Source code for dolfinx.mesh

# Copyright (C) 2017-2021 Chris N. Richardson and Garth N. Wells
#
# This file is part of DOLFINx (https://www.fenicsproject.org)
#
# SPDX-License-Identifier:    LGPL-3.0-or-later
"""Creation, refining and marking of meshes"""

from __future__ import annotations

import typing

import numpy as np
import numpy.typing as npt

import basix
import basix.ufl
import ufl
from dolfinx import cpp as _cpp
from dolfinx.cpp.mesh import (CellType, DiagonalType, GhostMode,
                              build_dual_graph, cell_dim,
                              create_cell_partitioner, exterior_facet_indices,
                              to_string, to_type)
from dolfinx.cpp.refinement import RefinementOption

from mpi4py import MPI as _MPI

__all__ = ["meshtags_from_entities", "locate_entities", "locate_entities_boundary",
           "refine", "create_mesh", "Mesh", "MeshTags", "meshtags", "CellType",
           "GhostMode", "build_dual_graph", "cell_dim", "compute_midpoints",
           "exterior_facet_indices", "compute_incident_entities", "create_cell_partitioner",
           "create_interval", "create_unit_interval", "create_rectangle", "create_unit_square",
           "create_box", "create_unit_cube", "to_type", "to_string"]


[docs]def compute_incident_entities(topology, entities: npt.NDArray[np.int32], d0: int, d1: int):
    return _cpp.mesh.compute_incident_entities(topology, entities, d0, d1)


[docs]def compute_midpoints(mesh: Mesh, dim: int, entities: npt.NDArray[np.int32]):
    return _cpp.mesh.compute_midpoints(mesh._cpp_object, dim, entities)


[docs]class Mesh:
    def __init__(self, mesh: _cpp.mesh.Mesh, domain: ufl.Mesh):
        """A class for representing meshes

        Args:
            mesh: The C++ mesh object
            domain: The UFL domain

        Note:
            Mesh objects should not usually be created using this class directly.

        """
        self._cpp_object = mesh
        self._ufl_domain = domain
        self._ufl_domain._ufl_cargo = self._cpp_object

    @property
    def comm(self):
        return self._cpp_object.comm

    @property
    def name(self):
        return self._cpp_object.name

    @name.setter
    def name(self, value):
        self._cpp_object.name = value

[docs]    def ufl_cell(self) -> ufl.Cell:
        """Return the UFL cell type"""
        return ufl.Cell(self.topology.cell_name(), geometric_dimension=self.geometry.dim)

[docs]    def ufl_domain(self) -> ufl.Mesh:
        """Return the ufl domain corresponding to the mesh."""
        return self._ufl_domain

[docs]    def basix_cell(self) -> ufl.Cell:
        """Return the Basix cell type."""
        return getattr(basix.CellType, self.topology.cell_name())

[docs]    def h(self, dim: int, entities: npt.NDArray[np.int32]) -> npt.NDArray[np.float64]:
        """Size measure for each cell."""
        return _cpp.mesh.h(self._cpp_object, dim, entities)

    @property
    def topology(self):
        return self._cpp_object.topology

    @property
    def geometry(self):
        return self._cpp_object.geometry


[docs]def locate_entities(mesh: Mesh, dim: int, marker: typing.Callable) -> np.ndarray:
    """Compute mesh entities satisfying a geometric marking function

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

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

    """
    return _cpp.mesh.locate_entities(mesh._cpp_object, dim, marker)


[docs]def locate_entities_boundary(mesh: Mesh, dim: int, marker: typing.Callable) -> np.ndarray:
    """Compute mesh entities that are connected to an owned boundary
    facet and satisfy a geometric marking function

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

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

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

    """
    return _cpp.mesh.locate_entities_boundary(mesh._cpp_object, dim, marker)


_uflcell_to_dolfinxcell = {
    "interval": CellType.interval,
    "interval2D": CellType.interval,
    "interval3D": CellType.interval,
    "triangle": CellType.triangle,
    "triangle3D": CellType.triangle,
    "quadrilateral": CellType.quadrilateral,
    "quadrilateral3D": CellType.quadrilateral,
    "tetrahedron": CellType.tetrahedron,
    "hexahedron": CellType.hexahedron
}


def transfer_meshtag(meshtag: MeshTags, mesh1: Mesh, parent_cell: npt.NDArray[np.int32],
                     parent_facet: typing.Optional[npt.NDArray[np.int8]] = None) -> MeshTags:
    """Generate cell mesh tags on a refined mesh from the mesh tags on the coarse parent mesh.

        Args:
            meshtag: Mesh tags on the coarse, parent mesh
            mesh1: The refined mesh
            parent_cell: Index of the parent cell for each cell in the refined mesh
            parent_facet: Index of the local parent facet for each cell
                in the refined mesh. Only required for transfer tags on facets.

        Returns:
            Mesh tags on the refined mesh.

    """
    if meshtag.dim == meshtag.topology.dim:
        mt = _cpp.refinement.transfer_cell_meshtag(meshtag._cpp_object, mesh1.topology, parent_cell)
        return MeshTags(mt)
    elif meshtag.dim == meshtag.topology.dim - 1:
        assert parent_facet is not None
        mt = _cpp.refinement.transfer_facet_meshtag(meshtag._cpp_object, mesh1.topology, parent_cell, parent_facet)
        return MeshTags(mt)
    else:
        raise RuntimeError("MeshTag transfer is supported on on cells or facets.")


[docs]def refine(mesh: Mesh, edges: typing.Optional[np.ndarray] = None, redistribute: bool = True) -> Mesh:
    """Refine a mesh.

    Args:
        mesh: Mesh from which to create the refined mesh.
        edges: Indices of edges to split during refinement. If `None`,
            uniform refinement is uses.
        redistribute:
            Refined mesh is re-partitioned if `True`

    Returns:
       Refined mesh

    """
    if edges is None:
        mesh1 = _cpp.refinement.refine(mesh._cpp_object, redistribute)
    else:
        mesh1 = _cpp.refinement.refine(mesh._cpp_object, edges, redistribute)
    element = mesh._ufl_domain.ufl_coordinate_element()
    domain = ufl.Mesh(element)
    return Mesh(mesh1, domain)


def refine_plaza(mesh: Mesh, edges: typing.Optional[np.ndarray] = None, redistribute: bool = True,
                 option: RefinementOption = RefinementOption.none) -> tuple[Mesh, npt.NDArray[np.int32],
                                                                            npt.NDArray[np.int32]]:
    """Refine a mesh.

    Args:
        mesh: Mesh from which to create the refined mesh.
        edges: Indices of edges to split during refinement. If `None`,
            uniform refinement is uses.
        redistribute:
            Refined mesh is re-partitioned if `True`
        option:
            Control computation of the parent-refined mesh data.

    Returns:
       Refined mesh, list of parent cell for each refine cell, and list
       of parent facets.

    """
    if edges is None:
        mesh1, cells, facets = _cpp.refinement.refine_plaza(mesh._cpp_object, redistribute)
    else:
        mesh1, cells, facets = _cpp.refinement.refine_plaza(mesh._cpp_object, edges, redistribute)
    element = mesh._ufl_domain.ufl_coordinate_element()
    domain = ufl.Mesh(element)
    return Mesh(mesh1, domain), cells, facets


[docs]def create_mesh(comm: _MPI.Comm, cells: typing.Union[np.ndarray, _cpp.graph.AdjacencyList_int64],
                x: np.ndarray, domain: ufl.Mesh,
                partitioner=_cpp.mesh.create_cell_partitioner(GhostMode.none)) -> Mesh:
    """Create a mesh from topology and geometry arrays.

    Args:
        comm: MPI communicator to define the mesh on.
        cells: Cells of the mesh. `cells[i]` is the 'nodes' of cell `i`.
        x: Mesh geometry ('node' coordinates), with shape ``(num_nodes, gdim)``
        domain: UFL mesh.
        ghost_mode: The ghost mode used in the mesh partitioning.
        partitioner: Function that computes the parallel distribution of
            cells across MPI ranks.

    Returns:
        A mesh.

    """
    ufl_element = domain.ufl_coordinate_element()
    cell_shape = ufl_element.cell().cellname()
    cell_degree = ufl_element.degree()
    try:
        variant = ufl_element.lagrange_variant
    except AttributeError:
        variant = basix.LagrangeVariant.unset

    x = np.asarray(x, order='C')
    if x.dtype == np.float32:
        cmap = _cpp.fem.CoordinateElement_float32(_uflcell_to_dolfinxcell[cell_shape], cell_degree, variant)
    elif x.dtype == np.float64:
        cmap = _cpp.fem.CoordinateElement_float64(_uflcell_to_dolfinxcell[cell_shape], cell_degree, variant)

    try:
        mesh = _cpp.mesh.create_mesh(comm, cells, cmap, x, partitioner)
    except TypeError:
        mesh = _cpp.mesh.create_mesh(comm, _cpp.graph.AdjacencyList_int64(np.cast['int64'](cells)),
                                     cmap, x, partitioner)
    return Mesh(mesh, domain)


def create_submesh(msh, dim, entities):
    submsh, entity_map, vertex_map, geom_map = _cpp.mesh.create_submesh(msh._cpp_object, dim, entities)
    assert len(submsh.geometry.cmaps) == 1
    submsh_ufl_cell = ufl.Cell(submsh.topology.cell_name(), geometric_dimension=submsh.geometry.dim)
    submsh_domain = ufl.Mesh(basix.ufl.element(
        "Lagrange", submsh_ufl_cell.cellname(), submsh.geometry.cmaps[0].degree, submsh.geometry.cmaps[0].variant,
        shape=(submsh.geometry.dim, ), gdim=submsh.geometry.dim))
    return (Mesh(submsh, submsh_domain), entity_map, vertex_map, geom_map)


[docs]class MeshTags:
    def __init__(self, meshtags):
        """Mesh tags associate data (markers) with a subset of mesh entities of a given dimension.

        Args:
            meshtags: C++ mesh tags object.

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

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

        """
        self._cpp_object = meshtags

[docs]    def ufl_id(self) -> int:
        return id(self)

    @property
    def topology(self) -> _cpp.mesh.Topology:
        """Mesh topology with which the the tags are associated."""
        return self._cpp_object.topology

    @property
    def dim(self) -> int:
        """Topological dimension of the tagged entities."""
        return self._cpp_object.dim

    @property
    def indices(self) -> npt.NDArray[np.int32]:
        """Indices of tagged mesh entities."""
        return self._cpp_object.indices

    @property
    def values(self):
        """Values associated with tagged mesh entities."""
        return self._cpp_object.values

    @property
    def name(self) -> str:
        return self._cpp_object.name

    @name.setter
    def name(self, value):
        self._cpp_object.name = value

[docs]    def find(self, value) -> npt.NDArray[np.int32]:
        """Get a list of all entity indices with a given value.

        Args:
            value: Mesh tag value to search for

        Return:
            Indices of entities with tag `value`

        """
        return self._cpp_object.find(value)


[docs]def meshtags(mesh: Mesh, dim: int, entities: npt.NDArray[np.int32],
             values: typing.Union[np.ndarray, int, float]) -> MeshTags:
    """Create a MeshTags object that associates data with a subset of mesh entities.

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

    Returns:
        A MeshTags object

    Note:
        The type of the returned MeshTags is inferred from the type of
        ``values``.

    """

    if isinstance(values, int):
        assert np.can_cast(values, np.int32)
        values = np.full(entities.shape, values, dtype=np.int32)
    elif isinstance(values, float):
        values = np.full(entities.shape, values, dtype=np.double)

    values = np.asarray(values)
    if values.dtype == np.int8:
        ftype = _cpp.mesh.MeshTags_int8
    elif values.dtype == np.int32:
        ftype = _cpp.mesh.MeshTags_int32
    elif values.dtype == np.int64:
        ftype = _cpp.mesh.MeshTags_int64
    elif values.dtype == np.float64:
        ftype = _cpp.mesh.MeshTags_float64
    else:
        raise NotImplementedError(f"Type {values.dtype} not supported.")

    return MeshTags(ftype(mesh.topology, dim, np.asarray(entities, dtype=np.int32), values))


[docs]def meshtags_from_entities(mesh: Mesh, dim: int, entities: _cpp.graph.AdjacencyList_int32,
                           values: npt.NDArray[typing.Any]):
    """Create a MeshTags object that associates data with a subset of
    mesh entities, where the entities are defined by their vertices.

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

    Returns:
        A MeshTags object

    Note:
        The type of the returned MeshTags is inferred from the type of
        ``values``.

    """

    if isinstance(values, int):
        assert np.can_cast(values, np.int32)
        values = np.full(entities.num_nodes, values, dtype=np.int32)
    elif isinstance(values, float):
        values = np.full(entities.num_nodes, values, dtype=np.double)

    values = np.asarray(values)
    return MeshTags(_cpp.mesh.create_meshtags(mesh.topology, dim, entities, values))


[docs]def create_interval(comm: _MPI.Comm, nx: int, points: npt.ArrayLike,
                    ghost_mode=GhostMode.shared_facet, partitioner=None) -> Mesh:
    """Create an interval mesh.

    Args:
        comm: MPI communicator
        nx: Number of cells
        points: Coordinates of the end points
        ghost_mode: Ghost mode used in the mesh partitioning. Options
            are `GhostMode.none' and `GhostMode.shared_facet`.
        partitioner: Partitioning function to use for determining the
            parallel distribution of cells across MPI ranks

    Returns:
        An interval mesh

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    domain = ufl.Mesh(basix.ufl.element("Lagrange", "interval", 1, rank=1))
    mesh = _cpp.mesh.create_interval_float64(comm, nx, points, ghost_mode, partitioner)
    return Mesh(mesh, domain)


[docs]def create_unit_interval(comm: _MPI.Comm, nx: int, ghost_mode=GhostMode.shared_facet,
                         partitioner=None) -> Mesh:
    """Create a mesh on the unit interval.

    Args:
        comm: MPI communicator
        nx: Number of cells
        points: Coordinates of the end points
        ghost_mode: Ghost mode used in the mesh partitioning. Options
            are `GhostMode.none' and `GhostMode.shared_facet`.
        partitioner: Partitioning function to use for determining the
            parallel distribution of cells across MPI ranks

    Returns:
        A unit interval mesh with end points at 0 and 1

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    return create_interval(comm, nx, [0.0, 1.0], ghost_mode, partitioner)


[docs]def create_rectangle(comm: _MPI.Comm, points: npt.ArrayLike, n: npt.ArrayLike,
                     cell_type=CellType.triangle, ghost_mode=GhostMode.shared_facet,
                     partitioner=None, diagonal: DiagonalType = DiagonalType.right) -> Mesh:
    """Create a rectangle mesh.

    Args:
        comm: MPI communicator
        points: Coordinates of the lower-left and upper-right corners of the
            rectangle
        n: Number of cells in each direction
        cell_type: Mesh cell type
        ghost_mode: Ghost mode used in the mesh partitioning
        partitioner: Function that computes the parallel distribution of
            cells across MPI ranks
        diagonal: Direction of diagonal of triangular meshes. The
            options are ``left``, ``right``, ``crossed``, ``left/right``,
            ``right/left``.

    Returns:
        A mesh of a rectangle

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    domain = ufl.Mesh(basix.ufl.element("Lagrange", cell_type.name, 1, rank=1))
    mesh = _cpp.mesh.create_rectangle_float64(comm, points, n, cell_type, partitioner, diagonal)
    return Mesh(mesh, domain)


[docs]def create_unit_square(comm: _MPI.Comm, nx: int, ny: int, cell_type=CellType.triangle,
                       ghost_mode=GhostMode.shared_facet, partitioner=None,
                       diagonal: DiagonalType = DiagonalType.right) -> Mesh:
    """Create a mesh of a unit square.

    Args:
        comm: MPI communicator
        nx: Number of cells in the "x" direction
        ny: Number of cells in the "y" direction
        cell_type: Mesh cell type
        ghost_mode: Ghost mode used in the mesh partitioning
        partitioner:Function that computes the parallel distribution of cells across
            MPI ranks
        diagonal:
            Direction of diagonal

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

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    return create_rectangle(comm, [np.array([0.0, 0.0]),
                                   np.array([1.0, 1.0])], [nx, ny], cell_type, ghost_mode,
                            partitioner, diagonal)


[docs]def create_box(comm: _MPI.Comm, points: typing.List[npt.ArrayLike], n: list,
               cell_type=CellType.tetrahedron, ghost_mode=GhostMode.shared_facet,
               partitioner=None) -> Mesh:
    """Create a box mesh.

    Args:
        comm: MPI communicator
        points: Coordinates of the 'lower-left' and 'upper-right'
            corners of the box
        n: List of cells in each direction
        cell_type: The cell type
        ghost_mode: The ghost mode used in the mesh partitioning
        partitioner: Function that computes the parallel distribution of
            cells across MPI ranks

    Returns:
        A mesh of a box domain

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    domain = ufl.Mesh(basix.ufl.element("Lagrange", cell_type.name, 1, rank=1))
    mesh = _cpp.mesh.create_box_float64(comm, points, n, cell_type, partitioner)
    return Mesh(mesh, domain)


[docs]def create_unit_cube(comm: _MPI.Comm, nx: int, ny: int, nz: int, cell_type=CellType.tetrahedron,
                     ghost_mode=GhostMode.shared_facet, partitioner=None) -> Mesh:
    """Create a mesh of a unit cube.

    Args:
        comm: MPI communicator
        nx: Number of cells in "x" direction
        ny: Number of cells in "y" direction
        nz: Number of cells in "z" direction
        cell_type: Mesh cell type
        ghost_mode: Ghost mode used in the mesh partitioning
        partitioner: Function that computes the parallel distribution of
            cells across MPI ranks

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

    """
    if partitioner is None:
        partitioner = _cpp.mesh.create_cell_partitioner(ghost_mode)
    return create_box(comm, [np.array([0.0, 0.0, 0.0]), np.array([1.0, 1.0, 1.0])],
                      [nx, ny, nz], cell_type, ghost_mode, partitioner)