dolfinx.mesh

Creation, refining and marking of meshes.

Functions

`compute_incident_entities`(topology, ...)	Compute all entities of `d1` connected to `entities` of dimension `d0`.
`compute_midpoints`(msh, dim, entities)	Compute the midpoints of a set of mesh entities.
`create_box`(comm, points, n[, cell_type, ...])	Create a box mesh.
`create_geometry`(index_map, dofmap, element, ...)	Create a Geometry object.
`create_interval`(comm, nx, points[, dtype, ...])	Create an interval mesh.
`create_mesh`(comm, cells, x, e[, partitioner])	Create a mesh from topology and geometry arrays.
`create_rectangle`(comm, points, n[, ...])	Create a rectangle mesh.
`create_submesh`(msh, dim, entities)	Create a mesh with specified entities from another mesh.
`create_unit_cube`(comm, nx, ny, nz[, ...])	Create a mesh of a unit cube.
`create_unit_interval`(comm, nx[, dtype, ...])	Create a mesh on the unit interval.
`create_unit_square`(comm, nx, ny[, ...])	Create a mesh of a unit square.
`entities_to_geometry`(msh, dim, entities[, ...])	Compute the geometric DOFs associated with the closure of the given mesh entities.
`exterior_facet_indices`(topology)	Compute the indices of all exterior facets that are owned by the caller.
`locate_entities`(msh, dim, marker)	Compute mesh entities satisfying a geometric marking function.
`locate_entities_boundary`(msh, dim, marker)	Compute mesh entities that are connected to an owned boundary facet and satisfy a geometric marking function.
`meshtags`(msh, dim, entities, values)	Create a MeshTags object that associates data with a subset of mesh entities.
`meshtags_from_entities`(msh, dim, entities, ...)	Create a :class:dolfinx.mesh.MeshTags` object that associates data with a subset of mesh entities, where the entities are defined by their vertices.
`refine`(msh[, edges, partitioner, option])	Refine a mesh.
`transfer_meshtag`(meshtag, msh1, parent_cell)	Generate cell mesh tags on a refined mesh from the mesh tags on the coarse parent mesh.

Classes

`CellType`(value[, names, module, qualname, ...])
`Geometry`(geometry)	The geometry of a `dolfinx.mesh.Mesh`
`GhostMode`(value[, names, module, qualname, ...])
`Mesh`(msh, domain)	A mesh.
`MeshTags`(meshtags)	Mesh tags associate data (markers) with a subset of mesh entities of a given dimension.
`Topology`(topology)	Topology for a `dolfinx.mesh.Mesh`

class dolfinx.mesh.CellType(value, names=<not given>, *values, module=None, qualname=None, type=None, start=1, boundary=None)

Bases: Enum

hexahedron = -8

interval = 2

property name: (self) -> object

point = 1

prism = -6

pyramid = -5

quadrilateral = -4

tetrahedron = 4

triangle = 3

class dolfinx.mesh.Geometry(geometry: Geometry_float32 | Geometry_float64)[source]

Bases: object

The geometry of a dolfinx.mesh.Mesh

Initialize a geometry from a C++ geometry.

Parameters:: geometry – The C++ geometry object.

Note

Geometry objects should usually be constructed with the create_geometry() and not using this class initializer. This class is combined with different base classes that depend on the scalar type used in the Geometry.

property cmap: CoordinateElement: Element that describes the geometry map.

property dim: Dimension of the Euclidean coordinate system.

property dofmap: ndarray[Any, dtype[int32]]: Dofmap for the geometry, shape (num_cells, dofs_per_cell).

index_map() → IndexMap[source]: Index map describing the layout of the geometry points (nodes).

property input_global_indices: ndarray[Any, dtype[int64]]: Global input indices of the geometry nodes.

property x: ndarray[Any, dtype[float32]] | ndarray[Any, dtype[float64]]: Geometry coordinate points, shape=(num_points, 3).

class dolfinx.mesh.GhostMode(value, names=<not given>, *values, module=None, qualname=None, type=None, start=1, boundary=None)

Bases: Enum

none = 0

shared_facet = 1

shared_vertex = 2

class dolfinx.mesh.Mesh(msh, domain: Mesh | None)[source]

Bases: object

A mesh.

Initialize mesh from a C++ mesh.

Parameters:

msh – A C++ mesh object.
domain – A UFL domain.

Note

Mesh objects should usually be constructed using create_mesh() and not using this class initializer. This class is combined with different base classes that depend on the scalar type used in the Mesh.

basix_cell() → Cell[source]: Return the Basix cell type.

property comm

property geometry: Geometry: Mesh geometry.

h(dim: int, entities: ndarray[Any, dtype[int32]]) → ndarray[Any, dtype[float64]][source]

Geometric size measure of cell entities.

Parameters:

dim – Topological dimension of the entities to compute the size measure of.
entities – Indices of entities of dimension dim to compute size measure of.

Returns:

Size measure for each requested entity.

property name

property topology: Topology: Mesh topology.

ufl_cell() → Cell[source]: Return the UFL cell type.

Note

This method is required for UFL compatibility.

ufl_domain() → Mesh[source]

Return the ufl domain corresponding to the mesh.

Returns:: The UFL domain. Is None if the domain has not been set.

Note

This method is required for UFL compatibility.

class dolfinx.mesh.MeshTags(meshtags)[source]

Bases: object

Mesh tags associate data (markers) with a subset of mesh entities of a given dimension.

Initialize tags from a C++ MeshTags object.

Parameters:: meshtags – C++ mesh tags object.

Note

MeshTags objects should not usually be created using this initializer directly.

A Python mesh is passed to the initializer as it may have UFL data attached that is not attached the C + + Mesh that is associated with the C + + meshtags object. If mesh is passed, mesh and meshtags must share the same C + + mesh.

property dim: int: Topological dimension of the tagged entities.

find(value) → ndarray[Any, dtype[int32]][source]

Get a list of all entity indices with a given value.

Parameters:: value – Tag value to search for.
Returns:: Indices of entities with tag value.

property indices: ndarray[Any, dtype[int32]]: Indices of tagged mesh entities.

property name: str: Name of the mesh tags object.

property topology: Topology: Mesh topology with which the the tags are associated.

ufl_id() → int[source]: Identiftying integer used by UFL.

property values: Values associated with tagged mesh entities.

class dolfinx.mesh.Topology(topology: Topology)[source]

Bases: object

Topology for a dolfinx.mesh.Mesh

Initialize a topology from a C++ topology. :param topology: The C++ topology object

Note

Topology objects should usually be constructed with the dolfinx.cpp.mesh.create_topology() and not this class initializer.

cell_name() → str[source]: String representation of the cell-type of the topology

property cell_type: CellType: Get the cell type of the topology.

property comm

connectivity(d0: int, d1: int) → AdjacencyList_int32[source]

Return connectivity from entities of dimension d0 to entities of dimension d1.

Parameters:

d0 – Dimension of entity one is mapping from
d1 – Dimension of entity one is mapping to

create_connectivity(d0: int, d1: int)[source]

Build entity connectivity d0 -> d1.

Parameters:

d0 – Dimension of entities connectivity is from.
d1 – Dimension of entities connectivity is to.

create_entities(dim: int) → bool[source]

Create entities of given topological dimension.

Parameters:: dim – Topological dimension of entities to create.
Returns:: True` is entities are created, ``False is if entities already existed.

create_entity_permutations()[source]: Compute entity permutations and reflections.

property dim: int: Return the topological dimension of the mesh.

property entity_types: list[list[CellType]]: Entity types in the topology for all topological dimensions.

get_cell_permutation_info() → ndarray[Any, dtype[uint32]][source]

Get permutation information.

The returned data is used for packing coefficients and assembling of tensors. The bits of each integer encodes the number of reflections and permutations for each sub-entity of the cell to be able to map it to the reference element.

get_facet_permutations() → ndarray[Any, dtype[uint8]][source]

Get the permutation integer to apply to facets.

The bits of each integer describes the number of reflections and rotations that has to be applied to a facet to map between a facet in the mesh (relative to a cell) and the corresponding facet on the reference element. The data has the shape (num_cells, num_facets_per_cell), flattened row-wise. The number of cells include potential ghost cells.

Note

The data can be unpacked with numpy.unpack_bits.

index_map(dim: int) → IndexMap[source]

Get the IndexMap that describes the parallel distribution of the mesh entities.

Parameters:: dim – Topological dimension.
Returns:: Index map for the entities of dimension dim.

interprocess_facets() → ndarray[Any, dtype[int32]][source]: List of inter-process facets, if facet topology has been computed.

property original_cell_index: ndarray[Any, dtype[int64]]: Get the original cell index

dolfinx.mesh.compute_incident_entities(topology: Topology, entities: ndarray[Any, dtype[int32]], d0: int, d1: int) → ndarray[Any, dtype[int32]][source]

Compute all entities of d1 connected to entities of dimension d0.

Parameters:

topology – The topology.
entities – List of entities fo dimension d0.
d0 – Topological dimension.
d1 – Topological dimension to map to.

Returns:

Incident entity indices.

dolfinx.mesh.compute_midpoints(msh: Mesh, dim: int, entities: ndarray[Any, dtype[int32]])[source]

Compute the midpoints of a set of mesh entities.

Parameters:

msh – The mesh.
dim – Topological dimension of the mesh entities to consider.
entities – Indices of entities in mesh to consider.

Returns:

Midpoints of the entities, shape (num_entities, 3).

Create a box mesh.

Parameters:

comm – MPI communicator.
points – Coordinates of the ‘lower-left’ and ‘upper-right’ corners of the box.
n – List of cells in each direction
cell_type – The cell type.
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64).
ghost_mode – The ghost mode used in the mesh partitioning.
partitioner – Function that computes the parallel distribution of cells across MPI ranks.

Returns:

A mesh of a box domain.

dolfinx.mesh.create_geometry(index_map: IndexMap, dofmap: ndarray[Any, dtype[int32]], element: CoordinateElement, x: ndarray, input_global_indices: ndarray[Any, dtype[int64]]) → Geometry[source]

Create a Geometry object.

Parameters:

index_map – Index map describing the layout of the geometry points (nodes).
dofmap – The geometry (point) dofmap. For a cell, it gives the row in the point coordinates x of each local geometry node. shape=(num_cells, num_dofs_per_cell).
element – Element that describes the cell geometry map.
x – The point coordinates. The shape is (num_points, geometric_dimension).
input_global_indices – The ‘global’ input index of each point, commonly from a mesh input file.

Create an interval mesh.

Parameters:

comm – MPI communicator.
nx – Number of cells.
points – Coordinates of the end points.
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64).
ghost_mode – Ghost mode used in the mesh partitioning. Options are GhostMode.none and GhostMode.shared_facet.
partitioner – Partitioning function to use for determining the parallel distribution of cells across MPI ranks.

Returns:

An interval mesh.

dolfinx.mesh.create_mesh(comm: Comm, cells: ndarray[Any, dtype[int64]], x: ndarray[Any, dtype[floating]], e: Mesh | FiniteElement | _BasixElement | CoordinateElement, partitioner: Callable | None = None) → Mesh[source]

Create a mesh from topology and geometry arrays.

Parameters:

comm – MPI communicator to define the mesh on.
cells – Cells of the mesh. cells[i] are the ‘nodes’ of cell i.
x – Mesh geometry (‘node’ coordinates), with shape (num_nodes, gdim).
e – UFL mesh. The mesh scalar type is determined by the scalar type of e.
partitioner – Function that determines the parallel distribution of cells across MPI ranks.

Note

If required, the coordinates x will be cast to the same scalar type as the domain/element e.

Returns:: A mesh.

Create a rectangle mesh.

Parameters:

comm – MPI communicator.
points – Coordinates of the lower - left and upper - right corners of the rectangle.
n – Number of cells in each direction.
cell_type – Mesh cell type.
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64)
ghost_mode – Ghost mode used in the mesh partitioning.
partitioner – Function that computes the parallel distribution of cells across MPI ranks.
diagonal – Direction of diagonal of triangular meshes. The options are left, right, crossed, left / right, right / left.

Returns:

A mesh of a rectangle.

dolfinx.mesh.create_submesh(msh: Mesh, dim: int, entities: ndarray[Any, dtype[int32]]) → tuple[Mesh, ndarray[Any, dtype[int32]], ndarray[Any, dtype[int32]], ndarray[Any, dtype[int32]]][source]

Create a mesh with specified entities from another mesh.

Parameters:

msh – Mesh to create the sub-mesh from.
dim – Topological dimension of the entities in msh to include in the sub-mesh.
entities – Indices of entities in msh to include in the sub-mesh.

Returns:

The (1) sub mesh, (2) entity map, (3) vertex map, and (4) node map (geometry). Each of the maps a local index of the sub mesh to a local index of msh.

dolfinx.mesh.create_unit_cube(comm: ~mpi4py.MPI.Comm, nx: int, ny: int, nz: int, cell_type=CellType.tetrahedron, dtype: ~numpy.dtype[~typing.Any] | None | type[~typing.Any] | ~numpy._typing._dtype_like._SupportsDType[~numpy.dtype[~typing.Any]] | str | tuple[~typing.Any, int] | tuple[~typing.Any, ~typing.SupportsIndex | ~collections.abc.Sequence[~typing.SupportsIndex]] | list[~typing.Any] | ~numpy._typing._dtype_like._DTypeDict | tuple[~typing.Any, ~typing.Any] = <class 'numpy.float64'>, ghost_mode=GhostMode.shared_facet, partitioner=None) → Mesh[source]

Create a mesh of a unit cube.

Parameters:

comm – MPI communicator.
nx – Number of cells in “x” direction.
ny – Number of cells in “y” direction.
nz – Number of cells in “z” direction.
cell_type – Mesh cell type
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64).
ghost_mode – Ghost mode used in the mesh partitioning.
partitioner – Function that computes the parallel distribution of cells across MPI ranks.

Returns:

A mesh of an axis-aligned unit cube with corners at (0, 0, 0) and (1, 1, 1).

dolfinx.mesh.create_unit_interval(comm: ~mpi4py.MPI.Comm, nx: int, dtype: ~numpy.dtype[~typing.Any] | None | type[~typing.Any] | ~numpy._typing._dtype_like._SupportsDType[~numpy.dtype[~typing.Any]] | str | tuple[~typing.Any, int] | tuple[~typing.Any, ~typing.SupportsIndex | ~collections.abc.Sequence[~typing.SupportsIndex]] | list[~typing.Any] | ~numpy._typing._dtype_like._DTypeDict | tuple[~typing.Any, ~typing.Any] = <class 'numpy.float64'>, ghost_mode=GhostMode.shared_facet, partitioner=None) → Mesh[source]

Create a mesh on the unit interval.

Parameters:

comm – MPI communicator.
nx – Number of cells.
points – Coordinates of the end points.
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64).
ghost_mode – Ghost mode used in the mesh partitioning. Options are GhostMode.none and GhostMode.shared_facet.
partitioner – Partitioning function to use for determining the parallel distribution of cells across MPI ranks.

Returns:

A unit interval mesh with end points at 0 and 1.

dolfinx.mesh.create_unit_square(comm: ~mpi4py.MPI.Comm, nx: int, ny: int, cell_type=CellType.triangle, dtype: ~numpy.dtype[~typing.Any] | None | type[~typing.Any] | ~numpy._typing._dtype_like._SupportsDType[~numpy.dtype[~typing.Any]] | str | tuple[~typing.Any, int] | tuple[~typing.Any, ~typing.SupportsIndex | ~collections.abc.Sequence[~typing.SupportsIndex]] | list[~typing.Any] | ~numpy._typing._dtype_like._DTypeDict | tuple[~typing.Any, ~typing.Any] = <class 'numpy.float64'>, ghost_mode=GhostMode.shared_facet, partitioner=None, diagonal: ~dolfinx.cpp.mesh.DiagonalType = DiagonalType.right) → Mesh[source]

Create a mesh of a unit square.

Parameters:

comm – MPI communicator.
nx – Number of cells in the “x” direction.
ny – Number of cells in the “y” direction.
cell_type – Mesh cell type.
dtype – Float type for the mesh geometry(numpy.float32 or numpy.float64).
ghost_mode – Ghost mode used in the mesh partitioning.
partitioner – Function that computes the parallel distribution of cells across MPI ranks.
diagonal – Direction of diagonal.

Returns:

A mesh of a square with corners at (0, 0) and (1, 1).

dolfinx.mesh.entities_to_geometry(msh: Mesh, dim: int, entities: ndarray[Any, dtype[int32]], permute=False) → ndarray[Any, dtype[int32]][source]

Compute the geometric DOFs associated with the closure of the given mesh entities.

Parameters:

msh – The mesh.
dim – Topological dimension of the entities of interest.
entities – Entity indices (local to the process).
permute – Permute the DOFs such that they are consistent with the orientation of dim-dimensional mesh entities. This requires create_entity_permutations to be called first.

Returns:

The geometric DOFs associated with the closure of the entities in entities.

dolfinx.mesh.exterior_facet_indices(topology: Topology) → ndarray[Any, dtype[int32]][source]

Compute the indices of all exterior facets that are owned by the caller.

An exterior facet (co-dimension 1) is one that is connected globally to only one cell of co-dimension 0).

Note

This is a collective operation that should be called on all processes.

Parameters:: topology – The topology
Returns:: Sorted list of owned facet indices that are exterior facets of the mesh.

dolfinx.mesh.locate_entities(msh: Mesh, dim: int, marker: Callable) → ndarray[source]

Compute mesh entities satisfying a geometric marking function.

Parameters:

msh – Mesh to locate entities on.
dim – Topological dimension of the mesh entities to consider.
marker – A function that takes an array of points x with shape (gdim, num_points) and returns an array of booleans of length num_points, evaluating to True for entities to be located.

Returns:

Indices (local to the process) of marked mesh entities.

dolfinx.mesh.locate_entities_boundary(msh: Mesh, dim: int, marker: Callable) → ndarray[source]

Compute mesh entities that are connected to an owned boundary facet and satisfy a geometric marking function.

For vertices and edges, in parallel this function will not necessarily mark all entities that are on the exterior boundary. For example, it is possible for a process to have a vertex that lies on the boundary without any of the attached facets being a boundary facet. When used to find degrees-of-freedom, e.g. using dolfinx.fem.locate_dofs_topological(), the function that uses the data returned by this function must typically perform some parallel communication.

Parameters:

msh – Mesh to locate boundary entities on.
dim – Topological dimension of the mesh entities to consider
marker – Function that takes an array of points x with shape (gdim, num_points) and returns an array of booleans of length num_points, evaluating to True for entities to be located.

Returns:

Indices (local to the process) of marked mesh entities.

dolfinx.mesh.meshtags(msh: Mesh, dim: int, entities: ndarray[Any, dtype[int32]], values: ndarray | int | float) → MeshTags[source]

Create a MeshTags object that associates data with a subset of mesh entities.

Parameters:

msh – The mesh.
dim – Topological dimension of the mesh entity.
entities – Indices(local to process) of entities to associate values with . The array must be sorted and must not contain duplicates.
values – The corresponding value for each entity.

Returns:

A mesh tags object.

Note

The type of the returned MeshTags is inferred from the type of values.

dolfinx.mesh.meshtags_from_entities(msh: Mesh, dim: int, entities: AdjacencyList, values: ndarray[Any, dtype[Any]])[source]

Create a :class:dolfinx.mesh.MeshTags` object that associates data with a subset of mesh entities, where the entities are defined by their vertices.

Parameters:

msh – The mesh.
dim – Topological dimension of the mesh entity.
entities – Entities to associated values with, with entities defined by their vertices.
values – The corresponding value for each entity.

Returns:

A mesh tags object.

Note

The type of the returned MeshTags is inferred from the type of values.

dolfinx.mesh.refine(msh: ~dolfinx.mesh.Mesh, edges: ~numpy.ndarray | None = None, partitioner: ~typing.Callable | None = <nanobind.nb_func object>, option: ~dolfinx.cpp.refinement.RefinementOption = RefinementOption.none) → tuple[Mesh, ndarray[Any, dtype[int32]], ndarray[Any, dtype[int8]]][source]

Refine a mesh.

Passing None for partitioner, refined cells will be on the same process as the parent cell.

Note

Using the default partitioner for the refined mesh, the refined mesh will not include ghosts cells (cells connected by facet to an owned cells) even if the parent mesh is ghosted.

Warning

Passing None for partitioner, the refined mesh will not have ghosts cells even if the parent mesh has ghost cells. The possibility to not re-partition the refined mesh and include ghost cells in the refined mesh will be added in a future release.

Parameters:

msh – Mesh from which to create the refined mesh.
edges – Indices of edges to split during refinement. If None, mesh refinement is uniform.
partitioner – Partitioner to distribute the refined mesh. If None no redistribution is performed, i.e. refined cells remain on the same process as the parent cell.
option – Controls whether parent cells and/or parent facets are computed.

Returns:

Refined mesh, (optional) parent cells, (optional) parent facets

dolfinx.mesh.transfer_meshtag(meshtag: MeshTags, msh1: Mesh, parent_cell: ndarray[Any, dtype[int32]], parent_facet: ndarray[Any, dtype[int8]] | None = None) → MeshTags[source]

Generate cell mesh tags on a refined mesh from the mesh tags on the coarse parent mesh.

Parameters:

meshtag – Mesh tags on the coarse, parent mesh.
msh1 – The refined mesh.
parent_cell – Index of the parent cell for each cell in the refined mesh.
parent_facet – Index of the local parent facet for each cell in the refined mesh. Only required for transfer tags on facets.

Returns:

Mesh tags on the refined mesh.