DOLFINx 0.9.0
DOLFINx C++ interface
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dolfinx::mesh Namespace Reference

Mesh data structures and algorithms on meshes. More...

Classes

class  Geometry
 Geometry stores the geometry imposed on a mesh. More...
 
class  Mesh
 A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data. More...
 
class  MeshTags
 MeshTags associate values with mesh topology entities. More...
 
class  Topology
 Topology stores the topology of a mesh, consisting of mesh entities and connectivity (incidence relations for the mesh entities). More...
 

Concepts

concept  MarkerFn
 Requirements on function for geometry marking.
 

Typedefs

using CellPartitionFunction
 Signature for the cell partitioning function. The function should compute the destination rank for cells currently on this rank.
 

Enumerations

enum class  CellType : int {
  point = 1 , interval = 2 , triangle = 3 , tetrahedron = 4 ,
  quadrilateral = -4 , pyramid = -5 , prism = -6 , hexahedron = -8
}
 Cell type identifier.
 
enum class  DiagonalType {
  left , right , crossed , shared_facet ,
  left_right , right_left
}
 Enum for different diagonal types.
 
enum class  GhostMode : int { none , shared_facet , shared_vertex }
 Enum for different partitioning ghost modes.
 

Functions

std::string to_string (CellType type)
 
CellType to_type (const std::string &cell)
 
CellType cell_entity_type (CellType type, int d, int index)
 Return type of cell for entity of dimension d at given entity index.
 
CellType cell_facet_type (CellType type, int index)
 
graph::AdjacencyList< int > get_entity_vertices (CellType type, int dim)
 
graph::AdjacencyList< int > get_sub_entities (CellType type, int dim0, int dim1)
 
int cell_dim (CellType type)
 Return topological dimension of cell type.
 
int cell_num_entities (CellType type, int dim)
 
bool is_simplex (CellType type)
 
int num_cell_vertices (CellType type)
 
std::map< std::array< int, 2 >, std::vector< std::set< int > > > cell_entity_closure (CellType cell_type)
 
basix::cell::type cell_type_to_basix_type (CellType celltype)
 Convert a cell type to a Basix cell type.
 
CellType cell_type_from_basix_type (basix::cell::type celltype)
 Get a cell type from a Basix cell type.
 
template<std::floating_point T = double>
Mesh< T > create_box (MPI_Comm comm, MPI_Comm subcomm, std::array< std::array< T, 3 >, 2 > p, std::array< std::int64_t, 3 > n, CellType celltype, CellPartitionFunction partitioner=nullptr)
 Create a uniform mesh::Mesh over rectangular prism spanned by the two points p.
 
template<std::floating_point T = double>
Mesh< T > create_box (MPI_Comm comm, std::array< std::array< T, 3 >, 2 > p, std::array< std::int64_t, 3 > n, CellType celltype, const CellPartitionFunction &partitioner=nullptr)
 Create a uniform mesh::Mesh over rectangular prism spanned by the two points p.
 
template<std::floating_point T = double>
Mesh< T > create_rectangle (MPI_Comm comm, std::array< std::array< T, 2 >, 2 > p, std::array< std::int64_t, 2 > n, CellType celltype, CellPartitionFunction partitioner, DiagonalType diagonal=DiagonalType::right)
 Create a uniform mesh::Mesh over the rectangle spanned by the two points p.
 
template<std::floating_point T = double>
Mesh< T > create_rectangle (MPI_Comm comm, std::array< std::array< T, 2 >, 2 > p, std::array< std::int64_t, 2 > n, CellType celltype, DiagonalType diagonal=DiagonalType::right)
 Create a uniform mesh::Mesh over the rectangle spanned by the two points p.
 
template<std::floating_point T = double>
Mesh< T > create_interval (MPI_Comm comm, std::int64_t n, std::array< T, 2 > p, mesh::GhostMode ghost_mode=mesh::GhostMode::none, CellPartitionFunction partitioner=nullptr)
 Interval mesh of the 1D line [a, b].
 
template<typename U >
Geometry< typename std::remove_reference_t< typename U::value_type > > create_geometry (const Topology &topology, const std::vector< fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > > &elements, std::span< const std::int64_t > nodes, std::span< const std::int64_t > xdofs, const U &x, int dim, std::function< std::vector< int >(const graph::AdjacencyList< std::int32_t > &)> reorder_fn=nullptr)
 Build Geometry from input data.
 
template<typename U >
Geometry< typename std::remove_reference_t< typename U::value_type > > create_geometry (const Topology &topology, const fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > &element, std::span< const std::int64_t > nodes, std::span< const std::int64_t > xdofs, const U &x, int dim, std::function< std::vector< int >(const graph::AdjacencyList< std::int32_t > &)> reorder_fn=nullptr)
 Build Geometry from input data.
 
std::tuple< graph::AdjacencyList< std::int32_t >, std::vector< std::int64_t >, std::size_t, std::vector< std::int32_t > > build_local_dual_graph (std::span< const CellType > celltypes, const std::vector< std::span< const std::int64_t > > &cells)
 Compute the local part of the dual graph (cell-cell connections via facets) and facets with only one attached cell.
 
graph::AdjacencyList< std::int64_t > build_dual_graph (MPI_Comm comm, std::span< const CellType > celltypes, const std::vector< std::span< const std::int64_t > > &cells)
 Build distributed mesh dual graph (cell-cell connections via facets) from minimal mesh data.
 
template<typename T >
MeshTags< T > create_meshtags (std::shared_ptr< const Topology > topology, int dim, const graph::AdjacencyList< std::int32_t > &entities, std::span< const T > values)
 Create MeshTags from arrays.
 
std::pair< std::vector< std::uint8_t >, std::vector< std::uint32_t > > compute_entity_permutations (const Topology &topology)
 
Topology create_topology (MPI_Comm comm, std::span< const std::int64_t > cells, std::span< const std::int64_t > original_cell_index, std::span< const int > ghost_owners, CellType cell_type, std::span< const std::int64_t > boundary_vertices)
 Create a mesh topology.
 
Topology create_topology (MPI_Comm comm, const std::vector< CellType > &cell_type, std::vector< std::span< const std::int64_t > > cells, std::vector< std::span< const std::int64_t > > original_cell_index, std::vector< std::span< const int > > ghost_owners, std::span< const std::int64_t > boundary_vertices)
 Create a topology of mixed cell type.
 
std::tuple< Topology, std::vector< int32_t >, std::vector< int32_t > > create_subtopology (const Topology &topology, int dim, std::span< const std::int32_t > entities)
 Create a topology for a subset of entities of a given topological dimension.
 
std::vector< std::int32_t > entities_to_index (const Topology &topology, int dim, std::span< const std::int32_t > entities)
 Get entity indices for entities defined by their vertices.
 
std::tuple< std::vector< std::shared_ptr< graph::AdjacencyList< std::int32_t > > >, std::shared_ptr< graph::AdjacencyList< std::int32_t > >, std::shared_ptr< common::IndexMap >, std::vector< std::int32_t > > compute_entities (MPI_Comm comm, const Topology &topology, int dim, int index)
 Compute mesh entities of given topological dimension by computing entity-to-vertex connectivity (dim, 0), and cell-to-entity connectivity (tdim, dim).
 
std::array< std::shared_ptr< graph::AdjacencyList< std::int32_t > >, 2 > compute_connectivity (const Topology &topology, std::pair< std::int8_t, std::int8_t > d0, std::pair< std::int8_t, std::int8_t > d1)
 Compute connectivity (d0 -> d1) for given pair of entity types, given by topological dimension and index, as found in Topology::entity_types()
 
std::vector< std::int32_t > exterior_facet_indices (const Topology &topology)
 Compute the indices of all exterior facets that are owned by the caller.
 
std::vector< std::int64_t > extract_topology (CellType cell_type, const fem::ElementDofLayout &layout, std::span< const std::int64_t > cells)
 Extract topology from cell data, i.e. extract cell vertices.
 
template<std::floating_point T>
std::vector< T > h (const Mesh< T > &mesh, std::span< const std::int32_t > entities, int dim)
 Compute greatest distance between any two vertices of the mesh entities (h).
 
template<std::floating_point T>
std::vector< T > cell_normals (const Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities)
 Compute normal to given cell (viewed as embedded in 3D)
 
template<std::floating_point T>
std::vector< T > compute_midpoints (const Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities)
 Compute the midpoints for mesh entities of a given dimension.
 
template<std::floating_point T, MarkerFn< T > U>
std::vector< std::int32_t > locate_entities (const Mesh< T > &mesh, int dim, U marker)
 Compute indices of all mesh entities that evaluate to true for the provided geometric marking function.
 
template<std::floating_point T, MarkerFn< T > U>
std::vector< std::int32_t > locate_entities_boundary (const Mesh< T > &mesh, int dim, U marker)
 Compute indices of all mesh entities that are attached to an owned boundary facet and evaluate to true for the provided geometric marking function.
 
template<std::floating_point T>
std::vector< std::int32_t > entities_to_geometry (const Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities, bool permute=false)
 Compute the geometry degrees of freedom associated with the closure of a given set of cell entities.
 
CellPartitionFunction create_cell_partitioner (mesh::GhostMode ghost_mode=mesh::GhostMode::none, const graph::partition_fn &partfn=&graph::partition_graph)
 
std::vector< std::int32_t > compute_incident_entities (const Topology &topology, std::span< const std::int32_t > entities, int d0, int d1)
 Compute incident indices.
 
template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh (MPI_Comm comm, MPI_Comm commt, std::span< const std::int64_t > cells, const fem::CoordinateElement< typename std::remove_reference_t< typename U::value_type > > &element, MPI_Comm commg, const U &x, std::array< std::size_t, 2 > xshape, const CellPartitionFunction &partitioner)
 Create a distributed mesh from mesh data using a provided graph partitioning function for determining the parallel distribution of the mesh.
 
template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh (MPI_Comm comm, MPI_Comm commt, const std::vector< std::span< const std::int64_t > > &cells, const std::vector< fem::CoordinateElement< typename std::remove_reference_t< typename U::value_type > > > &elements, MPI_Comm commg, const U &x, std::array< std::size_t, 2 > xshape, const CellPartitionFunction &partitioner)
 Create a distributed mixed-topology mesh from mesh data using a provided graph partitioning function for determining the parallel distribution of the mesh.
 
template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh (MPI_Comm comm, std::span< const std::int64_t > cells, const fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > &elements, const U &x, std::array< std::size_t, 2 > xshape, GhostMode ghost_mode)
 Create a distributed mesh from mesh data using the default graph partitioner to determine the parallel distribution of the mesh.
 
template<std::floating_point T>
std::pair< Geometry< T >, std::vector< int32_t > > create_subgeometry (const Mesh< T > &mesh, int dim, std::span< const std::int32_t > subentity_to_entity)
 Create a sub-geometry from a mesh and a subset of mesh entities to be included. A sub-geometry is simply a Geometry object containing only the geometric information for the subset of entities. The entities may differ in topological dimension from the original mesh.
 
template<std::floating_point T>
std::tuple< Mesh< T >, std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< std::int32_t > > create_submesh (const Mesh< T > &mesh, int dim, std::span< const std::int32_t > entities)
 Create a new mesh consisting of a subset of entities in a mesh.
 

Detailed Description

Mesh data structures and algorithms on meshes.

Representations of meshes and support for operations on meshes.

Typedef Documentation

◆ CellPartitionFunction

Initial value:
std::function<graph::AdjacencyList<std::int32_t>(
MPI_Comm comm, int nparts, const std::vector<CellType>& cell_types,
const std::vector<std::span<const std::int64_t>>& cells)>

Signature for the cell partitioning function. The function should compute the destination rank for cells currently on this rank.

Parameters
[in]commMPI Communicator
[in]npartsNumber of partitions
[in]cell_typesCell types in the mesh
[in]cellsLists of cells of each cell type. cells[i] is a flattened row major 2D array of shape (num_cells, num_cell_vertices) for cell_types[i] on this process, containing the global indices for the cell vertices. Each cell can appear only once across all processes. The cell vertex indices are not necessarily contiguous globally, i.e. the maximum index across all processes can be greater than the number of vertices. High-order 'nodes', e.g. mid-side points, should not be included.
Returns
Destination ranks for each cell on this process
Note
Cells can have multiple destination ranks, when ghosted.

Function Documentation

◆ build_dual_graph()

graph::AdjacencyList< std::int64_t > build_dual_graph ( MPI_Comm comm,
std::span< const CellType > celltypes,
const std::vector< std::span< const std::int64_t > > & cells )

Build distributed mesh dual graph (cell-cell connections via facets) from minimal mesh data.

The computed dual graph is typically passed to a graph partitioner.

Note
Collective function
Parameters
[in]commThe MPI communicator
[in]celltypesList of cell types
[in]cellsCollections of cells, defined by the cell vertices from which to build the dual graph, as flattened arrays for each cell type in celltypes.
Note
cells and celltypes must have the same size.
Returns
The dual graph

◆ build_local_dual_graph()

std::tuple< graph::AdjacencyList< std::int32_t >, std::vector< std::int64_t >, std::size_t, std::vector< std::int32_t > > build_local_dual_graph ( std::span< const CellType > celltypes,
const std::vector< std::span< const std::int64_t > > & cells )

Compute the local part of the dual graph (cell-cell connections via facets) and facets with only one attached cell.

Parameters
[in]celltypesList of cell types.
[in]cellsLists of cell vertices (stored as flattened lists, one for each cell type).
Returns
  1. Local dual graph
  2. Facets, defined by their vertices, that are shared by only one cell on this rank. The logically 2D array is flattened (row-major).
  3. The number of columns for the facet data array (2).
  4. The attached cell (local index) to each returned facet in (2).

Each row of the returned data (2) contains [v0, ... v_(n-1), x, .., / x], where v_i is a vertex global index, x is a padding value (all padding values will be equal).

Note
The cells of each cell type are numbered locally consecutively, i.e. if there are n cells of type 0 and m cells of type 1, then cells of type 0 are numbered 0..(n-1) and cells of type 1 are numbered n..(n+m-1) respectively, in the returned dual graph.

◆ cell_entity_closure()

std::map< std::array< int, 2 >, std::vector< std::set< int > > > cell_entity_closure ( CellType cell_type)

Closure entities for a cell, i.e., all lower-dimensional entities attached to a cell entity. Map from entity {dim_e, entity_e} to closure{sub_dim, (sub_entities)}

◆ cell_facet_type()

mesh::CellType cell_facet_type ( CellType type,
int index )

Return facet type of cell For simplex and hypercube cell types, this is independent of the facet index, but for prism and pyramid, it can be triangle or quadrilateral.

Parameters
[in]typeThe cell type
[in]indexThe facet index
Returns
The type of facet for this cell at this index

◆ cell_normals()

template<std::floating_point T>
std::vector< T > cell_normals ( const Mesh< T > & mesh,
int dim,
std::span< const std::int32_t > entities )

Compute normal to given cell (viewed as embedded in 3D)

Returns
The entity normals. The shape is (entities.size(), 3) and the storage is row-major.

◆ cell_num_entities()

int cell_num_entities ( CellType type,
int dim )

Number of entities of dimension dim

Parameters
[in]dimEntity dimension
[in]typeCell type
Returns
Number of entities in cell

◆ compute_connectivity()

std::array< std::shared_ptr< graph::AdjacencyList< std::int32_t > >, 2 > compute_connectivity ( const Topology & topology,
std::pair< std::int8_t, std::int8_t > d0,
std::pair< std::int8_t, std::int8_t > d1 )

Compute connectivity (d0 -> d1) for given pair of entity types, given by topological dimension and index, as found in Topology::entity_types()

Parameters
[in]topologyThe topology
[in]d0The dimension and index of the entities
[in]d1The dimension and index of the incident entities
Returns
The connectivities [(d0 -> d1), (d1 -> d0)] if they are computed. If (d0, d1) already exists then a nullptr is returned. If (d0, d1) is computed and the computation of (d1, d0) was required as part of computing (d0, d1), the (d1, d0) is returned as the second entry. The second entry is otherwise nullptr.

◆ compute_entities()

std::tuple< std::vector< std::shared_ptr< graph::AdjacencyList< std::int32_t > > >, std::shared_ptr< graph::AdjacencyList< std::int32_t > >, std::shared_ptr< common::IndexMap >, std::vector< std::int32_t > > compute_entities ( MPI_Comm comm,
const Topology & topology,
int dim,
int index )

Compute mesh entities of given topological dimension by computing entity-to-vertex connectivity (dim, 0), and cell-to-entity connectivity (tdim, dim).

Computed entities are oriented such that their local (to the process) orientation agrees with their global orientation

Parameters
[in]commMPI Communicator
[in]topologyMesh topology
[in]dimThe dimension of the entities to create
[in]indexIndex of entity in dimension dim as listed in Topology::entity_types(dim).
Returns
Tuple of (cell-entity connectivity, entity-vertex connectivity, index map, list of interprocess entities). Interprocess entities lie on the "true" boundary between owned cells of each process. If the entities already exists, then {nullptr, nullptr, nullptr, std::vector()} is returned.

◆ compute_entity_permutations()

std::pair< std::vector< std::uint8_t >, std::vector< std::uint32_t > > compute_entity_permutations ( const Topology & topology)

Compute (1) facet rotation and reflection data, and (2) cell permutation data. This information is used in the assembly of (1) facet integrals and (2) most non-Lagrange elements.

  1. The facet rotation and reflection data is encoded so that:

    • n % 2 gives the number of reflections to apply
    • n // 2 gives the number of rotations to apply

    The data is stored in a flattened 2D array, so that data[cell_index * / facets_per_cell + facet_index] contains the facet with index facet_index of the cell with index cell_index. This data passed to FFCx kernels, where it is used to permute the quadrature points on facet integrals when data from the cells on both sides of the facet is used.

  2. The cell permutation data contains information about the entities of each cell, relative to a low-to-high ordering. This data is packed so that a 32-bit int is used for each cell. For 2D cells, one bit is used for each edge, to represent whether or not the edge is reversed: the least significant bit is for edge 0, the next for edge 1, etc. For 3D cells, three bits are used for each face, and for each edge: the least significant bit says whether or not face 0 is reflected, the next 2 bits say how many times face 0 is rotated; the next three bits are for face 1, then three for face 2, etc; after all the faces, there is 1 bit for each edge to say whether or not they are reversed.

    For example, if a quadrilateral has cell permutation info ....0111 then (from right to left):

    • edge 0 is reflected (1)
    • edge 1 is reflected (1)
    • edge 2 is reflected (1)
    • edge 3 is not permuted (0)

    and if a tetrahedron has cell permutation info ....011010010101001000 then (from right to left):

    • face 0 is not permuted (000)
    • face 1 is reflected (001)
    • face 2 is rotated twice then reflected (101)
    • face 3 is rotated once (010)
    • edge 0 is not permuted (0)
    • edge 1 is reflected (1)
    • edge 2 is not permuted (0)
    • edge 3 is reflected (1)
    • edge 4 is reflected (1)
    • edge 5 is not permuted (0)

    This data is used to correct the direction of vector function on permuted facets.

Returns
Facet permutation and cells permutations

◆ compute_incident_entities()

std::vector< std::int32_t > compute_incident_entities ( const Topology & topology,
std::span< const std::int32_t > entities,
int d0,
int d1 )

Compute incident indices.

Parameters
[in]topologyThe topology
[in]entitiesList of indices of topological dimension d0
[in]d0Topological dimension
[in]d1Topological dimension
Returns
List of entities of topological dimension d1 that are incident to entities in entities (topological dimension d0)

◆ compute_midpoints()

template<std::floating_point T>
std::vector< T > compute_midpoints ( const Mesh< T > & mesh,
int dim,
std::span< const std::int32_t > entities )

Compute the midpoints for mesh entities of a given dimension.

Returns
The entity midpoints. The shape is (entities.size(), 3) and the storage is row-major.

◆ create_box() [1/2]

template<std::floating_point T = double>
Mesh< T > create_box ( MPI_Comm comm,
MPI_Comm subcomm,
std::array< std::array< T, 3 >, 2 > p,
std::array< std::int64_t, 3 > n,
CellType celltype,
CellPartitionFunction partitioner = nullptr )

Create a uniform mesh::Mesh over rectangular prism spanned by the two points p.

The order of the two points is not important in terms of minimum and maximum coordinates. The total number of vertices will be (n[0] + / 1)*(n[1] + 1)*(n[2] + 1). For tetrahedra there will be will be 6*n[0]*n[1]*n[2] cells. For hexahedra the number of cells will be n[0]*n[1]*n[2].

Parameters
[in]commMPI communicator to distribute the mesh on.
[in]subcommMPI communicator to construct and partition the mesh topology on. If the process should not be involved in the topology creation and partitioning then this communicator should be MPI_COMM_NULL.
[in]pCorner of the box.
[in]nNumber of cells in each direction.
[in]celltypeCell shape.
[in]partitionerPartitioning function for distributing cells across MPI ranks.
Returns
Mesh

◆ create_box() [2/2]

template<std::floating_point T = double>
Mesh< T > create_box ( MPI_Comm comm,
std::array< std::array< T, 3 >, 2 > p,
std::array< std::int64_t, 3 > n,
CellType celltype,
const CellPartitionFunction & partitioner = nullptr )

Create a uniform mesh::Mesh over rectangular prism spanned by the two points p.

The order of the two points is not important in terms of minimum and maximum coordinates. The total number of vertices will be (n[0] + / 1)*(n[1] + 1)*(n[2] + 1). For tetrahedra there will be will be 6*n[0]*n[1]*n[2] cells. For hexahedra the number of cells will be n[0]*n[1]*n[2].

Parameters
[in]commMPI communicator to distribute the mesh on.
[in]pCorner of the box.
[in]nNumber of cells in each direction.
[in]celltypeCell shape.
[in]partitionerPartitioning function for distributing cells across MPI ranks.
Returns
Mesh

◆ create_cell_partitioner()

mesh::CellPartitionFunction create_cell_partitioner ( mesh::GhostMode ghost_mode = mesh::GhostMode::none,
const graph::partition_fn & partfn = &graph::partition_graph )

Create a function that computes destination rank for mesh cells in this rank by applying the default graph partitioner to the dual graph of the mesh

Returns
Function that computes the destination ranks for each cell

◆ create_geometry() [1/2]

template<typename U >
Geometry< typename std::remove_reference_t< typename U::value_type > > create_geometry ( const Topology & topology,
const fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > & element,
std::span< const std::int64_t > nodes,
std::span< const std::int64_t > xdofs,
const U & x,
int dim,
std::function< std::vector< int >(const graph::AdjacencyList< std::int32_t > &)> reorder_fn = nullptr )

Build Geometry from input data.

This function should be called after the mesh topology is built and 'node' coordinate data has been distributed to the processes where it is required.

Parameters
[in]topologyMesh topology.
[in]elementElement that defines the geometry map for each cell.
[in]nodesGeometry node global indices for cells on this process. Must be sorted.
[in]xdofsGeometry degree-of-freedom map (using global indices) for cells on this process. nodes is a sorted and unique list of the indices in xdofs.
[in]xThe node coordinates (row-major, with shape (num_nodes, dim). The global index of each node is i + / rank_offset, where i is the local row index in x and rank_offset is the sum of x rows on all processed with a lower rank than the caller.
[in]dimGeometric dimension (1, 2, or 3).
[in]reorder_fnFunction for re-ordering the degree-of-freedom map associated with the geometry data.
Returns
A mesh geometry.

◆ create_geometry() [2/2]

template<typename U >
Geometry< typename std::remove_reference_t< typename U::value_type > > create_geometry ( const Topology & topology,
const std::vector< fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > > & elements,
std::span< const std::int64_t > nodes,
std::span< const std::int64_t > xdofs,
const U & x,
int dim,
std::function< std::vector< int >(const graph::AdjacencyList< std::int32_t > &)> reorder_fn = nullptr )

Build Geometry from input data.

This function should be called after the mesh topology is built and 'node' coordinate data has been distributed to the processes where it is required.

Parameters
[in]topologyMesh topology.
[in]elementsList of elements that defines the geometry map for each cell type.
[in]nodesGeometry node global indices for cells on this process.
Precondition
Must be sorted.
Parameters
[in]xdofsGeometry degree-of-freedom map (using global indices) for cells on this process. nodes is a sorted and unique list of the indices in xdofs.
[in]xThe node coordinates (row-major, with shape (num_nodes, dim). The global index of each node is i + / rank_offset, where i is the local row index in x and rank_offset is the sum of x rows on all processed with a lower rank than the caller.
[in]dimGeometric dimension (1, 2, or 3).
[in]reorder_fnFunction for re-ordering the degree-of-freedom map associated with the geometry data.
Note
Experimental new interface for multiple cmap/dofmap
Returns
A mesh geometry.

◆ create_interval()

template<std::floating_point T = double>
Mesh< T > create_interval ( MPI_Comm comm,
std::int64_t n,
std::array< T, 2 > p,
mesh::GhostMode ghost_mode = mesh::GhostMode::none,
CellPartitionFunction partitioner = nullptr )

Interval mesh of the 1D line [a, b].

Given n cells in the axial direction, the total number of intervals will be n and the total number of vertices will be n + 1.

Parameters
[in]commMPI communicator to build the mesh on.
[in]nNumber of cells.
[in]pEnd points of the interval.
[in]ghost_modeghost mode of the created mesh, defaults to none
[in]partitionerPartitioning function for distributing cells across MPI ranks.
Returns
A mesh.

◆ create_mesh() [1/3]

template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh ( MPI_Comm comm,
MPI_Comm commt,
const std::vector< std::span< const std::int64_t > > & cells,
const std::vector< fem::CoordinateElement< typename std::remove_reference_t< typename U::value_type > > > & elements,
MPI_Comm commg,
const U & x,
std::array< std::size_t, 2 > xshape,
const CellPartitionFunction & partitioner )

Create a distributed mixed-topology mesh from mesh data using a provided graph partitioning function for determining the parallel distribution of the mesh.

From mesh input data that is distributed across processes, a distributed mesh::Mesh is created. If the partitioning function is not callable, i.e. it does not store a callable function, no re-distribution of cells is done.

Note
This is an experimental specialised version of create_mesh for mixed topology meshes, and does not include cell reordering.
Parameters
[in]commCommunicator to build the mesh on.
[in]commtCommunicator that the topology data (cells) is distributed on. This should be MPI_COMM_NULL for ranks that should not participate in computing the topology partitioning.
[in]cellsCells on the calling process, as a list of lists, one list for each cell type (or an empty list if there are no cells of that type on this process). The cells are defined by their 'nodes' (using global indices) following the Basix ordering, and concatenated to form a flattened list. For lowest order cells this will be just the cell vertices. For higher-order cells, other cells 'nodes' will be included. See dolfinx::io::cells for examples of the Basix ordering.
[in]elementsCoordinate elements for the cells, one for each cell type in the mesh. In parallel, these must be the same on all processes.
[in]commgCommunicator for geometry
[in]xGeometry data ('node' coordinates). Row-major storage. The global index of the ith node (row) in x is taken as i plus the process offset oncomm, The offset is the sum of x rows on all processed with a lower rank than the caller.
[in]xshapeShape of the x data.
[in]partitionerGraph partitioner that computes the owning rank for each cell. If not callable, cells are not redistributed.
Returns
A mesh distributed on the communicator comm.

◆ create_mesh() [2/3]

template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh ( MPI_Comm comm,
MPI_Comm commt,
std::span< const std::int64_t > cells,
const fem::CoordinateElement< typename std::remove_reference_t< typename U::value_type > > & element,
MPI_Comm commg,
const U & x,
std::array< std::size_t, 2 > xshape,
const CellPartitionFunction & partitioner )

Create a distributed mesh from mesh data using a provided graph partitioning function for determining the parallel distribution of the mesh.

From mesh input data that is distributed across processes, a distributed mesh::Mesh is created. If the partitioning function is not callable, i.e. it does not store a callable function, no re-distribution of cells is done.

Parameters
[in]commCommunicator to build the mesh on.
[in]commtCommunicator that the topology data (cells) is distributed on. This should be MPI_COMM_NULL for ranks that should not participate in computing the topology partitioning.
[in]cellsCells on the calling process. Each cell (node in the AdjacencyList) is defined by its 'nodes' (using global indices) following the Basix ordering. For lowest order cells this will be just the cell vertices. For higher-order cells, other cells 'nodes' will be included. See dolfinx::io::cells for examples of the Basix ordering.
[in]elementCoordinate element for the cells.
[in]commgCommunicator for geometry
[in]xGeometry data ('node' coordinates). Row-major storage. The global index of the ith node (row) in x is taken as i plus the process offset oncomm, The offset is the sum of x rows on all processed with a lower rank than the caller.
[in]xshapeShape of the x data.
[in]partitionerGraph partitioner that computes the owning rank for each cell. If not callable, cells are not redistributed.
Returns
A mesh distributed on the communicator comm.

◆ create_mesh() [3/3]

template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh ( MPI_Comm comm,
std::span< const std::int64_t > cells,
const fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > & elements,
const U & x,
std::array< std::size_t, 2 > xshape,
GhostMode ghost_mode )

Create a distributed mesh from mesh data using the default graph partitioner to determine the parallel distribution of the mesh.

This function takes mesh input data that is distributed across processes and creates a mesh::Mesh, with the mesh cell distribution determined by the default cell partitioner. The default partitioner is based on graph partitioning.

Parameters
[in]commMPI communicator to build the mesh on.
[in]cellsCells on the calling process. See create_mesh for a detailed description.
[in]elementsCoordinate elements for the cells.
[in]xGeometry data ('node' coordinates). See create_mesh for a detailed description.
[in]xshapeThe shape of x. It should be (num_points, gdim).
[in]ghost_modeThe requested type of cell ghosting/overlap
Returns
A mesh distributed on the communicator comm.

◆ create_meshtags()

template<typename T >
MeshTags< T > create_meshtags ( std::shared_ptr< const Topology > topology,
int dim,
const graph::AdjacencyList< std::int32_t > & entities,
std::span< const T > values )

Create MeshTags from arrays.

Parameters
[in]topologyMesh topology that the tags are associated with.
[in]dimTopological dimension of tagged entities.
[in]entitiesLocal vertex indices for tagged entities.
[in]valuesTag values for each entity in entities. The length of values must be equal to number of rows in entities.
Note
Entities that do not exist on this rank are ignored.
Warning
entities must not contain duplicate entities.

◆ create_rectangle() [1/2]

template<std::floating_point T = double>
Mesh< T > create_rectangle ( MPI_Comm comm,
std::array< std::array< T, 2 >, 2 > p,
std::array< std::int64_t, 2 > n,
CellType celltype,
CellPartitionFunction partitioner,
DiagonalType diagonal = DiagonalType::right )

Create a uniform mesh::Mesh over the rectangle spanned by the two points p.

The order of the two points is not important in terms of minimum and maximum coordinates. The total number of vertices will be (n[0] + / 1)*(n[1] + 1). For triangles there will be will be 2*n[0]*n[1] cells. For quadrilaterals the number of cells will be n[0]*n[1].

Parameters
[in]commMPI communicator to build the mesh on.
[in]pBottom-left and top-right corners of the rectangle.
[in]nNumber of cells in each direction.
[in]celltypeCell shape.
[in]partitionerPartitioning function for distributing cells across MPI ranks.
[in]diagonalDirection of diagonals
Returns
Mesh

◆ create_rectangle() [2/2]

template<std::floating_point T = double>
Mesh< T > create_rectangle ( MPI_Comm comm,
std::array< std::array< T, 2 >, 2 > p,
std::array< std::int64_t, 2 > n,
CellType celltype,
DiagonalType diagonal = DiagonalType::right )

Create a uniform mesh::Mesh over the rectangle spanned by the two points p.

The order of the two points is not important in terms of minimum and maximum coordinates. The total number of vertices will be (n[0] + / 1)*(n[1] + 1). For triangles there will be will be 2*n[0]*n[1] cells. For quadrilaterals the number of cells will be n[0]*n[1].

Parameters
[in]commMPI communicator to build the mesh on
[in]pTwo corner points
[in]nNumber of cells in each direction
[in]celltypeCell shape
[in]diagonalDirection of diagonals
Returns
Mesh

◆ create_subgeometry()

template<std::floating_point T>
std::pair< Geometry< T >, std::vector< int32_t > > create_subgeometry ( const Mesh< T > & mesh,
int dim,
std::span< const std::int32_t > subentity_to_entity )

Create a sub-geometry from a mesh and a subset of mesh entities to be included. A sub-geometry is simply a Geometry object containing only the geometric information for the subset of entities. The entities may differ in topological dimension from the original mesh.

Parameters
[in]meshThe full mesh.
[in]dimTopological dimension of the sub-topology.
[in]subentity_to_entityMap from sub-topology entity to the entity in the parent topology.
Returns
A sub-geometry and a map from sub-geometry coordinate degree-of-freedom to the coordinate degree-of-freedom in geometry.

◆ create_submesh()

template<std::floating_point T>
std::tuple< Mesh< T >, std::vector< std::int32_t >, std::vector< std::int32_t >, std::vector< std::int32_t > > create_submesh ( const Mesh< T > & mesh,
int dim,
std::span< const std::int32_t > entities )

Create a new mesh consisting of a subset of entities in a mesh.

Parameters
[in]meshThe mesh
[in]dimEntity dimension
[in]entitiesList of entity indices in mesh to include in the new mesh
Returns
The new mesh, and maps from the new mesh entities, vertices, and geometry to the input mesh entities, vertices, and geometry.

◆ create_subtopology()

std::tuple< Topology, std::vector< int32_t >, std::vector< int32_t > > create_subtopology ( const Topology & topology,
int dim,
std::span< const std::int32_t > entities )

Create a topology for a subset of entities of a given topological dimension.

Parameters
topologyOriginal (parent) topology.
dimTopological dimension of the entities in the new topology.
entitiesIndices of entities in topology to include in the new topology.
Returns
New topology of dimension dim with all entities in entities, map from entities of dimension dim in new sub-topology to entities in topology, and map from vertices in new sub-topology to vertices in topology.

◆ create_topology() [1/2]

Topology create_topology ( MPI_Comm comm,
const std::vector< CellType > & cell_type,
std::vector< std::span< const std::int64_t > > cells,
std::vector< std::span< const std::int64_t > > original_cell_index,
std::vector< std::span< const int > > ghost_owners,
std::span< const std::int64_t > boundary_vertices )

Create a topology of mixed cell type.

Parameters
commMPI Communicator
cell_typeList of cell types
cellsLists of cells, using vertex indices, flattened, for each cell type.
original_cell_indexInput cell index for each cell type
ghost_ownersOwning rank for ghost cells (at end of each list of cells).
boundary_verticesVertices of undetermined ownership on external or inter-process boundary.
Returns

◆ create_topology() [2/2]

Topology create_topology ( MPI_Comm comm,
std::span< const std::int64_t > cells,
std::span< const std::int64_t > original_cell_index,
std::span< const int > ghost_owners,
CellType cell_type,
std::span< const std::int64_t > boundary_vertices )

Create a mesh topology.

This function creates a Topology from cells that have been distributed to the processes that own or ghost the cell.

Parameters
[in]commCommunicator across which the topology is distributed.
[in]cellsCell topology (list of vertices for each cell) using global indices for the vertices. It contains cells that have been distributed to this rank, e.g. via a graph partitioner. It must also contain all ghost cells via facet, i.e. cells that are on a neighboring process and which share a facet with a local cell. Ghost cells are the last n entries in cells, where n is given by the length of ghost_owners.
[in]original_cell_indexOriginal global index associated with each cell.
[in]ghost_ownersOwning rank of each ghost cell (ghost cells are always at the end of the list of cells).
[in]cell_typeA vector with cell shapes.
[in]boundary_verticesVertices on the 'exterior' (boundary) of the local topology. These vertices might appear on other processes.
Returns
A distributed mesh topology

◆ entities_to_geometry()

template<std::floating_point T>
std::vector< std::int32_t > entities_to_geometry ( const Mesh< T > & mesh,
int dim,
std::span< const std::int32_t > entities,
bool permute = false )

Compute the geometry degrees of freedom associated with the closure of a given set of cell entities.

Parameters
[in]meshThe mesh.
[in]dimTopological dimension of the entities of interest.
[in]entitiesEntity indices (local to process).
[in]permuteIf true, 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 geometry DOFs associated with the closure of each entity in entities. The shape is (num_entities, num_xdofs_per_entity) and the storage is row-major. The index indices[i, j] is the position in the geometry array of the j-th vertex of the entity[i].
Precondition
The mesh connectivities dim -> mesh.topology().dim() and mesh.topology().dim() -> dim must have been computed. Otherwise an exception is thrown.

◆ entities_to_index()

std::vector< std::int32_t > entities_to_index ( const Topology & topology,
int dim,
std::span< const std::int32_t > entities )

Get entity indices for entities defined by their vertices.

Warning
This function may be removed in the future.
Parameters
[in]topologyThe mesh topology
[in]dimTopological dimension of the entities
[in]entitiesThe mesh entities defined by their vertices
Returns
The index of the ith entity in entities
Note
If an entity cannot be found on this rank, -1 is returned as the index.

◆ exterior_facet_indices()

std::vector< std::int32_t > exterior_facet_indices ( const Topology & topology)

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
Collective
Parameters
[in]topologyMesh topology
Returns
Sorted list of owned facet indices that are exterior facets of the mesh.

◆ extract_topology()

std::vector< std::int64_t > extract_topology ( CellType cell_type,
const fem::ElementDofLayout & layout,
std::span< const std::int64_t > cells )

Extract topology from cell data, i.e. extract cell vertices.

Parameters
[in]cell_typeThe cell shape
[in]layoutThe layout of geometry 'degrees-of-freedom' on the reference cell
[in]cellsList of 'nodes' for each cell using global indices. The layout must be consistent with layout.
Returns
Cell topology. The global indices will, in general, have 'gaps' due to mid-side and other higher-order nodes being removed from the input cell.

◆ get_entity_vertices()

graph::AdjacencyList< int > get_entity_vertices ( CellType type,
int dim )

Return list of entities, where entities(e, k) is the local vertex index for the kth vertex of entity e of dimension dim

◆ get_sub_entities()

graph::AdjacencyList< int > get_sub_entities ( CellType type,
int dim0,
int dim1 )

Get entities of dimension dim1 and that make up entities of dimension dim0

◆ h()

template<std::floating_point T>
std::vector< T > h ( const Mesh< T > & mesh,
std::span< const std::int32_t > entities,
int dim )

Compute greatest distance between any two vertices of the mesh entities (h).

Parameters
[in]meshMesh that the entities belong to.
[in]entitiesIndices (local to process) of entities to compute h for.
[in]dimTopological dimension of the entities.
Returns
Greatest distance between any two vertices, h[i] corresponds to the entity entities[i].

◆ is_simplex()

bool is_simplex ( CellType type)

Check if cell is a simplex

Parameters
[in]typeCell type
Returns
True is the cell type is a simplex

◆ locate_entities()

template<std::floating_point T, MarkerFn< T > U>
std::vector< std::int32_t > locate_entities ( const Mesh< T > & mesh,
int dim,
U marker )

Compute indices of all mesh entities that evaluate to true for the provided geometric marking function.

An entity is considered marked if the marker function evaluates to true for all of its vertices.

Parameters
[in]meshMesh to mark entities on.
[in]dimTopological dimension of the entities to be considered.
[in]markerMarking function, returns true for a point that is 'marked', and false otherwise.
Returns
List of marked entity indices, including any ghost indices (indices local to the process)

◆ locate_entities_boundary()

template<std::floating_point T, MarkerFn< T > U>
std::vector< std::int32_t > locate_entities_boundary ( const Mesh< T > & mesh,
int dim,
U marker )

Compute indices of all mesh entities that are attached to an owned boundary facet and evaluate to true for the provided geometric marking function.

An entity is considered marked if the marker function evaluates to true for all of its vertices.

Note
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 fem::locate_dofs_topological, the function that uses the data returned by this function must typically perform some parallel communication.
Parameters
[in]meshMesh to mark entities on.
[in]dimTopological dimension of the entities to be considered. Must be less than the topological dimension of the mesh.
[in]markerMarking function, returns true for a point that is 'marked', and false otherwise.
Returns
List of marked entity indices (indices local to the process)

◆ num_cell_vertices()

int num_cell_vertices ( CellType type)

Number vertices for a cell type

Parameters
[in]typeCell type
Returns
The number of cell vertices

◆ to_string()

std::string to_string ( CellType type)

Get the cell string type for a cell type

Parameters
[in]typeThe cell type
Returns
The cell type string

◆ to_type()

mesh::CellType to_type ( const std::string & cell)

Get the cell type from a cell string

Parameters
[in]cellCell shape string
Returns
The cell type