes), dtype=np.int32)
facet_values = np.empty((0,), dtype=np.int32)
# Create distributed mesh
ufl_domain = ufl_mesh(cell_id, gdim, dtype=dtype)
gmsh_cell_perm = cell_perm_array(_cpp.mesh.to_type(str(ufl_domain.ufl_cell())), num_nodes)
cells = cells[:, gmsh_cell_perm].copy()
mesh = create_mesh(comm, cells, x[:, :gdim].astype(dtype, copy=False), ufl_domain, partitioner)
# Create MeshTags for cells
local_entities, local_values = distribute_entity_data(
mesh._cpp_object, mesh.topology.dim, cells, cell_values
)
mesh.topology.create_connectivity(mesh.topology.dim, 0)
adj = _cpp.graph.AdjacencyList_int32(local_entities)
ct = meshtags_from_entities(
mesh, mesh.topology.dim, adj, local_values.astype(np.int32, copy=False)
)
ct.name = "Cell tags"
# Create MeshTags for facets
topology = mesh.topology
tdim = topology.dim
if has_facet_data:
# Permute facets from MSH to DOLFINx ordering
# FIXME: This does not work for prism meshes
if topology.cell_type == CellType.prism or topology.cell_type == CellType.pyramid:
raise RuntimeError(f"Unsupported cell type {topology.cell_type}")
facet_type = _cpp.mesh.cell_entity_type(
_cpp.mesh.to_type(str(ufl_domain.ufl_cell())), tdim - 1, 0
)
gmsh_facet_perm = cell_perm_array(facet_type, num_facet_nodes)
marked_facets = marked_facets[:, gmsh_facet_perm]
local_entities, local_values = distribute_entity_data(
mesh._cpp_object, tdim - 1, marked_facets, facet_values
)
mesh.topology.create_connectivity(topology.dim - 1, tdim)
adj = _cpp.graph.AdjacencyList_int32(local_entities)
ft = meshtags_from_entities(mesh, tdim - 1, adj, local_values.astype(np.int32, copy=False))
ft.name = "Facet tags"
else:
ft = meshtags(mesh, tdim - 1, np.empty(0, dtype=np.int32), np.empty(0, dtype=np.int32))
return (mesh, ct, ft)
[docs]
def read_from_msh(
filename: str,
comm: _MPI.Comm,
rank: int = 0,
gdim: int = 3,
partitioner: typing.Optional[
typing.Callable[[_MPI.Comm, int, int, AdjacencyList_int32], AdjacencyList_int32]
] = None,
) -> tuple[Mesh, _cpp.mesh.MeshTags_int32, _cpp.mesh.MeshTags_int32]:
"""Read a Gmsh .msh file and return a :class:`dolfinx.mesh.Mesh` and cell facet markers.
Note:
This function requires the Gmsh Python module.
Args:
filename: Name of ``.msh`` file.
comm: MPI communicator to create the mesh on.
rank: Rank of ``comm`` responsible for reading the ``.msh``
file.
gdim: Geometric dimension of the mesh
Returns:
A triplet ``(mesh, cell_tags, facet_tags)`` with meshtags for
associated physical groups for cells and facets.
"""
try:
import gmsh
except ModuleNotFoundError:
# Python 3.11+ adds the add_note method to exceptions
# e.add_note("Gmsh must be installed to import dolfinx.io.gmshio")
raise ModuleNotFoundError(
"No module named 'gmsh': dolfinx.io.gmshio.read_from_msh requires Gmsh.", name="gmsh"
)
if comm.rank == rank:
gmsh.initialize()
gmsh.model.add("Mesh from file")
gmsh.merge(filename)
msh = model_to_mesh(gmsh.model, comm, rank, gdim=gdim, partitioner=partitioner)
gmsh.finalize()
return msh
else:
return model_to_mesh(gmsh.model, comm, rank, gdim=gdim, partitioner=partitioner)