Mesh (dolfinx::mesh)

Under development

namespace mesh

Mesh data structures and algorithms on meshes.

Representations of meshes and support for operations on meshes.

Typedefs

using CellPartitionFunction = std::function<graph::AdjacencyList<std::int32_t>(MPI_Comm comm, int nparts, CellType cell_type, 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.

Note

Cells can have multiple destination ranks, when ghosted.

Param comm:

[in] MPI Communicator

Param nparts:

[in] Number of partitions

Param cell_type:

[in] Type of cell in mesh

Param cells:

[in] 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.

Return:

Destination ranks for each cell on this process

Enums

enum class CellType : int

Cell type identifier.

Values:

enumerator point
enumerator interval
enumerator triangle
enumerator tetrahedron
enumerator quadrilateral
enumerator pyramid
enumerator prism
enumerator hexahedron
enum class DiagonalType

Enum for different diagonal types.

Values:

enumerator left
enumerator right
enumerator crossed
enumerator shared_facet
enumerator left_right
enumerator right_left
enum class GhostMode : int

Enum for different partitioning ghost modes.

Values:

enumerator none
enumerator shared_facet
enumerator shared_vertex

Functions

std::string to_string(CellType type)

Get the cell string type for a cell type.

Parameters:

type[in] The cell type

Returns:

The cell type string

CellType to_type(const std::string &cell)

Get the cell type from a cell string.

Parameters:

cell[in] Cell shape string

Returns:

The cell type

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.

Parameters:
  • type[in] The cell type

  • index[in] The facet index

Returns:

The type of facet for this cell at this index

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.

Parameters:
  • dim[in] Entity dimension

  • type[in] Cell type

Returns:

Number of entities in cell

bool is_simplex(CellType type)

Check if cell is a simplex.

Parameters:

type[in] Cell type

Returns:

True is the cell type is a simplex

int num_cell_vertices(CellType type)

Number vertices for a cell type.

Parameters:

type[in] Cell type

Returns:

The number of cell vertices

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, MPI_Comm subcomm, std::array<std::array<double, 3>, 2> p, std::array<std::size_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:
  • comm[in] MPI communicator to distribute the mesh on.

  • subcomm[in] MPI 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.

  • p[in] Corner of the box.

  • n[in] Number of cells in each direction.

  • celltype[in] Cell shape.

  • partitioner[in] Partitioning function for distributing cells across MPI ranks.

Returns:

Mesh

template<std::floating_point T = double>
Mesh<T> create_box(MPI_Comm comm, std::array<std::array<double, 3>, 2> p, std::array<std::size_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:
  • comm[in] MPI communicator to distribute the mesh on.

  • p[in] Corner of the box.

  • n[in] Number of cells in each direction.

  • celltype[in] Cell shape.

  • partitioner[in] Partitioning function for distributing cells across MPI ranks.

Returns:

Mesh

template<std::floating_point T = double>
Mesh<T> create_rectangle(MPI_Comm comm, std::array<std::array<double, 2>, 2> p, std::array<std::size_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:
  • comm[in] MPI communicator to build the mesh on.

  • p[in] Bottom-left and top-right corners of the rectangle.

  • n[in] Number of cells in each direction.

  • celltype[in] Cell shape.

  • partitioner[in] Partitioning function for distributing cells across MPI ranks.

  • diagonal[in] Direction of diagonals

Returns:

Mesh

template<std::floating_point T = double>
Mesh<T> create_rectangle(MPI_Comm comm, 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:
  • comm[in] MPI communicator to build the mesh on

  • p[in] Two corner points

  • n[in] Number of cells in each direction

  • celltype[in] Cell shape

  • diagonal[in] Direction of diagonals

Returns:

Mesh

template<std::floating_point T = double>
Mesh<T> create_interval(MPI_Comm comm, std::size_t nx, std::array<double, 2> p, 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:
  • comm[in] MPI communicator to build the mesh on

  • nx[in] Number of cells

  • p[in] End points of the interval

  • partitioner[in] Partitioning function for distributing cells across MPI ranks.

Returns:

A mesh

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.

Note

Experimental new interface for multiple cmap/dofmap

Parameters:
  • topology[in] Mesh topology.

  • elements[in] List of elements that defines the geometry map for each cell type.

  • nodes[in] Geometry node global indices for cells on this process.

  • xdofs[in] Geometry degree-of-freedom map (using global indices) for cells on this process. nodes is a sorted and unique list of the indices in xdofs.

  • x[in] 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.

  • dim[in] Geometric dimension (1, 2, or 3).

  • reorder_fn[in] Function for re-ordering the degree-of-freedom map associated with the geometry data.

Pre:

Must be sorted.

Returns:

A mesh geometry.

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:
  • topology[in] Mesh topology.

  • element[in] Element that defines the geometry map for each cell.

  • nodes[in] Geometry node global indices for cells on this process. Must be sorted.

  • xdofs[in] Geometry degree-of-freedom map (using global indices) for cells on this process. nodes is a sorted and unique list of the indices in xdofs.

  • x[in] 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.

  • dim[in] Geometric dimension (1, 2, or 3).

  • reorder_fn[in] Function for re-ordering the degree-of-freedom map associated with the geometry data.

Returns:

A mesh geometry.

template<std::floating_point T>
std::pair<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.

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

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

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.

Parameters:
  • celltype[in] Cell type.

  • cells[in] Cell vertices (stored as as a flattened list).

Returns:

  1. Local dual graph

  2. Facets, defined by their vertices, that are shared by only one cell on this rank. The logically 2D is array 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).

graph::AdjacencyList<std::int64_t> build_dual_graph(MPI_Comm comm, CellType celltype, const graph::AdjacencyList<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:
  • comm[in] The MPI communicator

  • celltype[in] The cell type

  • cells[in] Collection of cells, defined by the cell vertices from which to build the dual graph

Returns:

The dual graph

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.

Note

Entities that do not exist on this rank are ignored.

Warning

entities must not contain duplicate entities.

Parameters:
  • topology[in] Mesh topology that the tags are associated with

  • dim[in] Topological dimension of tagged entities

  • entities[in] Local vertex indices for tagged entities.

  • values[in] Tag values for each entity in entities. The length of values must be equal to number of rows in entities.

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.

  1. 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.

  2. 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

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:
  • comm[in] Communicator across which the topology is distributed.

  • cells[in] 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 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.

  • original_cell_index[in] Original global index associated with each cell.

  • ghost_owners[in] Owning rank of each ghost cell (ghost cells are always at the end of the list of cells).

  • cell_type[in] A vector with cell shapes.

  • boundary_vertices[in] Vertices on the ‘exterior’ (boundary) of the local topology. These vertices might appear on other processes.

Returns:

A distributed 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.

Parameters:
  • comm – MPI Communicator

  • cell_type – List of cell types

  • cells – Lists of cells, using vertex indices, flattened, for each cell type.

  • original_cell_index – Input cell index for each cell type

  • ghost_owners – Owning rank for ghost cells (at end of each list of cells).

  • boundary_vertices – Vertices of undetermined ownership on external or inter-process boundary.

Returns:

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 (parent) topology.

  • dim – Topological dimension of the entities in the new topology.

  • entities – Indices 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.

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.

Note

If an entity cannot be found on this rank, -1 is returned as the index.

Warning

This function may be removed in the future.

Parameters:
  • topology[in] The mesh topology

  • dim[in] Topological dimension of the entities

  • entities[in] The mesh entities defined by their vertices

Returns:

The index of the ith entity in 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).

Parameters:
  • comm[in] MPI Communicator

  • topology[in] Mesh topology

  • dim[in] The dimension of the entities to create

  • index[in] Index 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 exist, then {nullptr, nullptr, nullptr, std::vector()} is returned.

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:
  • topology[in] The topology

  • d0[in] The dimension and index of the entities

  • d1[in] The 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.

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:

topology[in] Mesh topology

Returns:

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

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:
  • cell_type[in] The cell shape

  • layout[in] The layout of geometry ‘degrees-of-freedom’ on the reference cell

  • cells[in] 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.

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:
  • mesh[in] Mesh that the entities belong to.

  • entities[in] Indices (local to process) of entities to compute h for.

  • dim[in] Topological dimension of the entities.

Returns:

Greatest distance between any two vertices, h[i] corresponds to the entity entities[i].

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.

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.

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:
  • mesh[in] Mesh to mark entities on.

  • dim[in] Topological dimension of the entities to be considered.

  • marker[in] 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)

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:
  • mesh[in] Mesh to mark entities on.

  • dim[in] Topological dimension of the entities to be considered. Must be less than the topological dimension of the mesh.

  • marker[in] Marking function, returns true for a point that is ‘marked’, and false otherwise.

Returns:

List of marked entity indices (indices local to the process)

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:
  • mesh[in] The mesh.

  • dim[in] Topological dimension of the entities of interest.

  • entities[in] Entity indices (local) to compute the vertex geometry indices for.

  • orient[in] 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].

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

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:
  • topology[in] The topology

  • entities[in] List of indices of topological dimension d0

  • d0[in] Topological dimension

  • d1[in] Topological dimension

Returns:

List of entities of topological dimension d1 that are incident to entities in entities (topological dimension d0)

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 a 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:
  • comm[in] Communicator to build the mesh on.

  • commt[in] Communicator 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.

  • cells[in] Cells 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.

  • element[in] Coordinate element for the cells.

  • commg[in]

  • x[in] Geometry 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.

  • xshape[in] Shape of the x data.

  • partitioner[in] Graph partitioner that computes the owning rank for each cell. If not callable, cells are not redistributed.

Returns:

A mesh distributed on the communicator comm.

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:
  • comm[in] MPI communicator to build the mesh on.

  • cells[in] Cells on the calling process. See create_mesh for a detailed description.

  • elements[in] Coordinate elements for the cells.

  • x[in] Geometry data (‘node’ coordinates). See create_mesh for a detailed description.

  • xshape[in] The shape of x. It should be (num_points, gdim).

  • ghost_mode[in] The requested type of cell ghosting/overlap

Returns:

A mesh distributed on the communicator comm.

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:
  • mesh[in] The mesh

  • dim[in] Entity dimension

  • entities[in] 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.

template<std::floating_point T>
class Geometry
#include <Geometry.h>

Geometry stores the geometry imposed on a mesh.

Public Types

using value_type = T

Value type.

Public Functions

template<typename U, typename V, typename W>
inline Geometry(std::shared_ptr<const common::IndexMap> index_map, U &&dofmap, const fem::CoordinateElement<typename std::remove_reference_t<typename V::value_type>> &element, V &&x, int dim, W &&input_global_indices)

Constructor of object that holds mesh geometry data.

Parameters:
  • index_map[in] Index map associated with the geometry dofmap

  • dofmap[in] The geometry (point) dofmap. For a cell, it gives the position in the point array of each local geometry node

  • element[in] Element that describes the cell geometry map.

  • x[in] The point coordinates. The shape is (num_points, 3) and the storage is row-major.

  • dim[in] The geometric dimension (0 < dim <= 3).

  • input_global_indices[in] The ‘global’ input index of each point, commonly from a mesh input file.

template<typename V, typename W>
inline Geometry(std::shared_ptr<const common::IndexMap> index_map, const std::vector<std::vector<std::int32_t>> &dofmaps, const std::vector<fem::CoordinateElement<typename std::remove_reference_t<typename V::value_type>>> &elements, V &&x, int dim, W &&input_global_indices)

Constructor of object that holds mesh geometry data.

Parameters:
  • index_map[in] Index map associated with the geometry dofmap

  • dofmaps[in] The geometry (point) dofmaps. For a cell, it gives the position in the point array of each local geometry node

  • elements[in] Elements that describes the cell geometry maps.

  • x[in] The point coordinates. The shape is (num_points, 3) and the storage is row-major.

  • dim[in] The geometric dimension (0 < dim <= 3).

  • input_global_indices[in] The ‘global’ input index of each point, commonly from a mesh input file.

Geometry(const Geometry&) = default

Copy constructor.

Geometry(Geometry&&) = default

Move constructor.

~Geometry() = default

Destructor.

Geometry &operator=(const Geometry&) = delete

Copy Assignment.

Geometry &operator=(Geometry&&) = default

Move Assignment.

inline int dim() const

Return Euclidean dimension of coordinate system.

inline MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<const std::int32_t, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>> dofmap() const

DofMap for the geometry.

Returns:

A 2D array with shape [num_cells, dofs_per_cell]

inline MDSPAN_IMPL_STANDARD_NAMESPACE::mdspan<const std::int32_t, MDSPAN_IMPL_STANDARD_NAMESPACE::dextents<std::size_t, 2>> dofmap(std::int32_t i) const

The dofmap associated with the ith coordinate map in the geometry.

Parameters:

i – Index

Returns:

A 2D array with shape [num_cells, dofs_per_cell]

inline std::shared_ptr<const common::IndexMap> index_map() const

Index map.

Returns:

The index map for the geometry dofs

inline std::span<const value_type> x() const

Access geometry degrees-of-freedom data (const version).

Returns:

The flattened row-major geometry data, where the shape is (num_points, 3)

inline std::span<value_type> x()

Access geometry degrees-of-freedom data (non-const version).

Returns:

The flattened row-major geometry data, where the shape is (num_points, 3)

inline const fem::CoordinateElement<value_type> &cmap() const

The element that describes the geometry map.

Returns:

The coordinate/geometry element

inline const fem::CoordinateElement<value_type> &cmap(std::int32_t i) const

The element that describe the ith geometry map.

Parameters:

i – Index of the coordinate element

Returns:

Coordinate element

inline const std::vector<std::int64_t> &input_global_indices() const

Global user indices.

template<std::floating_point T>
class Mesh
#include <Mesh.h>

A Mesh consists of a set of connected and numbered mesh topological entities, and geometry data.

Template Parameters:

The – floating point type for representing the geometry.

Public Types

using geometry_type = Geometry<T>

Value type.

Public Functions

template<typename V>
inline Mesh(MPI_Comm comm, std::shared_ptr<Topology> topology, V &&geometry)

Create a mesh.

Parameters:
  • comm[in] MPI Communicator

  • topology[in] Mesh topology

  • geometry[in] Mesh geometry

Mesh(const Mesh &mesh) = default

Copy constructor.

Parameters:

mesh[in] Mesh to be copied

Mesh(Mesh &&mesh) = default

Move constructor.

Parameters:

meshMesh to be moved.

~Mesh() = default

Destructor.

Mesh &operator=(Mesh &&mesh) = default

Assignment move operator.

Parameters:

mesh – Another Mesh object

inline std::shared_ptr<Topology> topology()

Get mesh topology.

Returns:

The topology object associated with the mesh.

inline std::shared_ptr<const Topology> topology() const

Get mesh topology (const version)

Returns:

The topology object associated with the mesh.

inline std::shared_ptr<Topology> topology_mutable() const

Get mesh topology if one really needs the mutable version.

Returns:

The topology object associated with the mesh.

inline Geometry<T> &geometry()

Get mesh geometry.

Returns:

The geometry object associated with the mesh

inline const Geometry<T> &geometry() const

Get mesh geometry (const version)

Returns:

The geometry object associated with the mesh

inline MPI_Comm comm() const

Mesh MPI communicator.

Returns:

The communicator on which the mesh is distributed

Public Members

std::string name = "mesh"

Name.

template<typename T>
class MeshTags
#include <MeshTags.h>

MeshTags associate values with mesh topology entities.

The entity index (local to process) identifies the entity. MeshTags is a sparse data storage class; it allows tags to be associated with an arbitrary subset of mesh entities. An entity can have only one associated tag.

Template Parameters:

Type

Public Functions

template<typename U, typename V>
inline MeshTags(std::shared_ptr<const Topology> topology, int dim, U &&indices, V &&values)

Create a MeshTag from entities of given dimension on a mesh.

Parameters:
  • topology[in] Mesh topology on which the tags are associated.

  • dim[in] Topological dimension of mesh entities to tag.

  • indices[in] List of entity indices (indices local to the process).

  • values[in] List of values for each index in indices. The size must be equal to the size of indices.

Pre:

indices must be sorted and unique.

MeshTags(const MeshTags &tags) = default

Copy constructor.

MeshTags(MeshTags &&tags) = default

Move constructor.

~MeshTags() = default

Destructor.

MeshTags &operator=(const MeshTags &tags) = default

Move assignment.

MeshTags &operator=(MeshTags &&tags) = default

Move assignment.

inline std::vector<std::int32_t> find(const T value) const

Find all entities with a given tag value.

Parameters:

value[in] The value

Returns:

Indices of tagged entities. The indices are sorted.

inline std::span<const std::int32_t> indices() const

Indices of tagged topology entities (local-to-process). The indices are sorted.

inline std::span<const T> values() const

Values attached to topology entities.

inline int dim() const

Return topological dimension of tagged entities.

inline std::shared_ptr<const Topology> topology() const

Return topology.

Public Members

std::string name = "mesh_tags"

Name.

class Topology
#include <Topology.h>

Topology stores the topology of a mesh, consisting of mesh entities and connectivity (incidence relations for the mesh entities).

A mesh entity e may be identified globally as a pair e = (dim, i), where dim is the topological dimension and i is the index of the entity within that topological dimension.

Todo:

Rework memory management and associated API. Currently, there is no clear caching policy implemented and no way of discarding cached data.

Public Functions

Topology(MPI_Comm comm, CellType cell_type)

Empty Topology constructor.

Parameters:
  • comm – MPI communicator

  • cell_type – Type of cell

Topology(MPI_Comm comm, const std::vector<CellType> &cell_type)

Create empty mesh topology with multiple cell types.

Warning

Experimental

Parameters:
  • comm – MPI communicator

  • cell_type – List of cell types

Topology(const Topology &topology) = default

Copy constructor.

Topology(Topology &&topology) = default

Move constructor.

~Topology() = default

Destructor.

Topology &operator=(const Topology &topology) = delete

Assignment.

Topology &operator=(Topology &&topology) = default

Assignment.

int dim() const noexcept

Return the topological dimension of the mesh.

void set_index_map(int dim, std::shared_ptr<const common::IndexMap> map)

Set the IndexMap for dimension dim.

Todo:

Merge with set_connectivity

Warning

This is experimental and likely to change

void set_index_map(std::int8_t dim, std::int8_t i, std::shared_ptr<const common::IndexMap> map)

Set the IndexMap for the ith celltype of dimension dim.

Todo:

Merge with set_connectivity

Warning

This is experimental and likely to change

Parameters:
  • dim – Topological dimension

  • i – Index of cell type within dimension dim. Cell types for each dimension can be obtained with entity_types(dim).

  • map – Map to set

std::shared_ptr<const common::IndexMap> index_map(int dim) const

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

Parameters:

dim[in] Topological dimension

Returns:

Index map for the entities of dimension dim. Returns nullptr if index map has not been set.

std::vector<std::shared_ptr<const common::IndexMap>> index_maps(std::int8_t dim) const

Warning

Experimental

Parameters:

dim – Topological dimension

Returns:

List of index maps, one for each cell type

std::shared_ptr<const graph::AdjacencyList<std::int32_t>> connectivity(int d0, int d1) const

Return connectivity from entities of dimension d0 to entities of dimension d1. Assumes only one entity type per dimension.

Parameters:
  • d0[in]

  • d1[in]

Returns:

The adjacency list that for each entity of dimension d0 gives the list of incident entities of dimension d1. Returns nullptr if connectivity has not been computed.

std::shared_ptr<const graph::AdjacencyList<std::int32_t>> connectivity(std::pair<std::int8_t, std::int8_t> d0, std::pair<std::int8_t, std::int8_t> d1) const

Return the connectivity from entities of topological dimension d0 to dimension d1. The entity type, and incident entity type are each described by a pair (dim, index). The index within a topological dimension dim, is that of the cell type given in entity_types(dim).

Parameters:
  • d0 – Pair of (topological dimension of entities, index of “entity type” within topological dimension)

  • d1 – Pair of (topological dimension of indicent entities, index of incident “entity type” within topological dimension)

Returns:

AdjacencyList of connectivity from entity type in d0 to entity types in d1, or nullptr if not yet computed.

void set_connectivity(std::shared_ptr<graph::AdjacencyList<std::int32_t>> c, int d0, int d1)

Set connectivity for given pair of topological dimensions.

Todo:

Merge with set_index_map

void set_connectivity(std::shared_ptr<graph::AdjacencyList<std::int32_t>> c, std::pair<std::int8_t, std::int8_t> d0, std::pair<std::int8_t, std::int8_t> d1)

Set connectivity for given pair of entity types, defined by dimension and index, as listed in entity_types(). General version for mixed topology. Connectivity from d0 to d1.

Warning

Experimental

Parameters:
  • c – Connectivity AdjacencyList

  • d0 – Pair of (topological dimension of entities, index of “entity type” within topological dimension)

  • d1 – Pair of (topological dimension of indicent entities, index of incident “entity type” within topological dimension)

const std::vector<std::uint32_t> &get_cell_permutation_info() const

Returns the permutation information.

const std::vector<std::uint8_t> &get_facet_permutations() const

Get the permutation number to apply to a facet.

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.

Note

An exception is raised if the permutations have not been computed

Returns:

The permutation number

CellType cell_type() const

Cell type.

Returns:

Cell type that the topology is for

std::vector<CellType> entity_types(std::int8_t dim) const

Get the entity types in the topology for a given dimension.

Parameters:

dim – Topological dimension

Returns:

List of entity types

std::int32_t create_entities(int dim)

Create entities of given topological dimension.

Parameters:

dim[in] Topological dimension

Returns:

Number of newly created entities, returns -1 if entities already existed

void create_connectivity(int d0, int d1)

Create connectivity between given pair of dimensions, d0 -> d1.

Parameters:
  • d0[in] Topological dimension

  • d1[in] Topological dimension

void create_entity_permutations()

Compute entity permutations and reflections.

const std::vector<std::int32_t> &interprocess_facets() const

List of inter-process facets, if facet topology has been computed.

const std::vector<std::int32_t> &interprocess_facets(std::int8_t index) const

List of inter-process facets, if facet topology has been computed, for the facet type in Topology::entity_types identified by index.

Parameters:

index – Index of facet type

MPI_Comm comm() const

Mesh MPI communicator.

Returns:

The communicator on which the topology is distributed

Public Members

std::vector<std::vector<std::int64_t>> original_cell_index

Original cell index for each cell type.

namespace impl

Functions

template<std::floating_point T>
Mesh<T> build_tri(MPI_Comm comm, std::array<std::array<double, 2>, 2> p, std::array<std::size_t, 2> n, const CellPartitionFunction &partitioner, DiagonalType diagonal)
template<std::floating_point T>
Mesh<T> build_quad(MPI_Comm comm, const std::array<std::array<double, 2>, 2> p, std::array<std::size_t, 2> n, const CellPartitionFunction &partitioner)
template<std::floating_point T>
std::vector<T> create_geom(MPI_Comm comm, std::array<std::array<double, 3>, 2> p, std::array<std::size_t, 3> n)
template<std::floating_point T>
Mesh<T> build_tet(MPI_Comm comm, MPI_Comm subcomm, std::array<std::array<double, 3>, 2> p, std::array<std::size_t, 3> n, const CellPartitionFunction &partitioner)
template<std::floating_point T>
Mesh<T> build_hex(MPI_Comm comm, MPI_Comm subcomm, std::array<std::array<double, 3>, 2> p, std::array<std::size_t, 3> n, const CellPartitionFunction &partitioner)
template<std::floating_point T>
Mesh<T> build_prism(MPI_Comm comm, MPI_Comm subcomm, std::array<std::array<double, 3>, 2> p, std::array<std::size_t, 3> n, const CellPartitionFunction &partitioner)
template<std::floating_point T>
mesh::Mesh<T> build_hex(MPI_Comm comm, MPI_Comm subcomm, std::array<std::array<double, 3>, 2> p, std::array<std::size_t, 3> n, const CellPartitionFunction &partitioner)
template<typename T>
void reorder_list(std::span<T> list, std::span<const std::int32_t> nodemap)

Re-order an adjacency list of fixed degree.

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

The coordinates of ‘vertices’ for for entities of a give dimension that are attached to specified facets.

Parameters:
  • mesh[in] Mesh to compute the vertex coordinates for

  • dim[in] Topological dimension of the entities

  • facets[in] List of facets on the meh boundary

Pre:

The provided facets must be on the boundary of the mesh.

Returns:

(0) Entities attached to the boundary facets, (1) vertex coordinates (shape is (3, num_vertices)) and (2) map from vertex in the full mesh to the position (column) in the vertex coordinates array (set to -1 if vertex in full mesh is not in the coordinate array).

template<std::floating_point T>
std::pair<std::vector<T>, std::array<std::size_t, 2>> compute_vertex_coords(const mesh::Mesh<T> &mesh)

The coordinates for all ‘vertices’ in the mesh.

Parameters:

mesh[in] Mesh to compute the vertex coordinates for

Returns:

The vertex coordinates. The shape is (3, num_vertices) and the jth column hold the coordinates of vertex j.