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 = std::function< graph::AdjacencyList< std::int32_t >(MPI_Comm comm, int nparts, int tdim, const graph::AdjacencyList< std::int64_t > &cells)>
	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)
	Get the cell string type for a cell type.

CellType	to_type (const std::string &cell)
	Get the cell type from a cell string.

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)
	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.

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.

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.

int	cell_dim (CellType type)
	Return topological dimension of cell type.

int	cell_num_entities (CellType type, int dim)
	Number of entities of dimension dim.

bool	is_simplex (CellType type)
	Check if cell is a simplex.

int	num_cell_vertices (CellType type)
	Number vertices for a cell type.

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)}.

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, const std::array< std::array< double, 3 >, 2 > &p, std::array< std::size_t, 3 > n, CellType celltype, mesh::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, const std::array< std::array< double, 2 >, 2 > &p, std::array< std::size_t, 2 > n, CellType celltype, const 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, const std::array< std::array< double, 2 >, 2 > &p, std::array< std::size_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::size_t nx, std::array< double, 2 > x, CellPartitionFunction partitioner=nullptr)
	Interval mesh of the 1D line `[a, b]`.

template<typename U >
mesh::Geometry< typename std::remove_reference_t< typename U::value_type > >	create_geometry (MPI_Comm comm, const Topology &topology, const std::vector< fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > > &elements, const graph::AdjacencyList< std::int64_t > &cell_nodes, 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<std::floating_point T>
std::pair< mesh::Geometry< T >, std::vector< int32_t > >	create_subgeometry (const Topology &topology, const Geometry< T > &geometry, int dim, std::span< const std::int32_t > subentity_to_entity)
	Create a sub-geometry for a subset of entities.

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 std::int64_t > cells, std::span< const std::int32_t > offsets, int tdim)
	Compute the local part of the dual graph (cell-cell connections via facets) and facet with only one attached cell.

graph::AdjacencyList< std::int64_t >	build_dual_graph (const MPI_Comm comm, const graph::AdjacencyList< std::int64_t > &cells, int tdim)
	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)
	Compute (1) facet rotation and reflection data, and (2) cell permutation data. This information is used assemble of (1) facet inetgrals and (2) vector elements.

Topology	create_topology (MPI_Comm comm, const graph::AdjacencyList< std::int64_t > &cells, std::span< const std::int64_t > original_cell_index, std::span< const int > ghost_owners, const std::vector< CellType > &cell_type, const std::vector< std::int32_t > &cell_group_offsets, std::span< const std::int64_t > boundary_vertices)
	Create a distributed mesh topology.

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, const graph::AdjacencyList< std::int32_t > &entities)
	Get entity indices for entities defined by their vertices.

std::tuple< 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)
	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, int d0, int d1)
	Compute connectivity (d0 -> d1) for given pair of topological dimensions.

std::vector< std::int32_t >	exterior_facet_indices (const Topology &topology)
	Compute the indices of all exterior facets that are owned by the caller.

graph::AdjacencyList< std::int64_t >	extract_topology (const CellType &cell_type, const fem::ElementDofLayout &layout, const graph::AdjacencyList< 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 orient)
	Determine the indices in the geometry data for each vertex of the given mesh entities.

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.

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, const graph::AdjacencyList< std::int64_t > &cells, const std::vector< fem::CoordinateElement< typename std::remove_reference_t< typename U::value_type > > > &elements, const U &x, std::array< std::size_t, 2 > xshape, CellPartitionFunction partitioner)
	Create a mesh using a provided mesh partitioning function.

template<typename U >
Mesh< typename std::remove_reference_t< typename U::value_type > >	create_mesh (MPI_Comm comm, const graph::AdjacencyList< std::int64_t > &cells, const std::vector< 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 mesh using the default partitioner.

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

using CellPartitionFunction = std::function<graph::AdjacencyList<std::int32_t>( MPI_Comm comm, int nparts, int tdim, const graph::AdjacencyList<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]	comm	MPI Communicator
[in]	nparts	Number of partitions
[in]	tdim	Topological dimension
[in]	cells	Cells on this process. The ith entry in list contains 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.
[in]	ghost_mode	How to overlap the cell partitioning: none, shared_facet or shared_vertex

Returns: Destination ranks for each cell on this process

Function Documentation

◆ build_dual_graph()

graph::AdjacencyList< std::int64_t > build_dual_graph	(	const MPI_Comm	comm,
		const graph::AdjacencyList< std::int64_t > &	cells,
		int	tdim
	)

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]	comm	The MPI communicator
[in]	cells	Collection of cells, defined by the cell vertices from which to build the dual graph
[in]	tdim	The topological dimension of the cells

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 std::int64_t >	cells,
		std::span< const std::int32_t >	offsets,
		int	tdim
	)

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

Parameters

[in]	cells	Array for cell vertices adjacency list
[in]	offsets	Adjacency list offsets, i.e. index of the first entry of cell `i` in `cell_vertices` `is offsets[i]`
[in]	tdim	The topological dimension of the cells

Returns

Local dual graph
Facets, defined by their vertices, that are shared by only one cell on this rank. The logically 2D is array flattened (row-major).
The number of columns for the facet data array (2).
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 return data will likely change once we support mixed topology meshes.

◆ 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]	type	The cell type
[in]	index	The 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]	dim	Entity dimension
[in]	type	Cell 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,
		int	d0,
		int	d1
	)

Compute connectivity (d0 -> d1) for given pair of topological dimensions.

Parameters

[in]	topology	The topology
[in]	d0	The dimension of the nodes in the adjacency list
[in]	d1	The dimension of the edges in the adjacency list

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::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
	)

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

Parameters

[in]	comm	MPI Communicator
[in]	topology	Mesh topology
[in]	dim	The dimension of the entities to create

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 exist, 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 assemble of (1) facet inetgrals and (2) vector elements.

Get the permutation numbers to apply to facets. The permutations are numbered so that:
- n % 2 gives the number of reflections to apply
- n // 2 gives the number of rotations to apply
Each column of the returned array represents a cell, and each row a facet of that cell. This data is used to permute the quadrature point on facet integrals when data from the cells on both sides of the facet is used.
Get the permutation 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]	topology	The topology
[in]	entities	List of indices of topological dimension `d0`
[in]	d0	Topological dimension
[in]	d1	Topological 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()

template<std::floating_point T = double>

Mesh< T > create_box	(	MPI_Comm	comm,
		const std::array< std::array< double, 3 >, 2 > &	p,
		std::array< std::size_t, 3 >	n,
		CellType	celltype,
		mesh::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]	comm	MPI communicator to build mesh on.
[in]	p	Corner of the box.
[in]	n	Number of cells in each direction.
[in]	celltype	Cell shape.
[in]	partitioner	Partitioning 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()

template<typename U >

mesh::Geometry< typename std::remove_reference_t< typename U::value_type > > create_geometry	(	MPI_Comm	comm,
		const Topology &	topology,
		const std::vector< fem::CoordinateElement< std::remove_reference_t< typename U::value_type > > > &	elements,
		const graph::AdjacencyList< std::int64_t > &	cell_nodes,
		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. It distributes the 'node' coordinate data to the required MPI process and then creates a mesh::Geometry object.

Parameters

[in]	comm	The MPI communicator to build the Geometry on
[in]	topology	The mesh topology
[in]	elements	The elements that defines the geometry map for each cell
[in]	cell_nodes	The mesh cells, including higher-order geometry 'nodes'
[in]	x	The 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]	dim	The geometric dimension (1, 2, or 3)
[in]	reorder_fn	Function for re-ordering the degree-of-freedom map associated with the geometry data

◆ create_interval()

template<std::floating_point T = double>

Mesh< T > create_interval	(	MPI_Comm	comm,
		std::size_t	nx,
		std::array< double, 2 >	x,
		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]	comm	MPI communicator to build the mesh on
[in]	nx	The number of cells
[in]	x	The end points of the interval
[in]	partitioner	Partitioning function for distributing cells across MPI ranks.

Returns: A mesh

◆ create_mesh() [1/2]

template<typename U >

Mesh< typename std::remove_reference_t< typename U::value_type > > create_mesh	(	MPI_Comm	comm,
		const graph::AdjacencyList< std::int64_t > &	cells,
		const std::vector< 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 mesh using the default partitioner.

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]	comm	The MPI communicator to build the mesh on.
[in]	cells	The cells on the this MPI rank. Each cell (node in the `AdjacencyList`) is defined by its 'nodes' (using global indices). For lowest order cells this will be just the cell vertices. For higher-order cells, other cells 'nodes' will be included.
[in]	elements	The coordinate elements that describe the geometric mapping for cells.
[in]	x	The coordinates of mesh nodes.
[in]	xshape	The shape of `x`. It should be `(num_points, gdim)`.
[in]	ghost_mode	The requested type of cell ghosting/overlap

Returns: A distributed Mesh.

◆ create_mesh() [2/2]

template<typename U >

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

Create a mesh using a provided mesh partitioning function.

If the partitioning function is not callable, i.e. it does not store a callable function, no re-distribution of cells is done.

◆ 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]	topology	Mesh topology that the tags are associated with
[in]	dim	Topological dimension of tagged entities
[in]	entities	Local vertex indices for tagged entities.
[in]	values	Tag 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,
		const std::array< std::array< double, 2 >, 2 > &	p,
		std::array< std::size_t, 2 >	n,
		CellType	celltype,
		const 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]	comm	MPI communicator to build the mesh on.
[in]	p	Bottom-left and top-right corners of the rectangle.
[in]	n	Number of cells in each direction.
[in]	celltype	Cell shape.
[in]	partitioner	Partitioning function for distributing cells across MPI ranks.
[in]	diagonal	Direction of diagonals

Returns: Mesh

◆ create_rectangle() [2/2]

template<std::floating_point T = double>

Mesh< T > create_rectangle	(	MPI_Comm	comm,
		const std::array< std::array< double, 2 >, 2 > &	p,
		std::array< std::size_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]	comm	MPI communicator to build the mesh on
[in]	p	Two corner points
[in]	n	Number of cells in each direction
[in]	celltype	Cell shape
[in]	diagonal	Direction of diagonals

Returns: Mesh

◆ create_subgeometry()

template<std::floating_point T>

std::pair< mesh::Geometry< T >, std::vector< int32_t > > create_subgeometry	(	const Topology &	topology,
		const Geometry< T > &	geometry,
		int	dim,
		std::span< const std::int32_t >	subentity_to_entity
	)

Create a sub-geometry for a subset of entities.

Parameters

topology	Full mesh topology
geometry	Full mesh geometry
dim	Topological dimension of the sub-topology
subentity_to_entity	Map 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]	mesh	The mesh
[in]	dim	Entity dimension
[in]	entities	List 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

topology	Original topology.
dim	Topological dimension of the entities in the new topology.
entities	The indices of the 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()

Topology create_topology	(	MPI_Comm	comm,
		const graph::AdjacencyList< std::int64_t > &	cells,
		std::span< const std::int64_t >	original_cell_index,
		std::span< const int >	ghost_owners,
		const std::vector< CellType > &	cell_type,
		const std::vector< std::int32_t > &	cell_group_offsets,
		std::span< const std::int64_t >	boundary_vertices
	)

Create a distributed mesh topology.

Parameters

[in]	comm	MPI communicator across which the topology is distributed
[in]	cells	The cell 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 share a facet with a local cell.
[in]	original_cell_index	The original global index associated with each cell
[in]	ghost_owners	The owning rank of each ghost cell (ghost cells are always at the end of the list of `cells`)
[in]	cell_type	A vector with cell shapes
[in]	cell_group_offsets	vector with each group offset, including ghosts.
[in]	boundary_vertices	List of vertices on the exterior of the local mesh which may be shared with 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	orient
	)

Determine the indices in the geometry data for each vertex of the given mesh entities.

Warning: This function should not be used unless there is no alternative. It may be removed in the future.

Parameters

[in]	mesh	The mesh
[in]	dim	Topological dimension of the entities of interest
[in]	entities	Entity indices (local) to compute the vertex geometry indices for
[in]	orient	If true, in 3D, reorients facets to have consistent normal direction

Returns: Indices in the geometry array for the entity vertices. The shape is (num_entities, num_vertices_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].

◆ entities_to_index()

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

Get entity indices for entities defined by their vertices.

Warning: This function may be removed in the future.

Parameters

[in]	topology	The mesh topology
[in]	dim	Topological dimension of the entities
[in]	entities	The 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] topology Mesh topology

Returns: Sorted list of owned facet indices that are exterior facets of the mesh.

◆ extract_topology()

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

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

Parameters

[in]	cell_type	The cell shape
[in]	layout	The layout of geometry 'degrees-of-freedom' on the reference cell
[in]	cells	List 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.

◆ 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]	mesh	Mesh that the entities belong to.
[in]	entities	Indices (local to process) of entities to compute `h` for.
[in]	dim	Topological 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] type Cell 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]	mesh	Mesh to mark entities on.
[in]	dim	Topological dimension of the entities to be considered.
[in]	marker	Marking 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]	mesh	Mesh to mark entities on.
[in]	dim	Topological dimension of the entities to be considered. Must be less than the topological dimension of the mesh.
[in]	marker	Marking 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] type Cell 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] type The 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] cell Cell shape string

Returns: The cell type

Classes

Concepts

Typedefs

Enumerations

Functions

Detailed Description

Typedef Documentation

◆ CellPartitionFunction

Function Documentation

◆ build_dual_graph()

◆ build_local_dual_graph()

◆ cell_facet_type()

◆ cell_normals()

◆ cell_num_entities()

◆ compute_connectivity()

◆ compute_entities()

◆ compute_entity_permutations()

◆ compute_incident_entities()

◆ compute_midpoints()

◆ create_box()

◆ create_cell_partitioner()

◆ create_geometry()

◆ create_interval()

◆ create_mesh() [1/2]

◆ create_mesh() [2/2]

◆ create_meshtags()

◆ create_rectangle() [1/2]

◆ create_rectangle() [2/2]

◆ create_subgeometry()

◆ create_submesh()

◆ create_subtopology()

◆ create_topology()

◆ entities_to_geometry()

◆ entities_to_index()

◆ exterior_facet_indices()

◆ extract_topology()

◆ h()

◆ is_simplex()

◆ locate_entities()

◆ locate_entities_boundary()

◆ num_cell_vertices()

◆ to_string()

◆ to_type()