import numpy as np
import ctypes
import os
import sys
import ufl
import finat.ufl
import FIAT
import weakref
from collections import OrderedDict, defaultdict
from collections.abc import Sequence
from ufl.classes import ReferenceGrad
from ufl.domain import extract_unique_domain
import enum
import numbers
import abc
import rtree
from textwrap import dedent
from pathlib import Path
from pyop2 import op2
from pyop2.mpi import (
MPI, COMM_WORLD, internal_comm, is_pyop2_comm, temp_internal_comm
)
from pyop2.utils import as_tuple
import firedrake.cython.dmcommon as dmcommon
import firedrake.cython.extrusion_numbering as extnum
import firedrake.extrusion_utils as eutils
import firedrake.cython.spatialindex as spatialindex
import firedrake.utils as utils
from firedrake.utils import as_cstr, IntType, RealType
from firedrake.logging import info_red
from firedrake.parameters import parameters
from firedrake.petsc import (
PETSc, OptionsManager, get_external_packages, DEFAULT_PARTITIONER
)
from firedrake.adjoint_utils import MeshGeometryMixin
from pyadjoint import stop_annotating
import gem
try:
import netgen
except ImportError:
netgen = None
ngsPETSc = None
# Only for docstring
import mpi4py # noqa: F401
from finat.element_factory import as_fiat_cell
__all__ = [
'Mesh', 'ExtrudedMesh', 'VertexOnlyMesh', 'RelabeledMesh',
'SubDomainData', 'unmarked', 'DistributedMeshOverlapType',
'DEFAULT_MESH_NAME', 'MeshGeometry', 'MeshTopology',
'AbstractMeshTopology', 'ExtrudedMeshTopology', 'VertexOnlyMeshTopology',
'VertexOnlyMeshMissingPointsError',
'Submesh'
]
_cells = {
0: {0: "vertex"},
1: {2: "interval"},
2: {3: "triangle", 4: "quadrilateral"},
3: {4: "tetrahedron", 6: "hexahedron"}
}
_supported_embedded_cell_types_and_gdims = [('interval', 2),
('triangle', 3),
("quadrilateral", 3),
("interval * interval", 3)]
unmarked = -1
"""A mesh marker that selects all entities that are not explicitly marked."""
DEFAULT_MESH_NAME = "_".join(["firedrake", "default"])
"""The default name of the mesh."""
def _generate_default_submesh_name(name):
"""Generate the default submesh name from the mesh name.
Parameters
----------
name : str
Name of the parent mesh.
Returns
-------
str
Default submesh name.
"""
return "_".join([name, "submesh"])
def _generate_default_mesh_coordinates_name(name):
"""Generate the default mesh coordinates name from the mesh name.
:arg name: the mesh name.
:returns: the default mesh coordinates name.
"""
return "_".join([name, "coordinates"])
def _generate_default_mesh_reference_coordinates_name(name):
"""Generate the default mesh reference coordinates name from the mesh name.
:arg name: the mesh name.
:returns: the default mesh reference coordinates name.
"""
return "_".join([name, "reference_coordinates"])
def _generate_default_mesh_topology_name(name):
"""Generate the default mesh topology name from the mesh name.
:arg name: the mesh name.
:returns: the default mesh topology name.
"""
return "_".join([name, "topology"])
def _generate_default_mesh_topology_distribution_name(comm_size, dist_param):
"""Generate the default mesh topology permutation name.
:arg comm_size: the size of comm.
:arg dist_param: the distribution_parameter dict.
:returns: the default mesh topology distribution name.
"""
return "_".join(["firedrake", "default",
str(comm_size),
str(dist_param["partition"]).replace(' ', ''),
str(dist_param["partitioner_type"]),
"(" + dist_param["overlap_type"][0].name + "," + str(dist_param["overlap_type"][1]) + ")"])
def _generate_default_mesh_topology_permutation_name(reorder):
"""Generate the default mesh topology permutation name.
:arg reorder: the flag indicating if the reordering happened or not.
:returns: the default mesh topology permutation name.
"""
return "_".join(["firedrake", "default", str(reorder)])
[docs]
class DistributedMeshOverlapType(enum.Enum):
"""How should the mesh overlap be grown for distributed meshes?
Possible options are:
- :attr:`NONE`: Don't overlap distributed meshes, only useful for problems with
no interior facet integrals.
- :attr:`FACET`: Add ghost entities in the closure of the star of
facets.
- :attr:`VERTEX`: Add ghost entities in the closure of the star
of vertices.
Defaults to :attr:`FACET`.
"""
NONE = 1
FACET = 2
VERTEX = 3
class _Facets(object):
"""Wrapper class for facet interation information on a :func:`Mesh`
.. warning::
The unique_markers argument **must** be the same on all processes."""
@PETSc.Log.EventDecorator()
def __init__(self, mesh, facets, classes, kind, facet_cell, local_facet_number,
unique_markers=None):
self.mesh = mesh
self.facets = facets
classes = as_tuple(classes, int, 3)
self.classes = classes
self.kind = kind
assert kind in ["interior", "exterior"]
if kind == "interior":
self._rank = 2
else:
self._rank = 1
self.facet_cell = facet_cell
if isinstance(self.set, op2.ExtrudedSet):
dset = op2.DataSet(self.set.parent, self._rank)
else:
dset = op2.DataSet(self.set, self._rank)
# Dat indicating which local facet of each adjacent cell corresponds
# to the current facet.
self.local_facet_dat = op2.Dat(dset, local_facet_number, np.uintc,
"%s_%s_local_facet_number" %
(self.mesh.name, self.kind))
self.unique_markers = [] if unique_markers is None else unique_markers
self._subsets = {}
@utils.cached_property
def set(self):
size = self.classes
if isinstance(self.mesh, ExtrudedMeshTopology):
label = "%s_facets" % self.kind
layers = self.mesh.entity_layers(1, label)
base = getattr(self.mesh._base_mesh, label).set
return op2.ExtrudedSet(base, layers=layers)
return op2.Set(size, "%sFacets" % self.kind.capitalize()[:3],
comm=self.mesh.comm)
@utils.cached_property
def _null_subset(self):
'''Empty subset for the case in which there are no facets with
a given marker value. This is required because not all
markers need be represented on all processors.'''
return op2.Subset(self.set, [])
@PETSc.Log.EventDecorator()
def measure_set(self, integral_type, subdomain_id,
all_integer_subdomain_ids=None):
"""Return an iteration set appropriate for the requested integral type.
:arg integral_type: The type of the integral (should be a facet measure).
:arg subdomain_id: The subdomain of the mesh to iterate over.
Either an integer, an iterable of integers or the special
subdomains ``"everywhere"`` or ``"otherwise"``.
:arg all_integer_subdomain_ids: Information to interpret the
``"otherwise"`` subdomain. ``"otherwise"`` means all
entities not explicitly enumerated by the integer
subdomains provided here. For example, if
all_integer_subdomain_ids is empty, then ``"otherwise" ==
"everywhere"``. If it contains ``(1, 2)``, then
``"otherwise"`` is all entities except those marked by
subdomains 1 and 2.
:returns: A :class:`pyop2.Subset` for iteration.
"""
if integral_type in ("exterior_facet_bottom",
"exterior_facet_top",
"interior_facet_horiz"):
# these iterate over the base cell set
return self.mesh.cell_subset(subdomain_id, all_integer_subdomain_ids)
elif not (integral_type.startswith("exterior_")
or integral_type.startswith("interior_")):
raise ValueError("Don't know how to construct measure for '%s'" % integral_type)
if subdomain_id == "everywhere":
return self.set
if subdomain_id == "otherwise":
if all_integer_subdomain_ids is None:
return self.set
key = ("otherwise", ) + all_integer_subdomain_ids
try:
return self._subsets[key]
except KeyError:
unmarked_points = self._collect_unmarked_points(all_integer_subdomain_ids)
_, indices, _ = np.intersect1d(self.facets, unmarked_points, return_indices=True)
return self._subsets.setdefault(key, op2.Subset(self.set, indices))
else:
return self.subset(subdomain_id)
@PETSc.Log.EventDecorator()
def subset(self, markers):
"""Return the subset corresponding to a given marker value.
:param markers: integer marker id or an iterable of marker ids
(or ``None``, for an empty subset).
"""
valid_markers = set([unmarked]).union(self.unique_markers)
markers = as_tuple(markers, numbers.Integral)
try:
return self._subsets[markers]
except KeyError:
# check that the given markers are valid
if len(set(markers).difference(valid_markers)) > 0:
invalid = set(markers).difference(valid_markers)
raise LookupError("{0} are not a valid markers (not in {1})".format(invalid, self.unique_markers))
# build a list of indices corresponding to the subsets selected by
# markers
marked_points_list = []
for i in markers:
if i == unmarked:
_markers = self.mesh.topology_dm.getLabelIdIS(dmcommon.FACE_SETS_LABEL).indices
# Can exclude points labeled with i\in markers here,
# as they will be included in the below anyway.
marked_points_list.append(self._collect_unmarked_points([_i for _i in _markers if _i not in markers]))
else:
if self.mesh.topology_dm.getStratumSize(dmcommon.FACE_SETS_LABEL, i):
marked_points_list.append(self.mesh.topology_dm.getStratumIS(dmcommon.FACE_SETS_LABEL, i).indices)
if marked_points_list:
_, indices, _ = np.intersect1d(self.facets, np.concatenate(marked_points_list), return_indices=True)
return self._subsets.setdefault(markers, op2.Subset(self.set, indices))
else:
return self._subsets.setdefault(markers, self._null_subset)
def _collect_unmarked_points(self, markers):
"""Collect points that are not marked by markers."""
plex = self.mesh.topology_dm
indices_list = []
for i in markers:
if plex.getStratumSize(dmcommon.FACE_SETS_LABEL, i):
indices_list.append(plex.getStratumIS(dmcommon.FACE_SETS_LABEL, i).indices)
if indices_list:
return np.setdiff1d(self.facets, np.concatenate(indices_list))
else:
return self.facets
@utils.cached_property
def facet_cell_map(self):
"""Map from facets to cells."""
return op2.Map(self.set, self.mesh.cell_set, self._rank, self.facet_cell,
"facet_to_cell_map")
@utils.cached_property
def local_facet_orientation_dat(self):
"""Dat for the local facet orientations."""
dtype = gem.uint_type
# Make a map from cell to facet orientations.
fiat_cell = as_fiat_cell(self.mesh.ufl_cell())
topo = fiat_cell.topology
num_entities = [0]
for d in range(len(topo)):
num_entities.append(len(topo[d]))
offsets = np.cumsum(num_entities)
local_facet_start = offsets[-3]
local_facet_end = offsets[-2]
map_from_cell_to_facet_orientations = self.mesh.entity_orientations[:, local_facet_start:local_facet_end]
# Make output data;
# this is a map from an exterior/interior facet to the corresponding local facet orientation/orientations.
# Halo data are required by design, but not actually used.
# -- Reshape as (-1, self._rank) to uniformly handle exterior and interior facets.
data = np.empty_like(self.local_facet_dat.data_ro_with_halos).reshape((-1, self._rank))
data.fill(np.iinfo(dtype).max)
# Set local facet orientations on the block corresponding to the owned facets; i.e., data[:shape[0], :] below.
local_facets = self.local_facet_dat.data_ro # do not need halos.
# -- Reshape as (-1, self._rank) to uniformly handle exterior and interior facets.
local_facets = local_facets.reshape((-1, self._rank))
shape = local_facets.shape
map_from_owned_facet_to_cells = self.facet_cell[:shape[0], :]
data[:shape[0], :] = np.take_along_axis(
map_from_cell_to_facet_orientations[map_from_owned_facet_to_cells],
local_facets.reshape(shape + (1, )), # reshape as required by take_along_axis.
axis=2,
).reshape(shape)
return op2.Dat(
self.local_facet_dat.dataset,
data,
dtype,
f"{self.mesh.name}_{self.kind}_local_facet_orientation"
)
@PETSc.Log.EventDecorator()
def _from_gmsh(filename, comm=None):
"""Read a Gmsh .msh file from `filename`.
:kwarg comm: Optional communicator to build the mesh on (defaults to
COMM_WORLD).
"""
comm = comm or COMM_WORLD
gmsh_plex = PETSc.DMPlex().createFromFile(filename, comm=comm)
return gmsh_plex
@PETSc.Log.EventDecorator()
def _from_exodus(filename, comm):
"""Read an Exodus .e or .exo file from `filename`.
:arg comm: communicator to build the mesh on.
"""
plex = PETSc.DMPlex().createExodusFromFile(filename, comm=comm)
return plex
@PETSc.Log.EventDecorator()
def _from_cgns(filename, comm):
"""Read a CGNS .cgns file from `filename`.
:arg comm: communicator to build the mesh on.
"""
plex = PETSc.DMPlex().createCGNSFromFile(filename, comm=comm)
return plex
@PETSc.Log.EventDecorator()
def _from_triangle(filename, dim, comm):
"""Read a set of triangle mesh files from `filename`.
:arg dim: The embedding dimension.
:arg comm: communicator to build the mesh on.
"""
basename, ext = os.path.splitext(filename)
with temp_internal_comm(comm) as icomm:
if icomm.rank == 0:
try:
facetfile = open(basename+".face")
tdim = 3
except FileNotFoundError:
try:
facetfile = open(basename+".edge")
tdim = 2
except FileNotFoundError:
facetfile = None
tdim = 1
if dim is None:
dim = tdim
icomm.bcast(tdim, root=0)
with open(basename+".node") as nodefile:
header = np.fromfile(nodefile, dtype=np.int32, count=2, sep=' ')
nodecount = header[0]
nodedim = header[1]
assert nodedim == dim
coordinates = np.loadtxt(nodefile, usecols=list(range(1, dim+1)), skiprows=1, dtype=np.double)
assert nodecount == coordinates.shape[0]
with open(basename+".ele") as elefile:
header = np.fromfile(elefile, dtype=np.int32, count=2, sep=' ')
elecount = header[0]
eledim = header[1]
eles = np.loadtxt(elefile, usecols=list(range(1, eledim+1)), dtype=np.int32, skiprows=1)
assert elecount == eles.shape[0]
cells = list(map(lambda c: c-1, eles))
else:
tdim = icomm.bcast(None, root=0)
cells = None
coordinates = None
plex = plex_from_cell_list(tdim, cells, coordinates, icomm)
# Apply boundary IDs
if icomm.rank == 0:
facets = None
try:
header = np.fromfile(facetfile, dtype=np.int32, count=2, sep=' ')
edgecount = header[0]
facets = np.loadtxt(facetfile, usecols=list(range(1, tdim+2)), dtype=np.int32, skiprows=0)
assert edgecount == facets.shape[0]
finally:
facetfile.close()
if facets is not None:
vStart, vEnd = plex.getDepthStratum(0) # vertices
for facet in facets:
bid = facet[-1]
vertices = list(map(lambda v: v + vStart - 1, facet[:-1]))
join = plex.getJoin(vertices)
plex.setLabelValue(dmcommon.FACE_SETS_LABEL, join[0], bid)
return plex
def plex_from_cell_list(dim, cells, coords, comm, name=None):
"""
Create a DMPlex from a list of cells and coords.
(Public interface to `_from_cell_list()`)
:arg dim: The topological dimension of the mesh
:arg cells: The vertices of each cell
:arg coords: The coordinates of each vertex
:arg comm: communicator to build the mesh on. Must be a PyOP2 internal communicator
:kwarg name: name of the plex
"""
with temp_internal_comm(comm) as icomm:
# These types are /correct/, DMPlexCreateFromCellList wants int
# and double (not PetscInt, PetscReal).
if comm.rank == 0:
cells = np.asarray(cells, dtype=np.int32)
coords = np.asarray(coords, dtype=np.double)
comm.bcast(cells.shape, root=0)
comm.bcast(coords.shape, root=0)
# Provide the actual data on rank 0.
plex = PETSc.DMPlex().createFromCellList(dim, cells, coords, comm=icomm)
else:
cell_shape = list(comm.bcast(None, root=0))
coord_shape = list(comm.bcast(None, root=0))
cell_shape[0] = 0
coord_shape[0] = 0
# Provide empty plex on other ranks
# A subsequent call to plex.distribute() takes care of parallel partitioning
plex = PETSc.DMPlex().createFromCellList(dim,
np.zeros(cell_shape, dtype=np.int32),
np.zeros(coord_shape, dtype=np.double),
comm=icomm)
if name is not None:
plex.setName(name)
return plex
@PETSc.Log.EventDecorator()
def _from_cell_list(dim, cells, coords, comm, name=None):
"""
Create a DMPlex from a list of cells and coords.
This function remains for backward compatibility, but will be deprecated after 01/06/2023
:arg dim: The topological dimension of the mesh
:arg cells: The vertices of each cell
:arg coords: The coordinates of each vertex
:arg comm: communicator to build the mesh on. Must be a PyOP2 internal communicator
:kwarg name: name of the plex
"""
import warnings
warnings.warn(
"Private function `_from_cell_list` will be deprecated after 01/06/2023;"
"use public fuction `plex_from_cell_list()` instead.",
DeprecationWarning
)
assert is_pyop2_comm(comm)
# These types are /correct/, DMPlexCreateFromCellList wants int
# and double (not PetscInt, PetscReal).
if comm.rank == 0:
cells = np.asarray(cells, dtype=np.int32)
coords = np.asarray(coords, dtype=np.double)
comm.bcast(cells.shape, root=0)
comm.bcast(coords.shape, root=0)
# Provide the actual data on rank 0.
plex = PETSc.DMPlex().createFromCellList(dim, cells, coords, comm=comm)
else:
cell_shape = list(comm.bcast(None, root=0))
coord_shape = list(comm.bcast(None, root=0))
cell_shape[0] = 0
coord_shape[0] = 0
# Provide empty plex on other ranks
# A subsequent call to plex.distribute() takes care of parallel partitioning
plex = PETSc.DMPlex().createFromCellList(dim,
np.zeros(cell_shape, dtype=np.int32),
np.zeros(coord_shape, dtype=np.double),
comm=comm)
if name is not None:
plex.setName(name)
return plex
[docs]
class AbstractMeshTopology(object, metaclass=abc.ABCMeta):
"""A representation of an abstract mesh topology without a concrete
PETSc DM implementation"""
def __init__(self, topology_dm, name, reorder, sfXB, perm_is, distribution_name, permutation_name, comm):
"""Initialise a mesh topology.
Parameters
----------
topology_dm : PETSc.DMPlex or PETSc.DMSwarm
`PETSc.DMPlex` or `PETSc.DMSwarm` representing the mesh topology.
name : str
Name of the mesh topology.
reorder : bool
Whether to reorder the mesh entities.
sfXB : PETSc.PetscSF
`PETSc.SF` that pushes forward the global point number
slab ``[0, NX)`` to input (naive) plex (only significant when
the mesh topology is loaded from file and only passed from inside
`~.CheckpointFile`).
perm_is : PETSc.IS
`PETSc.IS` that is used as ``_dm_renumbering``; only
makes sense if we know the exact parallel distribution of ``plex``
at the time of mesh topology construction like when we load mesh
along with its distribution. If given, ``reorder`` param will be ignored.
distribution_name : str
Name of the parallel distribution; if `None`, automatically generated.
permutation_name : str
Name of the entity permutation (reordering); if `None`, automatically generated.
comm : mpi4py.MPI.Comm
Communicator.
"""
utils._init()
dmcommon.validate_mesh(topology_dm)
topology_dm.setFromOptions()
self.topology_dm = topology_dm
r"The PETSc DM representation of the mesh topology."
self.sfBC = None
r"The PETSc SF that pushes the input (naive) plex to current (good) plex."
self.sfXB = sfXB
r"The PETSc SF that pushes the global point number slab [0, NX) to input (naive) plex."
# User comm
self.user_comm = comm
# Internal comm
self._comm = internal_comm(self.user_comm, self)
dmcommon.label_facets(self.topology_dm)
self._distribute()
self._grown_halos = False
def callback(self):
"""Finish initialisation."""
del self._callback
if self.comm.size > 1:
self._add_overlap()
if self.sfXB is not None:
self.sfXC = sfXB.compose(self.sfBC) if self.sfBC else self.sfXB
dmcommon.label_facets(self.topology_dm)
dmcommon.complete_facet_labels(self.topology_dm)
# TODO: Allow users to set distribution name if they want to save
# conceptually the same mesh but with different distributions,
# e.g., those generated by different partitioners.
# This currently does not make sense since those mesh instances
# of different distributions in general have different global
# point numbers (so they must be saved under different mesh names
# even though they are conceptually the same).
# The name set here almost uniquely identifies a distribution, but
# there is no gurantee that it really does or it continues to do so
# there are lots of parameters that can change distributions.
# Thus, when using CheckpointFile, it is recommended that the user set
# distribution_name explicitly.
# Mark OP2 entities and derive the resulting Plex renumbering
with PETSc.Log.Event("Mesh: numbering"):
self._mark_entity_classes()
self._entity_classes = dmcommon.get_entity_classes(self.topology_dm).astype(int)
if perm_is:
self._dm_renumbering = perm_is
else:
self._dm_renumbering = self._renumber_entities(reorder)
self._did_reordering = bool(reorder)
# Derive a cell numbering from the Plex renumbering
tdim = dmcommon.get_topological_dimension(self.topology_dm)
entity_dofs = np.zeros(tdim+1, dtype=IntType)
entity_dofs[-1] = 1
self._cell_numbering, _ = self.create_section(entity_dofs)
if tdim == 0:
self._vertex_numbering = self._cell_numbering
else:
entity_dofs[:] = 0
entity_dofs[0] = 1
self._vertex_numbering, _ = self.create_section(entity_dofs)
entity_dofs[:] = 0
entity_dofs[-2] = 1
facet_numbering, _ = self.create_section(entity_dofs)
self._facet_ordering = dmcommon.get_facet_ordering(self.topology_dm, facet_numbering)
self._callback = callback
self.name = name
# Set/Generate names to be used when checkpointing.
self._distribution_name = distribution_name or _generate_default_mesh_topology_distribution_name(self.topology_dm.comm.size, self._distribution_parameters)
self._permutation_name = permutation_name or _generate_default_mesh_topology_permutation_name(reorder)
# A cache of shared function space data on this mesh
self._shared_data_cache = defaultdict(dict)
# Cell subsets for integration over subregions
self._subsets = {}
# A set of weakrefs to meshes that are explicitly labelled as being
# parallel-compatible for interpolation/projection/supermeshing
# To set, do e.g.
# target_mesh._parallel_compatible = {weakref.ref(source_mesh)}
self._parallel_compatible = None
# submesh
self.submesh_parent = None
layers = None
"""No layers on unstructured mesh"""
variable_layers = False
"""No variable layers on unstructured mesh"""
@abc.abstractmethod
def _distribute(self):
"""Distribute the mesh toplogy."""
pass
@abc.abstractmethod
def _add_overlap(self):
"""Add overlap."""
pass
@abc.abstractmethod
def _mark_entity_classes(self):
"""Mark entities with pyop2 classes."""
pass
@abc.abstractmethod
def _renumber_entities(self, reorder):
"""Renumber entities."""
pass
@property
def comm(self):
return self.user_comm
[docs]
def mpi_comm(self):
"""The MPI communicator this mesh is built on (an mpi4py object)."""
return self.comm
[docs]
@PETSc.Log.EventDecorator("CreateMesh")
def init(self):
"""Finish the initialisation of the mesh."""
if hasattr(self, '_callback'):
self._callback(self)
@property
def topology(self):
"""The underlying mesh topology object."""
return self
@property
def topological(self):
"""Alias of topology.
This is to ensure consistent naming for some multigrid codes."""
return self
@property
def _topology_dm(self):
"""Alias of topology_dm"""
from warnings import warn
warn("_topology_dm is deprecated (use topology_dm instead)", DeprecationWarning, stacklevel=2)
return self.topology_dm
[docs]
def ufl_cell(self):
"""The UFL :class:`~ufl.classes.Cell` associated with the mesh.
.. note::
By convention, the UFL cells which specifically
represent a mesh topology have geometric dimension equal their
topological dimension. This is true even for immersed manifold
meshes.
"""
return self._ufl_cell
[docs]
def ufl_mesh(self):
"""The UFL :class:`~ufl.classes.Mesh` associated with the mesh.
.. note::
By convention, the UFL cells which specifically
represent a mesh topology have geometric dimension equal their
topological dimension. This convention will be reflected in this
UFL mesh and is true even for immersed manifold meshes.
"""
return self._ufl_mesh
@property
@abc.abstractmethod
def cell_closure(self):
"""2D array of ordered cell closures
Each row contains ordered cell entities for a cell, one row per cell.
"""
pass
@property
@abc.abstractmethod
def entity_orientations(self):
"""2D array of entity orientations
`entity_orientations` has the same shape as `cell_closure`.
Each row of this array contains orientations of the entities
in the closure of the associated cell. Here, for each cell in the mesh,
orientation of an entity, say e, encodes how the the canonical
representation of the entity defined by Cone(e) compares to
that of the associated entity in the reference FInAT (FIAT) cell. (Note
that `cell_closure` defines how each cell in the mesh is mapped to
the FInAT (FIAT) reference cell and each entity of the FInAT (FIAT)
reference cell has a canonical representation based on the entity ids of
the lower dimensional entities.) Orientations of vertices are always 0.
See ``FIAT.reference_element.Simplex`` and
``FIAT.reference_element.UFCQuadrilateral`` for example computations
of orientations.
"""
pass
@abc.abstractmethod
def _facets(self, kind):
pass
@property
@abc.abstractmethod
def exterior_facets(self):
pass
@property
@abc.abstractmethod
def interior_facets(self):
pass
@property
@abc.abstractmethod
def cell_to_facets(self):
"""Returns a :class:`pyop2.types.dat.Dat` that maps from a cell index to the local
facet types on each cell, including the relevant subdomain markers.
The `i`-th local facet on a cell with index `c` has data
`cell_facet[c][i]`. The local facet is exterior if
`cell_facet[c][i][0] == 0`, and interior if the value is `1`.
The value `cell_facet[c][i][1]` returns the subdomain marker of the
facet.
"""
pass
[docs]
def create_section(self, nodes_per_entity, real_tensorproduct=False, block_size=1, boundary_set=None):
"""Create a PETSc Section describing a function space.
:arg nodes_per_entity: number of function space nodes per topological entity.
:arg real_tensorproduct: If True, assume extruded space is actually Foo x Real.
:arg block_size: The integer by which nodes_per_entity is uniformly multiplied
to get the true data layout.
:arg boundary_set: A set of boundary markers, indicating the subdomains
a boundary condition is specified on.
:returns: a new PETSc Section.
"""
return dmcommon.create_section(self, nodes_per_entity, on_base=real_tensorproduct, block_size=block_size, boundary_set=boundary_set)
[docs]
def node_classes(self, nodes_per_entity, real_tensorproduct=False):
"""Compute node classes given nodes per entity.
:arg nodes_per_entity: number of function space nodes per topological entity.
:returns: the number of nodes in each of core, owned, and ghost classes.
"""
return tuple(np.dot(nodes_per_entity, self._entity_classes))
[docs]
def make_cell_node_list(self, global_numbering, entity_dofs, entity_permutations, offsets):
"""Builds the DoF mapping.
:arg global_numbering: Section describing the global DoF numbering
:arg entity_dofs: FInAT element entity DoFs
:arg entity_permutations: FInAT element entity permutations
:arg offsets: layer offsets for each entity dof (may be None).
"""
return dmcommon.get_cell_nodes(self, global_numbering,
entity_dofs, entity_permutations, offsets)
[docs]
def make_dofs_per_plex_entity(self, entity_dofs):
"""Returns the number of DoFs per plex entity for each stratum,
i.e. [#dofs / plex vertices, #dofs / plex edges, ...].
:arg entity_dofs: FInAT element entity DoFs
"""
return [len(entity_dofs[d][0]) for d in sorted(entity_dofs)]
[docs]
def make_offset(self, entity_dofs, ndofs, real_tensorproduct=False):
"""Returns None (only for extruded use)."""
return None
def _order_data_by_cell_index(self, column_list, cell_data):
return cell_data[column_list]
[docs]
@abc.abstractmethod
def num_cells(self):
pass
[docs]
@abc.abstractmethod
def num_facets(self):
pass
[docs]
@abc.abstractmethod
def num_faces(self):
pass
[docs]
@abc.abstractmethod
def num_edges(self):
pass
[docs]
@abc.abstractmethod
def num_vertices(self):
pass
[docs]
@abc.abstractmethod
def num_entities(self, d):
pass
[docs]
def size(self, d):
return self.num_entities(d)
[docs]
def cell_dimension(self):
"""Returns the cell dimension."""
return self.ufl_cell().topological_dimension()
[docs]
def facet_dimension(self):
"""Returns the facet dimension."""
# Facets have co-dimension 1
return self.ufl_cell().topological_dimension() - 1
@property
@abc.abstractmethod
def cell_set(self):
pass
[docs]
@PETSc.Log.EventDecorator()
def cell_subset(self, subdomain_id, all_integer_subdomain_ids=None):
"""Return a subset over cells with the given subdomain_id.
:arg subdomain_id: The subdomain of the mesh to iterate over.
Either an integer, an iterable of integers or the special
subdomains ``"everywhere"`` or ``"otherwise"``.
:arg all_integer_subdomain_ids: Information to interpret the
``"otherwise"`` subdomain. ``"otherwise"`` means all
entities not explicitly enumerated by the integer
subdomains provided here. For example, if
all_integer_subdomain_ids is empty, then ``"otherwise" ==
"everywhere"``. If it contains ``(1, 2)``, then
``"otherwise"`` is all entities except those marked by
subdomains 1 and 2.
:returns: A :class:`pyop2.types.set.Subset` for iteration.
"""
if subdomain_id == "everywhere":
return self.cell_set
if subdomain_id == "otherwise":
if all_integer_subdomain_ids is None:
return self.cell_set
key = ("otherwise", ) + all_integer_subdomain_ids
else:
key = subdomain_id
try:
return self._subsets[key]
except KeyError:
if subdomain_id == "otherwise":
ids = tuple(dmcommon.get_cell_markers(self.topology_dm,
self._cell_numbering,
sid)
for sid in all_integer_subdomain_ids)
to_remove = np.unique(np.concatenate(ids))
indices = np.arange(self.cell_set.total_size, dtype=IntType)
indices = np.delete(indices, to_remove)
else:
indices = dmcommon.get_cell_markers(self.topology_dm,
self._cell_numbering,
subdomain_id)
return self._subsets.setdefault(key, op2.Subset(self.cell_set, indices))
[docs]
@PETSc.Log.EventDecorator()
def measure_set(self, integral_type, subdomain_id,
all_integer_subdomain_ids=None):
"""Return an iteration set appropriate for the requested integral type.
:arg integral_type: The type of the integral (should be a valid UFL measure).
:arg subdomain_id: The subdomain of the mesh to iterate over.
Either an integer, an iterable of integers or the special
subdomains ``"everywhere"`` or ``"otherwise"``.
:arg all_integer_subdomain_ids: Information to interpret the
``"otherwise"`` subdomain. ``"otherwise"`` means all
entities not explicitly enumerated by the integer
subdomains provided here. For example, if
all_integer_subdomain_ids is empty, then ``"otherwise" ==
"everywhere"``. If it contains ``(1, 2)``, then
``"otherwise"`` is all entities except those marked by
subdomains 1 and 2. This should be a dict mapping
``integral_type`` to the explicitly enumerated subdomain ids.
:returns: A :class:`pyop2.types.set.Subset` for iteration.
"""
if all_integer_subdomain_ids is not None:
all_integer_subdomain_ids = all_integer_subdomain_ids.get(integral_type, None)
if integral_type == "cell":
return self.cell_subset(subdomain_id, all_integer_subdomain_ids)
elif integral_type in ("exterior_facet", "exterior_facet_vert",
"exterior_facet_top", "exterior_facet_bottom"):
return self.exterior_facets.measure_set(integral_type, subdomain_id,
all_integer_subdomain_ids)
elif integral_type in ("interior_facet", "interior_facet_vert",
"interior_facet_horiz"):
return self.interior_facets.measure_set(integral_type, subdomain_id,
all_integer_subdomain_ids)
else:
raise ValueError("Unknown integral type '%s'" % integral_type)
[docs]
@abc.abstractmethod
def mark_entities(self, tf, label_value, label_name=None):
"""Mark selected entities.
:arg tf: The :class:`.CoordinatelessFunction` object that marks
selected entities as 1. f.function_space().ufl_element()
must be "DP" or "DQ" (degree 0) to mark cell entities and
"P" (degree 1) in 1D or "HDiv Trace" (degree 0) in 2D or 3D
to mark facet entities.
Can use "Q" (degree 2) functions for 3D hex meshes until
we support "HDiv Trace" elements on hex.
:arg lable_value: The value used in the label.
:arg label_name: The name of the label to store entity selections.
All entities must live on the same topological dimension. Currently,
one can only mark cell or facet entities.
"""
pass
@utils.cached_property
def extruded_periodic(self):
return self.cell_set._extruded_periodic
# submesh
@utils.cached_property
def submesh_ancesters(self):
"""Tuple of submesh ancesters."""
if self.submesh_parent:
return (self, ) + self.submesh_parent.submesh_ancesters
else:
return (self, )
[docs]
def submesh_youngest_common_ancester(self, other):
"""Return the youngest common ancester of self and other.
Parameters
----------
other : AbstractMeshTopology
The other mesh.
Returns
-------
AbstractMeshTopology or None
Youngest common ancester or None if not found.
"""
# self --- ... --- m --- common --- common --- common
# /
# other --- ... --- m
self_ancesters = list(self.submesh_ancesters)
other_ancesters = list(other.submesh_ancesters)
c = None
while self_ancesters and other_ancesters:
a = self_ancesters.pop()
b = other_ancesters.pop()
if a is b:
c = a
else:
break
return c
[docs]
def submesh_map_child_parent(self, source_integral_type, source_subset_points, reverse=False):
"""Return the map from submesh child entities to submesh parent entities or its reverse.
Parameters
----------
source_integral_type : str
Integral type on the source mesh.
source_subset_points : numpy.ndarray
Subset points on the source mesh.
reverse : bool
If True, return the map from parent entities to child entities.
Returns
-------
tuple
(map from source to target, integral type on the target mesh, subset points on the target mesh).
"""
raise NotImplementedError(f"Not implemented for {type(self)}")
[docs]
def submesh_map_composed(self, other, other_integral_type, other_subset_points):
"""Create entity-entity map from ``other`` to `self`.
Parameters
----------
other : AbstractMeshTopology
Base mesh topology.
other_integral_type : str
Integral type on ``other``.
other_subset_points : numpy.ndarray
Subset points on ``other``; only used to identify (facet) integral_type on ``self``.
Returns
-------
tuple
Tuple of `op2.ComposedMap` from other to self, integral_type on self, and points on self.
"""
common = self.submesh_youngest_common_ancester(other)
if common is None:
raise ValueError(f"Unable to create composed map between (sub)meshes: {self} and {other} are unrelated")
maps = []
integral_type = other_integral_type
subset_points = other_subset_points
aa = other.submesh_ancesters
for a in aa[:aa.index(common)]:
m, integral_type, subset_points = a.submesh_map_child_parent(integral_type, subset_points)
maps.append(m)
bb = self.submesh_ancesters
for b in reversed(bb[:bb.index(common)]):
m, integral_type, subset_points = b.submesh_map_child_parent(integral_type, subset_points, reverse=True)
maps.append(m)
return op2.ComposedMap(*reversed(maps)), integral_type, subset_points
# trans mesh
[docs]
def trans_mesh_entity_map(self, base_mesh, base_integral_type, base_subdomain_id, base_all_integer_subdomain_ids):
"""Create entity-entity (composed) map from base_mesh to `self`.
Parameters
----------
base_mesh : AbstractMeshTopology
Base mesh topology.
base_integral_type : str
Integral type on ``base_mesh``.
base_subdomain_id : int
Subdomain ID on ``base_mesh``.
base_all_integer_subdomain_ids : tuple
``all_integer_subdomain_ids`` corresponding to ``base_mesh`` and ``base_integral_type``.
Returns
-------
tuple
`tuple` of `op2.ComposedMap` from base_mesh to `self` and integral_type on `self`.
"""
raise NotImplementedError(f"Not implemented for {type(self)}")
[docs]
class MeshTopology(AbstractMeshTopology):
"""A representation of mesh topology implemented on a PETSc DMPlex."""
@PETSc.Log.EventDecorator("CreateMesh")
def __init__(self, plex, name, reorder, distribution_parameters, sfXB=None, perm_is=None, distribution_name=None, permutation_name=None, comm=COMM_WORLD):
"""Initialise a mesh topology.
Parameters
----------
plex : PETSc.DMPlex
`PETSc.DMPlex` representing the mesh topology.
name : str
Name of the mesh topology.
reorder : bool
Whether to reorder the mesh entities.
distribution_parameters : dict
Options controlling mesh distribution; see `Mesh` for details.
sfXB : PETSc.PetscSF
`PETSc.SF` that pushes forward the global point number
slab ``[0, NX)`` to input (naive) plex (only significant when
the mesh topology is loaded from file and only passed from inside
`~.CheckpointFile`).
perm_is : PETSc.IS
`PETSc.IS` that is used as ``_dm_renumbering``; only
makes sense if we know the exact parallel distribution of ``plex``
at the time of mesh topology construction like when we load mesh
along with its distribution. If given, ``reorder`` param will be ignored.
distribution_name : str
Name of the parallel distribution; if `None`, automatically generated.
permutation_name : str
Name of the entity permutation (reordering); if `None`, automatically generated.
comm : mpi4py.MPI.Comm
Communicator.
"""
self._distribution_parameters = {}
distribute = distribution_parameters.get("partition")
if distribute is None:
distribute = True
self._distribution_parameters["partition"] = distribute
partitioner_type = distribution_parameters.get("partitioner_type")
self._set_partitioner(plex, distribute, partitioner_type)
self._distribution_parameters["partitioner_type"] = self._get_partitioner(plex).getType()
self._distribution_parameters["overlap_type"] = distribution_parameters.get("overlap_type",
(DistributedMeshOverlapType.FACET, 1))
# Disable auto distribution and reordering before setFromOptions is called.
plex.distributeSetDefault(False)
plex.reorderSetDefault(PETSc.DMPlex.ReorderDefaultFlag.FALSE)
super().__init__(plex, name, reorder, sfXB, perm_is, distribution_name, permutation_name, comm)
def _distribute(self):
# Distribute/redistribute the dm to all ranks
distribute = self._distribution_parameters["partition"]
if self.comm.size > 1 and distribute:
plex = self.topology_dm
# We distribute with overlap zero, in case we're going to
# refine this mesh in parallel. Later, when we actually use
# it, we grow the halo.
original_name = plex.getName()
sfBC = plex.distribute(overlap=0)
plex.setName(original_name)
self.sfBC = sfBC
# plex carries a new dm after distribute, which
# does not inherit partitioner from the old dm.
# It probably makes sense as chaco does not work
# once distributed.
def _add_overlap(self):
overlap_type, overlap = self._distribution_parameters["overlap_type"]
if overlap < 0:
raise ValueError("Overlap depth must be >= 0")
if overlap_type == DistributedMeshOverlapType.NONE:
if overlap > 0:
raise ValueError("Can't have NONE overlap with overlap > 0")
elif overlap_type == DistributedMeshOverlapType.FACET:
dmcommon.set_adjacency_callback(self.topology_dm)
original_name = self.topology_dm.getName()
sfBC = self.topology_dm.distributeOverlap(overlap)
self.topology_dm.setName(original_name)
self.sfBC = self.sfBC.compose(sfBC) if self.sfBC else sfBC
dmcommon.clear_adjacency_callback(self.topology_dm)
self._grown_halos = True
elif overlap_type == DistributedMeshOverlapType.VERTEX:
# Default is FEM (vertex star) adjacency.
original_name = self.topology_dm.getName()
sfBC = self.topology_dm.distributeOverlap(overlap)
self.topology_dm.setName(original_name)
self.sfBC = self.sfBC.compose(sfBC) if self.sfBC else sfBC
self._grown_halos = True
else:
raise ValueError("Unknown overlap type %r" % overlap_type)
def _mark_entity_classes(self):
dmcommon.mark_entity_classes(self.topology_dm)
@utils.cached_property
def _ufl_cell(self):
plex = self.topology_dm
tdim = plex.getDimension()
# Allow empty local meshes on a process
cStart, cEnd = plex.getHeightStratum(0) # cells
if cStart == cEnd:
nfacets = -1
else:
nfacets = plex.getConeSize(cStart)
# TODO: this needs to be updated for mixed-cell meshes.
nfacets = self._comm.allreduce(nfacets, op=MPI.MAX)
# Note that the geometric dimension of the cell is not set here
# despite it being a property of a UFL cell. It will default to
# equal the topological dimension.
# Firedrake mesh topologies, by convention, which specifically
# represent a mesh topology (as here) have geometric dimension
# equal their topological dimension. This is reflected in the
# corresponding UFL mesh.
return ufl.Cell(_cells[tdim][nfacets])
@utils.cached_property
def _ufl_mesh(self):
cell = self._ufl_cell
return ufl.Mesh(finat.ufl.VectorElement("Lagrange", cell, 1, dim=cell.topological_dimension()))
@property
def _default_reordering(self):
with PETSc.Log.Event("Mesh: reorder"):
old_to_new = self.topology_dm.getOrdering(PETSc.Mat.OrderingType.RCM).indices
reordering = np.empty_like(old_to_new)
reordering[old_to_new] = np.arange(old_to_new.size, dtype=old_to_new.dtype)
return reordering
def _renumber_entities(self, reorder):
if reorder:
reordering = self._default_reordering
else:
# No reordering
reordering = None
return dmcommon.plex_renumbering(self.topology_dm, self._entity_classes, reordering)
@utils.cached_property
def cell_closure(self):
"""2D array of ordered cell closures
Each row contains ordered cell entities for a cell, one row per cell.
"""
plex = self.topology_dm
tdim = plex.getDimension()
# Cell numbering and global vertex numbering
cell_numbering = self._cell_numbering
vertex_numbering = self._vertex_numbering.createGlobalSection(plex.getPointSF())
cell = self.ufl_cell()
assert tdim == cell.topological_dimension()
if self.submesh_parent is not None:
return dmcommon.submesh_create_cell_closure_cell_submesh(plex,
self.submesh_parent.topology_dm,
cell_numbering,
self.submesh_parent._cell_numbering,
self.submesh_parent.cell_closure)
elif cell.is_simplex():
topology = FIAT.ufc_cell(cell).get_topology()
entity_per_cell = np.zeros(len(topology), dtype=IntType)
for d, ents in topology.items():
entity_per_cell[d] = len(ents)
return dmcommon.closure_ordering(plex, vertex_numbering,
cell_numbering, entity_per_cell)
elif cell.cellname() == "quadrilateral":
from firedrake_citations import Citations
Citations().register("Homolya2016")
Citations().register("McRae2016")
# Quadrilateral mesh
cell_ranks = dmcommon.get_cell_remote_ranks(plex)
facet_orientations = dmcommon.quadrilateral_facet_orientations(
plex, vertex_numbering, cell_ranks)
cell_orientations = dmcommon.orientations_facet2cell(
plex, vertex_numbering, cell_ranks,
facet_orientations, cell_numbering)
dmcommon.exchange_cell_orientations(plex,
cell_numbering,
cell_orientations)
return dmcommon.quadrilateral_closure_ordering(
plex, vertex_numbering, cell_numbering, cell_orientations)
elif cell.cellname() == "hexahedron":
# TODO: Should change and use create_cell_closure() for all cell types.
topology = FIAT.ufc_cell(cell).get_topology()
closureSize = sum([len(ents) for _, ents in topology.items()])
return dmcommon.create_cell_closure(plex, cell_numbering, closureSize)
else:
raise NotImplementedError("Cell type '%s' not supported." % cell)
@utils.cached_property
def entity_orientations(self):
return dmcommon.entity_orientations(self, self.cell_closure)
@PETSc.Log.EventDecorator()
def _facets(self, kind):
if kind not in ["interior", "exterior"]:
raise ValueError("Unknown facet type '%s'" % kind)
dm = self.topology_dm
facets, classes = dmcommon.get_facets_by_class(dm, (kind + "_facets"),
self._facet_ordering)
label = dmcommon.FACE_SETS_LABEL
if dm.hasLabel(label):
from mpi4py import MPI
local_markers = set(dm.getLabelIdIS(label).indices)
def merge_ids(x, y, datatype):
return x.union(y)
op = MPI.Op.Create(merge_ids, commute=True)
unique_markers = np.asarray(sorted(self._comm.allreduce(local_markers, op=op)),
dtype=IntType)
op.Free()
else:
unique_markers = None
local_facet_number, facet_cell = \
dmcommon.facet_numbering(dm, kind, facets,
self._cell_numbering,
self.cell_closure)
point2facetnumber = np.full(facets.max(initial=0)+1, -1, dtype=IntType)
point2facetnumber[facets] = np.arange(len(facets), dtype=IntType)
obj = _Facets(self, facets, classes, kind,
facet_cell, local_facet_number,
unique_markers=unique_markers)
obj.point2facetnumber = point2facetnumber
return obj
@utils.cached_property
def exterior_facets(self):
return self._facets("exterior")
@utils.cached_property
def interior_facets(self):
return self._facets("interior")
@utils.cached_property
def cell_to_facets(self):
"""Returns a :class:`pyop2.types.dat.Dat` that maps from a cell index to the local
facet types on each cell, including the relevant subdomain markers.
The `i`-th local facet on a cell with index `c` has data
`cell_facet[c][i]`. The local facet is exterior if
`cell_facet[c][i][0] == 0`, and interior if the value is `1`.
The value `cell_facet[c][i][1]` returns the subdomain marker of the
facet.
"""
cell_facets = dmcommon.cell_facet_labeling(self.topology_dm,
self._cell_numbering,
self.cell_closure)
if isinstance(self.cell_set, op2.ExtrudedSet):
dataset = op2.DataSet(self.cell_set.parent, dim=cell_facets.shape[1:])
else:
dataset = op2.DataSet(self.cell_set, dim=cell_facets.shape[1:])
return op2.Dat(dataset, cell_facets, dtype=cell_facets.dtype,
name="cell-to-local-facet-dat")
[docs]
def num_cells(self):
cStart, cEnd = self.topology_dm.getHeightStratum(0)
return cEnd - cStart
[docs]
def num_facets(self):
fStart, fEnd = self.topology_dm.getHeightStratum(1)
return fEnd - fStart
[docs]
def num_faces(self):
fStart, fEnd = self.topology_dm.getDepthStratum(2)
return fEnd - fStart
[docs]
def num_edges(self):
eStart, eEnd = self.topology_dm.getDepthStratum(1)
return eEnd - eStart
[docs]
def num_vertices(self):
vStart, vEnd = self.topology_dm.getDepthStratum(0)
return vEnd - vStart
[docs]
def num_entities(self, d):
eStart, eEnd = self.topology_dm.getDepthStratum(d)
return eEnd - eStart
@utils.cached_property
def cell_set(self):
size = list(self._entity_classes[self.cell_dimension(), :])
return op2.Set(size, "Cells", comm=self._comm)
@PETSc.Log.EventDecorator()
def _set_partitioner(self, plex, distribute, partitioner_type=None):
"""Set partitioner for (re)distributing underlying plex over comm.
:arg distribute: Boolean or (sizes, points)-tuple. If (sizes, point)-
tuple is given, it is used to set shell partition. If Boolean, no-op.
:kwarg partitioner_type: Partitioner to be used: "chaco", "ptscotch", "parmetis",
"shell", or `None` (unspecified). Ignored if the distribute parameter
specifies the distribution.
"""
if plex.comm.size == 1 or distribute is False:
return
partitioner = plex.getPartitioner()
if distribute is True:
if partitioner_type:
if partitioner_type not in ["chaco", "ptscotch", "parmetis", "simple", "shell"]:
raise ValueError(
f"Unexpected partitioner_type: {partitioner_type}")
if partitioner_type in ["chaco", "ptscotch", "parmetis"] and \
partitioner_type not in get_external_packages():
raise ValueError(
f"Unable to use {partitioner_type} as PETSc is not "
f"installed with {partitioner_type}."
)
if partitioner_type == "chaco" and plex.isDistributed():
raise ValueError(
"Unable to use 'chaco' mesh partitioner, 'chaco' is a "
"serial partitioner, but the mesh is distributed."
)
else:
partitioner_type = DEFAULT_PARTITIONER
partitioner.setType({
"chaco": partitioner.Type.CHACO,
"ptscotch": partitioner.Type.PTSCOTCH,
"parmetis": partitioner.Type.PARMETIS,
"shell": partitioner.Type.SHELL,
"simple": partitioner.Type.SIMPLE
}[partitioner_type])
else:
sizes, points = distribute
partitioner.setType(partitioner.Type.SHELL)
partitioner.setShellPartition(plex.comm.size, sizes, points)
# Command line option `-petscpartitioner_type <type>` overrides.
# partitioner.setFromOptions() is called from inside plex.setFromOptions().
@PETSc.Log.EventDecorator()
def _get_partitioner(self, plex):
"""Get partitioner actually used for (re)distributing underlying plex over comm."""
return plex.getPartitioner()
[docs]
def mark_entities(self, tf, label_value, label_name=None):
import firedrake.function as function
if not isinstance(label_value, numbers.Integral):
raise TypeError(f"label_value must be an integer: got {label_value}")
if label_name and not isinstance(label_name, str):
raise TypeError(f"label_name must be `None` or a string: got {label_name}")
if label_name in ("depth",
"celltype",
"ghost",
"exterior_facets",
"interior_facets",
"pyop2_core",
"pyop2_owned",
"pyop2_ghost"):
raise ValueError(f"Label name {label_name} is reserved")
if not isinstance(tf, function.CoordinatelessFunction):
raise TypeError(f"tf must be an instance of CoordinatelessFunction: {type(tf)} is not CoordinatelessFunction")
tV = tf.function_space()
elem = tV.ufl_element()
if tV.mesh() is not self:
raise RuntimeError(f"tf must be defined on {self}: {tf.mesh()} is not {self}")
if elem.reference_value_shape != ():
raise RuntimeError(f"tf must be scalar: {elem.reference_value_shape} != ()")
if elem.family() in {"Discontinuous Lagrange", "DQ"} and elem.degree() == 0:
# cells
height = 0
label_name = label_name or dmcommon.CELL_SETS_LABEL
elif (elem.family() == "HDiv Trace" and elem.degree() == 0 and self.cell_dimension() > 1) or \
(elem.family() == "Lagrange" and elem.degree() == 1 and self.cell_dimension() == 1) or \
(elem.family() == "Q" and elem.degree() == 2 and self.ufl_cell().cellname() == "hexahedron"):
# facets
height = 1
label_name = label_name or dmcommon.FACE_SETS_LABEL
else:
raise ValueError(f"indicator functions must be 'DP' or 'DQ' (degree 0) to mark cells and 'P' (degree 1) in 1D or 'HDiv Trace' (degree 0) in 2D or 3D to mark facets: got (family, degree) = ({elem.family()}, {elem.degree()})")
plex = self.topology_dm
if not plex.hasLabel(label_name):
plex.createLabel(label_name)
plex.clearLabelStratum(label_name, label_value)
label = plex.getLabel(label_name)
section = tV.dm.getSection()
array = tf.dat.data_ro_with_halos.real.astype(IntType)
dmcommon.mark_points_with_function_array(plex, section, height, array, label, label_value)
# submesh
def _submesh_make_entity_entity_map(self, from_set, to_set, from_points, to_points, child_parent_map):
assert from_set.total_size == len(from_points)
assert to_set.total_size == len(to_points)
with self.topology_dm.getSubpointIS() as subpoints:
if child_parent_map:
_, from_indices, to_indices = np.intersect1d(subpoints[from_points], to_points, return_indices=True)
else:
_, from_indices, to_indices = np.intersect1d(from_points, subpoints[to_points], return_indices=True)
values = np.full(from_set.total_size, -1, dtype=IntType)
values[from_indices] = to_indices
return op2.Map(from_set, to_set, 1, values.reshape((-1, 1)), f"{self}_submesh_map_{from_set}_{to_set}")
@utils.cached_property
def submesh_child_cell_parent_cell_map(self):
return self._submesh_make_entity_entity_map(self.cell_set, self.submesh_parent.cell_set, self.cell_closure[:, -1], self.submesh_parent.cell_closure[:, -1], True)
@utils.cached_property
def submesh_child_exterior_facet_parent_exterior_facet_map(self):
return self._submesh_make_entity_entity_map(self.exterior_facets.set, self.submesh_parent.exterior_facets.set, self.exterior_facets.facets, self.submesh_parent.exterior_facets.facets, True)
@utils.cached_property
def submesh_child_exterior_facet_parent_interior_facet_map(self):
return self._submesh_make_entity_entity_map(self.exterior_facets.set, self.submesh_parent.interior_facets.set, self.exterior_facets.facets, self.submesh_parent.interior_facets.facets, True)
@utils.cached_property
def submesh_child_interior_facet_parent_exterior_facet_map(self):
raise RuntimeError("Should never happen")
@utils.cached_property
def submesh_child_interior_facet_parent_interior_facet_map(self):
return self._submesh_make_entity_entity_map(self.interior_facets.set, self.submesh_parent.interior_facets.set, self.interior_facets.facets, self.submesh_parent.interior_facets.facets, True)
@utils.cached_property
def submesh_parent_cell_child_cell_map(self):
return self._submesh_make_entity_entity_map(self.submesh_parent.cell_set, self.cell_set, self.submesh_parent.cell_closure[:, -1], self.cell_closure[:, -1], False)
@utils.cached_property
def submesh_parent_exterior_facet_child_exterior_facet_map(self):
return self._submesh_make_entity_entity_map(self.submesh_parent.exterior_facets.set, self.exterior_facets.set, self.submesh_parent.exterior_facets.facets, self.exterior_facets.facets, False)
@utils.cached_property
def submesh_parent_exterior_facet_child_interior_facet_map(self):
raise RuntimeError("Should never happen")
@utils.cached_property
def submesh_parent_interior_facet_child_exterior_facet_map(self):
return self._submesh_make_entity_entity_map(self.submesh_parent.interior_facets.set, self.exterior_facets.set, self.submesh_parent.interior_facets.facets, self.exterior_facets.facets, False)
@utils.cached_property
def submesh_parent_interior_facet_child_interior_facet_map(self):
return self._submesh_make_entity_entity_map(self.submesh_parent.interior_facets.set, self.interior_facets.set, self.submesh_parent.interior_facets.facets, self.interior_facets.facets, False)
[docs]
def submesh_map_child_parent(self, source_integral_type, source_subset_points, reverse=False):
"""Return the map from submesh child entities to submesh parent entities or its reverse.
Parameters
----------
source_integral_type : str
Integral type on the source mesh.
source_subset_points : numpy.ndarray
Subset points on the source mesh.
reverse : bool
If True, return the map from parent entities to child entities.
Returns
-------
tuple
(map from source to target, integral type on the target mesh, subset points on the target mesh).
"""
if self.submesh_parent is None:
raise RuntimeError("Must only be called on submesh")
if reverse:
source = self.submesh_parent
target = self
else:
source = self
target = self.submesh_parent
target_dim = target.topology_dm.getDimension()
source_dim = source.topology_dm.getDimension()
if source_dim != target_dim:
raise NotImplementedError(f"Not implemented for (source_dim, target_dim) == ({source_dim}, {target_dim})")
if source_integral_type == "cell":
target_integral_type = "cell"
target_subset_points = None
elif source_integral_type in ["interior_facet", "exterior_facet"]:
with self.topology_dm.getSubpointIS() as subpoints:
if reverse:
_, target_indices_int, source_indices_int = np.intersect1d(subpoints[target.interior_facets.facets], source_subset_points, return_indices=True)
_, target_indices_ext, source_indices_ext = np.intersect1d(subpoints[target.exterior_facets.facets], source_subset_points, return_indices=True)
else:
target_subset_points = subpoints[source_subset_points]
_, target_indices_int, source_indices_int = np.intersect1d(target.interior_facets.facets, target_subset_points, return_indices=True)
_, target_indices_ext, source_indices_ext = np.intersect1d(target.exterior_facets.facets, target_subset_points, return_indices=True)
n_int = len(source_indices_int)
n_ext = len(source_indices_ext)
n_int_max = self._comm.allreduce(n_int, op=MPI.MAX)
n_ext_max = self._comm.allreduce(n_ext, op=MPI.MAX)
if n_int_max > 0:
if n_ext_max != 0:
raise RuntimeError(f"integral_type on the target mesh is interior facet, but {n_ext_max} exterior facet entities are also included")
if n_int > len(source_subset_points):
raise RuntimeError("Found inconsistent data")
target_integral_type = "interior_facet"
elif n_ext_max > 0:
if n_int_max != 0:
raise RuntimeError(f"integral_type on the target mesh is exterior facet, but {n_int_max} interior facet entities are also included")
if n_ext > len(source_subset_points):
raise RuntimeError("Found inconsistent data")
target_integral_type = "exterior_facet"
else:
raise RuntimeError("Can not find a map from source to target.")
if reverse:
if target_integral_type == "interior_facet":
target_subset_points = target.interior_facets.facets[target_indices_int]
elif target_integral_type == "exterior_facet":
target_subset_points = target.exterior_facets.facets[target_indices_ext]
else:
raise NotImplementedError(f"Not implemented for (source_dim, target_dim, source_integral_type) == ({source_dim}, {target_dim}, {source_integral_type})")
if reverse:
map_ = getattr(self, f"submesh_parent_{source_integral_type}_child_{target_integral_type}_map")
else:
map_ = getattr(self, f"submesh_child_{source_integral_type}_parent_{target_integral_type}_map")
return map_, target_integral_type, target_subset_points
# trans mesh
[docs]
def trans_mesh_entity_map(self, base_mesh, base_integral_type, base_subdomain_id, base_all_integer_subdomain_ids):
"""Create entity-entity (composed) map from base_mesh to `self`.
Parameters
----------
base_mesh : AbstractMeshTopology
Base mesh topology.
base_integral_type : str
Integral type on ``base_mesh``.
base_subdomain_id : int
Subdomain ID on ``base_mesh``.
base_all_integer_subdomain_ids : tuple
``all_integer_subdomain_ids`` corresponding to ``base_mesh`` and ``base_integral_type``.
Returns
-------
tuple
`tuple` of `op2.ComposedMap` from base_mesh to `self` and integral_type on `self`.
"""
common = self.submesh_youngest_common_ancester(base_mesh)
if common is None:
raise NotImplementedError(f"Currently only implemented for (sub)meshes in the same family: got {self} and {base_mesh}")
elif base_mesh is self:
raise NotImplementedError("Currenlty can not return identity map")
else:
if base_integral_type == "cell":
base_subset_points = None
elif base_integral_type in ["interior_facet", "exterior_facet"]:
base_subset = base_mesh.measure_set(base_integral_type, base_subdomain_id, all_integer_subdomain_ids=base_all_integer_subdomain_ids)
if base_integral_type == "interior_facet":
base_subset_points = base_mesh.interior_facets.facets[base_subset.indices]
elif base_integral_type == "exterior_facet":
base_subset_points = base_mesh.exterior_facets.facets[base_subset.indices]
else:
raise NotImplementedError(f"Unknown integration type : {base_integral_type}")
composed_map, integral_type, _ = self.submesh_map_composed(base_mesh, base_integral_type, base_subset_points)
return composed_map, integral_type
[docs]
class ExtrudedMeshTopology(MeshTopology):
"""Representation of an extruded mesh topology."""
@PETSc.Log.EventDecorator()
def __init__(self, mesh, layers, periodic=False, name=None):
"""Build an extruded mesh topology from an input mesh topology
:arg mesh: the unstructured base mesh topology
:arg layers: number of occurence of base layer in the "vertical" direction.
:arg periodic: the flag for periodic extrusion; if True, only constant layer extrusion is allowed.
:arg name: optional name of the extruded mesh topology.
"""
# TODO: refactor to call super().__init__
from firedrake_citations import Citations
Citations().register("McRae2016")
Citations().register("Bercea2016")
# A cache of shared function space data on this mesh
self._shared_data_cache = defaultdict(dict)
if isinstance(mesh.topology, VertexOnlyMeshTopology):
raise NotImplementedError("Extrusion not implemented for VertexOnlyMeshTopology")
if layers.shape and periodic:
raise ValueError("Must provide constant layer for periodic extrusion")
mesh.init()
self._base_mesh = mesh
self.user_comm = mesh.comm
self._comm = internal_comm(mesh._comm, self)
if name is not None and name == mesh.name:
raise ValueError("Extruded mesh topology and base mesh topology can not have the same name")
self.name = name if name is not None else mesh.name + "_extruded"
# TODO: These attributes are copied so that FunctionSpaceBase can
# access them directly. Eventually we would want a better refactoring
# of responsibilities between mesh and function space.
self.topology_dm = mesh.topology_dm
r"The PETSc DM representation of the mesh topology."
self._dm_renumbering = mesh._dm_renumbering
self._cell_numbering = mesh._cell_numbering
self._entity_classes = mesh._entity_classes
self._did_reordering = mesh._did_reordering
self._distribution_parameters = mesh._distribution_parameters
self._subsets = {}
if layers.shape:
self.variable_layers = True
extents = extnum.layer_extents(self.topology_dm,
self._cell_numbering,
layers)
if np.any(extents[:, 3] - extents[:, 2] <= 0):
raise NotImplementedError("Vertically disconnected cells unsupported")
self.layer_extents = extents
"""The layer extents for all mesh points.
For variable layers, the layer extent does not match those for cells.
A numpy array of layer extents (in PyOP2 format
:math:`[start, stop)`), of shape ``(num_mesh_points, 4)`` where
the first two extents are used for allocation and the last
two for iteration.
"""
else:
self.variable_layers = False
self.cell_set = op2.ExtrudedSet(mesh.cell_set, layers=layers, extruded_periodic=periodic)
# submesh
self.submesh_parent = None
@utils.cached_property
def _ufl_cell(self):
return ufl.TensorProductCell(self._base_mesh.ufl_cell(), ufl.interval)
@utils.cached_property
def _ufl_mesh(self):
cell = self._ufl_cell
return ufl.Mesh(finat.ufl.VectorElement("Lagrange", cell, 1, dim=cell.topological_dimension()))
@utils.cached_property
def cell_closure(self):
"""2D array of ordered cell closures
Each row contains ordered cell entities for a cell, one row per cell.
"""
return self._base_mesh.cell_closure
@utils.cached_property
def entity_orientations(self):
return self._base_mesh.entity_orientations
def _facets(self, kind):
if kind not in ["interior", "exterior"]:
raise ValueError("Unknown facet type '%s'" % kind)
base = getattr(self._base_mesh, "%s_facets" % kind)
return _Facets(self, base.facets, base.classes,
kind,
base.facet_cell,
base.local_facet_dat.data_ro_with_halos,
unique_markers=base.unique_markers)
[docs]
def make_cell_node_list(self, global_numbering, entity_dofs, entity_permutations, offsets):
"""Builds the DoF mapping.
:arg global_numbering: Section describing the global DoF numbering
:arg entity_dofs: FInAT element entity DoFs
:arg entity_permutations: FInAT element entity permutations
:arg offsets: layer offsets for each entity dof.
"""
if entity_permutations is None:
# FInAT entity_permutations not yet implemented
entity_dofs = eutils.flat_entity_dofs(entity_dofs)
return super().make_cell_node_list(global_numbering, entity_dofs, None, offsets)
assert sorted(entity_dofs.keys()) == sorted(entity_permutations.keys()), "Mismatching dimension tuples"
for key in entity_dofs.keys():
assert sorted(entity_dofs[key].keys()) == sorted(entity_permutations[key].keys()), "Mismatching entity tuples"
assert all(v in {0, 1} for _, v in entity_permutations), "Vertical dim index must be in [0, 1]"
entity_dofs = eutils.flat_entity_dofs(entity_dofs)
entity_permutations = eutils.flat_entity_permutations(entity_permutations)
return super().make_cell_node_list(global_numbering, entity_dofs, entity_permutations, offsets)
[docs]
def make_dofs_per_plex_entity(self, entity_dofs):
"""Returns the number of DoFs per plex entity for each stratum,
i.e. [#dofs / plex vertices, #dofs / plex edges, ...].
each entry is a 2-tuple giving the number of dofs on, and
above the given plex entity.
:arg entity_dofs: FInAT element entity DoFs
"""
dofs_per_entity = np.zeros((1 + self._base_mesh.cell_dimension(), 2), dtype=IntType)
for (b, v), entities in entity_dofs.items():
dofs_per_entity[b, v] += len(entities[0])
# Convert to a tuple of tuples with int (not numpy.intXX) values. This is
# to give us a string representation like ((0, 1), (2, 3)) instead of
# ((numpy.int32(0), numpy.int32(1)), (numpy.int32(2), numpy.int32(3))).
return tuple(
tuple(int(d_) for d_ in d)
for d in dofs_per_entity
)
[docs]
@PETSc.Log.EventDecorator()
def node_classes(self, nodes_per_entity, real_tensorproduct=False):
"""Compute node classes given nodes per entity.
:arg nodes_per_entity: number of function space nodes per topological entity.
:returns: the number of nodes in each of core, owned, and ghost classes.
"""
if real_tensorproduct:
nodes = np.asarray(nodes_per_entity)
nodes_per_entity = sum(nodes[:, i] for i in range(2))
return super(ExtrudedMeshTopology, self).node_classes(nodes_per_entity)
elif self.variable_layers:
return extnum.node_classes(self, nodes_per_entity)
else:
nodes = np.asarray(nodes_per_entity)
if self.extruded_periodic:
nodes_per_entity = sum(nodes[:, i]*(self.layers - 1) for i in range(2))
else:
nodes_per_entity = sum(nodes[:, i]*(self.layers - i) for i in range(2))
return super(ExtrudedMeshTopology, self).node_classes(nodes_per_entity)
@utils.cached_property
def layers(self):
"""Return the layers parameter used to construct the mesh topology,
which is the number of layers represented by the number of occurences
of the base mesh for non-variable layer mesh and an array of size
(num_cells, 2), each row representing the
(first layer index, last layer index + 1) pair for the associated cell,
for variable layer mesh."""
if self.variable_layers:
return self.cell_set.layers_array
else:
return self.cell_set.layers
[docs]
def entity_layers(self, height, label=None):
"""Return the number of layers on each entity of a given plex
height.
:arg height: The height of the entity to compute the number of
layers (0 -> cells, 1 -> facets, etc...)
:arg label: An optional label name used to select points of
the given height (if None, then all points are used).
:returns: a numpy array of the number of layers on the asked
for entities (or a single layer number for the constant
layer case).
"""
if self.variable_layers:
return extnum.entity_layers(self, height, label)
else:
return self.cell_set.layers
[docs]
def cell_dimension(self):
"""Returns the cell dimension."""
return (self._base_mesh.cell_dimension(), 1)
[docs]
def facet_dimension(self):
"""Returns the facet dimension.
.. note::
This only returns the dimension of the "side" (vertical) facets,
not the "top" or "bottom" (horizontal) facets.
"""
return (self._base_mesh.facet_dimension(), 1)
def _order_data_by_cell_index(self, column_list, cell_data):
cell_list = []
for col in column_list:
cell_list += list(range(col, col + (self.layers - 1)))
return cell_data[cell_list]
@property
def _distribution_name(self):
return self._base_mesh._distribution_name
@property
def _permutation_name(self):
return self._base_mesh._permutation_name
[docs]
def mark_entities(self, tf, label_value, label_name=None):
raise NotImplementedError("Currently not implemented for ExtrudedMesh")
# TODO: Could this be merged with MeshTopology given that dmcommon.pyx
# now covers DMSwarms and DMPlexes?
[docs]
class VertexOnlyMeshTopology(AbstractMeshTopology):
"""
Representation of a vertex-only mesh topology immersed within
another mesh.
"""
@PETSc.Log.EventDecorator()
def __init__(self, swarm, parentmesh, name, reorder, input_ordering_swarm=None, perm_is=None, distribution_name=None, permutation_name=None):
"""Initialise a mesh topology.
Parameters
----------
swarm : PETSc.DMSwarm
`PETSc.DMSwarm` representing Particle In Cell (PIC) vertices
immersed within a `PETSc.DM` stored in the ``parentmesh``.
parentmesh : AbstractMeshTopology
Mesh topology within which the vertex-only mesh topology is immersed.
name : str
Name of the mesh topology.
reorder : bool
Whether to reorder the mesh entities.
input_ordering_swarm : PETSc.DMSwarm
The swarm from which the input-ordering vertex-only mesh is constructed.
perm_is : PETSc.IS
`PETSc.IS` that is used as ``_dm_renumbering``; only
makes sense if we know the exact parallel distribution of ``plex``
at the time of mesh topology construction like when we load mesh
along with its distribution. If given, ``reorder`` param will be ignored.
distribution_name : str
Name of the parallel distribution; if `None`, automatically generated.
permutation_name : str
Name of the entity permutation (reordering); if `None`, automatically generated.
"""
if MPI.Comm.Compare(parentmesh.comm, swarm.comm.tompi4py()) not in {MPI.CONGRUENT, MPI.IDENT}:
ValueError("Parent mesh communicator and swarm communicator are not congruent")
self._distribution_parameters = {"partition": False,
"partitioner_type": None,
"overlap_type": (DistributedMeshOverlapType.NONE, 0)}
self.input_ordering_swarm = input_ordering_swarm
super().__init__(swarm, name, reorder, None, perm_is, distribution_name, permutation_name, parentmesh.comm)
self._parent_mesh = parentmesh
def _distribute(self):
pass
def _add_overlap(self):
pass
def _mark_entity_classes(self):
if self.input_ordering_swarm:
assert isinstance(self._parent_mesh, MeshTopology)
dmcommon.mark_entity_classes_using_cell_dm(self.topology_dm)
else:
# Have an input-ordering vertex-only mesh. These should mark
# all entities as pyop2 core, which mark_entity_classes will do.
assert isinstance(self._parent_mesh, VertexOnlyMeshTopology)
dmcommon.mark_entity_classes(self.topology_dm)
@utils.cached_property
def _ufl_cell(self):
return ufl.Cell(_cells[0][0])
@utils.cached_property
def _ufl_mesh(self):
cell = self._ufl_cell
return ufl.Mesh(finat.ufl.VectorElement("DG", cell, 0, dim=cell.topological_dimension()))
def _renumber_entities(self, reorder):
if reorder:
swarm = self.topology_dm
parent = self._parent_mesh.topology_dm
swarm_parent_cell_nums = swarm.getField("DMSwarm_cellid").ravel()
parent_renum = self._parent_mesh._dm_renumbering.getIndices()
pStart, _ = parent.getChart()
parent_renum_inv = np.empty_like(parent_renum)
parent_renum_inv[parent_renum - pStart] = np.arange(len(parent_renum))
# Use kind = 'stable' to make the ordering deterministic.
perm = np.argsort(parent_renum_inv[swarm_parent_cell_nums - pStart], kind='stable').astype(IntType)
swarm.restoreField("DMSwarm_cellid")
perm_is = PETSc.IS().create(comm=swarm.comm)
perm_is.setType("general")
perm_is.setIndices(perm)
return perm_is
else:
return dmcommon.plex_renumbering(self.topology_dm, self._entity_classes, None)
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_closure(self):
"""2D array of ordered cell closures
Each row contains ordered cell entities for a cell, one row per cell.
"""
swarm = self.topology_dm
tdim = 0
# Cell numbering and global vertex numbering
cell_numbering = self._cell_numbering
vertex_numbering = self._vertex_numbering.createGlobalSection(swarm.getPointSF())
cell = self.ufl_cell()
assert tdim == cell.topological_dimension()
assert cell.is_simplex()
import FIAT
topology = FIAT.ufc_cell(cell).get_topology()
entity_per_cell = np.zeros(len(topology), dtype=IntType)
for d, ents in topology.items():
entity_per_cell[d] = len(ents)
return dmcommon.closure_ordering(swarm, vertex_numbering,
cell_numbering, entity_per_cell)
entity_orientations = None
def _facets(self, kind):
"""Raises an AttributeError since cells in a
`VertexOnlyMeshTopology` have no facets.
"""
if kind not in ["interior", "exterior"]:
raise ValueError("Unknown facet type '%s'" % kind)
raise AttributeError("Cells in a VertexOnlyMeshTopology have no facets.")
@utils.cached_property # TODO: Recalculate if mesh moves
def exterior_facets(self):
return self._facets("exterior")
@utils.cached_property # TODO: Recalculate if mesh moves
def interior_facets(self):
return self._facets("interior")
@utils.cached_property
def cell_to_facets(self):
"""Raises an AttributeError since cells in a
`VertexOnlyMeshTopology` have no facets.
"""
raise AttributeError("Cells in a VertexOnlyMeshTopology have no facets.")
[docs]
def num_cells(self):
return self.num_vertices()
[docs]
def num_facets(self):
return 0
[docs]
def num_faces(self):
return 0
[docs]
def num_edges(self):
return 0
[docs]
def num_vertices(self):
return self.topology_dm.getLocalSize()
[docs]
def num_entities(self, d):
if d > 0:
return 0
else:
return self.num_vertices()
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_set(self):
size = list(self._entity_classes[self.cell_dimension(), :])
return op2.Set(size, "Cells", comm=self.comm)
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_cell_list(self):
"""Return a list of parent mesh cells numbers in vertex only
mesh cell order.
"""
cell_parent_cell_list = np.copy(self.topology_dm.getField("parentcellnum").ravel())
self.topology_dm.restoreField("parentcellnum")
return cell_parent_cell_list[self.cell_closure[:, -1]]
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_cell_map(self):
"""Return the :class:`pyop2.types.map.Map` from vertex only mesh cells to
parent mesh cells.
"""
return op2.Map(self.cell_set, self._parent_mesh.cell_set, 1,
self.cell_parent_cell_list, "cell_parent_cell")
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_base_cell_list(self):
"""Return a list of parent mesh base cells numbers in vertex only
mesh cell order.
"""
if not isinstance(self._parent_mesh, ExtrudedMeshTopology):
raise AttributeError("Parent mesh is not extruded")
cell_parent_base_cell_list = np.copy(self.topology_dm.getField("parentcellbasenum").ravel())
self.topology_dm.restoreField("parentcellbasenum")
return cell_parent_base_cell_list[self.cell_closure[:, -1]]
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_base_cell_map(self):
"""Return the :class:`pyop2.types.map.Map` from vertex only mesh cells to
parent mesh base cells.
"""
if not isinstance(self._parent_mesh, ExtrudedMeshTopology):
raise AttributeError("Parent mesh is not extruded.")
return op2.Map(self.cell_set, self._parent_mesh.cell_set, 1,
self.cell_parent_base_cell_list, "cell_parent_base_cell")
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_extrusion_height_list(self):
"""Return a list of parent mesh extrusion heights in vertex only
mesh cell order.
"""
if not isinstance(self._parent_mesh, ExtrudedMeshTopology):
raise AttributeError("Parent mesh is not extruded.")
cell_parent_extrusion_height_list = np.copy(self.topology_dm.getField("parentcellextrusionheight").ravel())
self.topology_dm.restoreField("parentcellextrusionheight")
return cell_parent_extrusion_height_list[self.cell_closure[:, -1]]
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_parent_extrusion_height_map(self):
"""Return the :class:`pyop2.types.map.Map` from vertex only mesh cells to
parent mesh extrusion heights.
"""
if not isinstance(self._parent_mesh, ExtrudedMeshTopology):
raise AttributeError("Parent mesh is not extruded.")
return op2.Map(self.cell_set, self._parent_mesh.cell_set, 1,
self.cell_parent_extrusion_height_list, "cell_parent_extrusion_height")
[docs]
def mark_entities(self, tf, label_value, label_name=None):
raise NotImplementedError("Currently not implemented for VertexOnlyMesh")
@utils.cached_property # TODO: Recalculate if mesh moves
def cell_global_index(self):
"""Return a list of unique cell IDs in vertex only mesh cell order."""
cell_global_index = np.copy(self.topology_dm.getField("globalindex").ravel())
self.topology_dm.restoreField("globalindex")
return cell_global_index
@utils.cached_property # TODO: Recalculate if mesh moves
def input_ordering(self):
"""
Return the input ordering of the mesh vertices as a
:class:`~.VertexOnlyMeshTopology` whilst preserving other information, such as
the global indices and parent mesh cell information.
Notes
-----
If ``redundant=True`` at mesh creation, all the vertices will
be returned on rank 0.
Any points that were not found in the original mesh when it was created
will still be present here in their originally supplied order.
"""
if not isinstance(self.topology, VertexOnlyMeshTopology):
raise AttributeError("Input ordering is only defined for vertex-only meshes.")
# Make the VOM which uses the original ordering of the points
if self.input_ordering_swarm:
return VertexOnlyMeshTopology(
self.input_ordering_swarm,
self,
name=self.input_ordering_swarm.getName(),
reorder=False,
)
@staticmethod
def _make_input_ordering_sf(swarm, nroots, ilocal):
# ilocal = None -> leaves are swarm points [0, 1, 2, ...).
# ilocal can also be Firedrake cell numbers.
sf = PETSc.SF().create(comm=swarm.comm)
input_ranks = swarm.getField("inputrank").ravel()
input_indices = swarm.getField("inputindex").ravel()
nleaves = len(input_ranks)
if ilocal is not None and nleaves != len(ilocal):
swarm.restoreField("inputrank")
swarm.restoreField("inputindex")
raise RuntimeError(f"Mismatching leaves: nleaves {nleaves} != len(ilocal) {len(ilocal)}")
input_ranks_and_idxs = np.empty(2 * nleaves, dtype=IntType)
input_ranks_and_idxs[0::2] = input_ranks
input_ranks_and_idxs[1::2] = input_indices
swarm.restoreField("inputrank")
swarm.restoreField("inputindex")
sf.setGraph(nroots, ilocal, input_ranks_and_idxs)
return sf
@utils.cached_property # TODO: Recalculate if mesh moves
def input_ordering_sf(self):
"""
Return a PETSc SF which has :func:`~.VertexOnlyMesh` input ordering
vertices as roots and this mesh's vertices (including any halo cells)
as leaves.
"""
if not isinstance(self.topology, VertexOnlyMeshTopology):
raise AttributeError("Input ordering is only defined for vertex-only meshes.")
nroots = self.input_ordering.num_cells()
e_p_map = self.cell_closure[:, -1] # cell-entity -> swarm-point map
ilocal = np.empty_like(e_p_map)
if len(e_p_map) > 0:
cStart = e_p_map.min() # smallest swarm point number
ilocal[e_p_map - cStart] = np.arange(len(e_p_map))
return VertexOnlyMeshTopology._make_input_ordering_sf(self.topology_dm, nroots, ilocal)
@utils.cached_property # TODO: Recalculate if mesh moves
def input_ordering_without_halos_sf(self):
"""
Return a PETSc SF which has :func:`~.VertexOnlyMesh` input ordering
vertices as roots and this mesh's non-halo vertices as leaves.
"""
# The leaves have been ordered according to the pyop2 classes with non-halo
# cells first; self.cell_set.size is the number of rank-local non-halo cells.
return self.input_ordering_sf.createEmbeddedLeafSF(np.arange(self.cell_set.size, dtype=IntType))
class CellOrientationsRuntimeError(RuntimeError):
"""Exception raised when there are problems with cell orientations."""
pass
class MeshGeometryCargo:
"""Helper class carrying data for a :class:`MeshGeometry`.
It is required because it permits Firedrake to have stripped forms
that still know that they are on an extruded mesh (for example).
"""
def __init__(self, ufl_id):
self._ufl_id = ufl_id
def ufl_id(self):
return self._ufl_id
def init(self, coordinates):
"""Initialise the cargo.
This function is separate to __init__ because of the two-step process we have
for initialising a :class:`MeshGeometry`.
"""
self.topology = coordinates.function_space().mesh()
self.coordinates = coordinates
self.geometric_shared_data_cache = defaultdict(dict)
[docs]
class MeshGeometry(ufl.Mesh, MeshGeometryMixin):
"""A representation of mesh topology and geometry."""
def __new__(cls, element, comm):
"""Create mesh geometry object."""
utils._init()
mesh = super(MeshGeometry, cls).__new__(cls)
uid = utils._new_uid(internal_comm(comm, mesh))
mesh.uid = uid
cargo = MeshGeometryCargo(uid)
assert isinstance(element, finat.ufl.FiniteElementBase)
ufl.Mesh.__init__(mesh, element, ufl_id=mesh.uid, cargo=cargo)
return mesh
@MeshGeometryMixin._ad_annotate_init
def __init__(self, coordinates):
"""Initialise a mesh geometry from coordinates.
Parameters
----------
coordinates : CoordinatelessFunction
The `CoordinatelessFunction` containing the coordinates.
"""
topology = coordinates.function_space().mesh()
# this is codegen information so we attach it to the MeshGeometry rather than its cargo
self.extruded = isinstance(topology, ExtrudedMeshTopology)
self.variable_layers = self.extruded and topology.variable_layers
# initialise the mesh cargo
self.ufl_cargo().init(coordinates)
# Cache mesh object on the coordinateless coordinates function
coordinates._as_mesh_geometry = weakref.ref(self)
# submesh
self.submesh_parent = None
def _ufl_signature_data_(self, *args, **kwargs):
return (type(self), self.extruded, self.variable_layers,
super()._ufl_signature_data_(*args, **kwargs))
[docs]
def init(self):
"""Finish the initialisation of the mesh. Most of the time
this is carried out automatically, however, in some cases (for
example accessing a property of the mesh directly after
constructing it) you need to call this manually."""
if hasattr(self, '_callback'):
self._callback(self)
def _init_topology(self, topology):
"""Initialise the topology.
:arg topology: The :class:`.MeshTopology` object.
A mesh is fully initialised with its topology and coordinates.
In this method we partially initialise the mesh by registering
its topology. We also set the `_callback` attribute that is
later called to set its coordinates and finalise the initialisation.
"""
import firedrake.functionspace as functionspace
import firedrake.function as function
self._topology = topology
def callback(self):
"""Finish initialisation."""
del self._callback
# Finish the initialisation of mesh topology
self.topology.init()
coordinates_fs = functionspace.FunctionSpace(self.topology, self.ufl_coordinate_element())
coordinates_data = dmcommon.reordered_coords(topology.topology_dm, coordinates_fs.dm.getDefaultSection(),
(self.num_vertices(), self.geometric_dimension()))
coordinates = function.CoordinatelessFunction(coordinates_fs,
val=coordinates_data,
name=_generate_default_mesh_coordinates_name(self.name))
self.__init__(coordinates)
self._callback = callback
@property
def topology(self):
"""The underlying mesh topology object."""
return self.ufl_cargo().topology
@topology.setter
def topology(self, val):
self.ufl_cargo().topology = val
@property
def _topology(self):
return self.topology
@_topology.setter
def _topology(self, val):
self.topology = val
@property
def _parent_mesh(self):
return self.ufl_cargo()._parent_mesh
@_parent_mesh.setter
def _parent_mesh(self, val):
self.ufl_cargo()._parent_mesh = val
@property
def _coordinates(self):
return self.ufl_cargo().coordinates
@property
def _geometric_shared_data_cache(self):
return self.ufl_cargo().geometric_shared_data_cache
@property
def topological(self):
"""Alias of topology.
This is to ensure consistent naming for some multigrid codes."""
return self._topology
@property
def _topology_dm(self):
"""Alias of topology_dm"""
from warnings import warn
warn("_topology_dm is deprecated (use topology_dm instead)", DeprecationWarning, stacklevel=2)
return self.topology_dm
@property
@MeshGeometryMixin._ad_annotate_coordinates_function
def _coordinates_function(self):
"""The :class:`.Function` containing the coordinates of this mesh."""
import firedrake.functionspaceimpl as functionspaceimpl
import firedrake.function as function
if hasattr(self.ufl_cargo(), "_coordinates_function"):
return self.ufl_cargo()._coordinates_function
else:
self.init()
coordinates_fs = self._coordinates.function_space()
V = functionspaceimpl.WithGeometry.create(coordinates_fs, self)
f = function.Function(V, val=self._coordinates)
self.ufl_cargo()._coordinates_function = f
return f
@property
def coordinates(self):
"""The :class:`.Function` containing the coordinates of this mesh."""
return self._coordinates_function
@coordinates.setter
def coordinates(self, value):
message = """Cannot re-assign the coordinates.
You are free to change the coordinate values, but if you need a
different coordinate function space, use Mesh(f) to create a new mesh
object whose coordinates are f's values. (This will not copy the
values from f.)"""
raise AttributeError(message)
@utils.cached_property
def cell_sizes(self):
"""A :class:`~.Function` in the :math:`P^1` space containing the local mesh size.
This is computed by the :math:`L^2` projection of the local mesh element size."""
from firedrake.ufl_expr import CellSize
from firedrake.functionspace import FunctionSpace
from firedrake.projection import project
P1 = FunctionSpace(self, "Lagrange", 1)
return project(CellSize(self), P1)
[docs]
def clear_cell_sizes(self):
"""Reset the :attr:`cell_sizes` field on this mesh geometry.
Use this if you move the mesh.
"""
try:
del self.cell_size
except AttributeError:
pass
@property
def tolerance(self):
"""The relative tolerance (i.e. as defined on the reference cell) for
the distance a point can be from a cell and still be considered to be
in the cell.
Increase this if points at mesh boundaries (either rank local or
global) are reported as being outside the mesh, for example when
creating a :class:`VertexOnlyMesh`. Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear distance) so will
scale with the dimension of the mesh.
If this property is not set (i.e. set to ``None``) no tolerance is
added to the bounding box and points deemed at all outside the mesh,
even by floating point error distances, will be deemed to be outside
it.
Notes
-----
After changing tolerance any requests for :attr:`spatial_index` will cause
the spatial index to be rebuilt with the new tolerance which may take some time.
"""
return self._tolerance
@tolerance.setter
def tolerance(self, value):
if not isinstance(value, numbers.Number):
raise TypeError("tolerance must be a number")
if value != self._tolerance:
self.clear_spatial_index()
self._tolerance = value
[docs]
def clear_spatial_index(self):
"""Reset the :attr:`spatial_index` on this mesh geometry.
Use this if you move the mesh (for example by reassigning to
the coordinate field)."""
try:
del self.spatial_index
except AttributeError:
pass
@utils.cached_property
def spatial_index(self):
"""Spatial index to quickly find which cell contains a given point.
Notes
-----
If this mesh has a :attr:`tolerance` property, which
should be a float, this tolerance is added to the extrama of the
spatial index so that points just outside the mesh, within tolerance,
can be found.
"""
from firedrake import function, functionspace
from firedrake.parloops import par_loop, READ, MIN, MAX
gdim = self.geometric_dimension()
if gdim <= 1:
info_red("libspatialindex does not support 1-dimension, falling back on brute force.")
return None
# Calculate the bounding boxes for all cells by running a kernel
V = functionspace.VectorFunctionSpace(self, "DG", 0, dim=gdim)
coords_min = function.Function(V, dtype=RealType)
coords_max = function.Function(V, dtype=RealType)
coords_min.dat.data.fill(np.inf)
coords_max.dat.data.fill(-np.inf)
if utils.complex_mode:
if not np.allclose(self.coordinates.dat.data_ro.imag, 0):
raise ValueError("Coordinate field has non-zero imaginary part")
coords = function.Function(self.coordinates.function_space(),
val=self.coordinates.dat.data_ro_with_halos.real.copy(),
dtype=RealType)
else:
coords = self.coordinates
cell_node_list = self.coordinates.function_space().cell_node_list
_, nodes_per_cell = cell_node_list.shape
domain = "{{[d, i]: 0 <= d < {0} and 0 <= i < {1}}}".format(gdim, nodes_per_cell)
instructions = """
for d, i
f_min[0, d] = fmin(f_min[0, d], f[i, d])
f_max[0, d] = fmax(f_max[0, d], f[i, d])
end
"""
par_loop((domain, instructions), ufl.dx,
{'f': (coords, READ),
'f_min': (coords_min, MIN),
'f_max': (coords_max, MAX)})
# Reorder bounding boxes according to the cell indices we use
column_list = V.cell_node_list.reshape(-1)
coords_min = self._order_data_by_cell_index(column_list, coords_min.dat.data_ro_with_halos)
coords_max = self._order_data_by_cell_index(column_list, coords_max.dat.data_ro_with_halos)
# Change min and max to refer to an n-hypercube, where n is the
# geometric dimension of the mesh, centred on the midpoint of the
# bounding box. Its side length is the L1 diameter of the bounding box.
# This aids point evaluation on immersed manifolds and other cases
# where points may be just off the mesh but should be evaluated.
# TODO: This is perhaps unnecessary when we aren't in these special
# cases.
# We also push max and min out so we can find points on the boundary
# within the mesh tolerance.
# NOTE: getattr doesn't work here due to the inheritance games that are
# going on in getattr.
tolerance = self.tolerance if hasattr(self, "tolerance") else 0.0
coords_mid = (coords_max + coords_min)/2
d = np.max(coords_max - coords_min, axis=1)[:, None]
coords_min = coords_mid - (tolerance + 0.5)*d
coords_max = coords_mid + (tolerance + 0.5)*d
# Build spatial index
return spatialindex.from_regions(coords_min, coords_max)
[docs]
@PETSc.Log.EventDecorator()
def locate_cell(self, x, tolerance=None, cell_ignore=None):
"""Locate cell containing a given point.
:arg x: point coordinates
:kwarg tolerance: Tolerance for checking if a point is in a cell.
Default is this mesh's :attr:`tolerance` property. Changing
this from default will cause the spatial index to be rebuilt which
can take some time.
:kwarg cell_ignore: Cell number to ignore in the search.
:returns: cell number (int), or None (if the point is not
in the domain)
"""
return self.locate_cell_and_reference_coordinate(x, tolerance=tolerance, cell_ignore=cell_ignore)[0]
[docs]
def locate_reference_coordinate(self, x, tolerance=None, cell_ignore=None):
"""Get reference coordinates of a given point in its cell. Which
cell the point is in can be queried with the locate_cell method.
:arg x: point coordinates
:kwarg tolerance: Tolerance for checking if a point is in a cell.
Default is this mesh's :attr:`tolerance` property. Changing
this from default will cause the spatial index to be rebuilt which
can take some time.
:kwarg cell_ignore: Cell number to ignore in the search.
:returns: reference coordinates within cell (numpy array) or
None (if the point is not in the domain)
"""
return self.locate_cell_and_reference_coordinate(x, tolerance=tolerance, cell_ignore=cell_ignore)[1]
[docs]
def locate_cell_and_reference_coordinate(self, x, tolerance=None, cell_ignore=None):
"""Locate cell containing a given point and the reference
coordinates of the point within the cell.
:arg x: point coordinates
:kwarg tolerance: Tolerance for checking if a point is in a cell.
Default is this mesh's :attr:`tolerance` property. Changing
this from default will cause the spatial index to be rebuilt which
can take some time.
:kwarg cell_ignore: Cell number to ignore in the search.
:returns: tuple either
(cell number, reference coordinates) of type (int, numpy array),
or, when point is not in the domain, (None, None).
"""
x = np.asarray(x)
if x.size != self.geometric_dimension():
raise ValueError("Point must have the same geometric dimension as the mesh")
x = x.reshape((1, self.geometric_dimension()))
cells, ref_coords, _ = self.locate_cells_ref_coords_and_dists(x, tolerance=tolerance, cells_ignore=[[cell_ignore]])
if cells[0] == -1:
return None, None
return cells[0], ref_coords[0]
[docs]
def locate_cells_ref_coords_and_dists(self, xs, tolerance=None, cells_ignore=None):
"""Locate cell containing a given point and the reference
coordinates of the point within the cell.
:arg xs: 1 or more point coordinates of shape (npoints, gdim)
:kwarg tolerance: Tolerance for checking if a point is in a cell.
Default is this mesh's :attr:`tolerance` property. Changing
this from default will cause the spatial index to be rebuilt which
can take some time.
:kwarg cells_ignore: Cell numbers to ignore in the search for each
point in xs. Shape should be (npoints, n_ignore_pts). Each column
corresponds to a single coordinate in xs. To not ignore any cells,
pass None. To ensure a full cell search for any given point, set
the corresponding entries to -1.
:returns: tuple either
(cell numbers array, reference coordinates array, ref_cell_dists_l1 array)
of type
(array of ints, array of floats of size (npoints, gdim), array of floats).
The cell numbers array contains -1 for points not in the domain:
the reference coordinates and distances are meaningless for these
points.
"""
if self.variable_layers:
raise NotImplementedError("Cell location not implemented for variable layers")
if tolerance is None:
tolerance = self.tolerance
else:
self.tolerance = tolerance
xs = np.asarray(xs, dtype=utils.ScalarType)
xs = xs.real.copy()
if xs.shape[1] != self.geometric_dimension():
raise ValueError("Point coordinate dimension does not match mesh geometric dimension")
Xs = np.empty_like(xs)
npoints = len(xs)
if cells_ignore is None or cells_ignore[0][0] is None:
cells_ignore = np.full((npoints, 1), -1, dtype=IntType, order="C")
else:
cells_ignore = np.asarray(cells_ignore, dtype=IntType, order="C")
if cells_ignore.shape[0] != npoints:
raise ValueError("Number of cells to ignore does not match number of points")
assert cells_ignore.shape == (npoints, cells_ignore.shape[1])
ref_cell_dists_l1 = np.empty(npoints, dtype=utils.RealType)
cells = np.empty(npoints, dtype=IntType)
assert xs.size == npoints * self.geometric_dimension()
self._c_locator(tolerance=tolerance)(self.coordinates._ctypes,
xs.ctypes.data_as(ctypes.POINTER(ctypes.c_double)),
Xs.ctypes.data_as(ctypes.POINTER(ctypes.c_double)),
ref_cell_dists_l1.ctypes.data_as(ctypes.POINTER(ctypes.c_double)),
cells.ctypes.data_as(ctypes.POINTER(ctypes.c_int)),
npoints,
cells_ignore.shape[1],
cells_ignore)
return cells, Xs, ref_cell_dists_l1
def _c_locator(self, tolerance=None):
from pyop2 import compilation
from pyop2.utils import get_petsc_dir
import firedrake.function as function
import firedrake.pointquery_utils as pq_utils
cache = self.__dict__.setdefault("_c_locator_cache", {})
try:
return cache[tolerance]
except KeyError:
IntTypeC = as_cstr(IntType)
src = pq_utils.src_locate_cell(self, tolerance=tolerance)
src += dedent(f"""
int locator(struct Function *f, double *x, double *X, double *ref_cell_dists_l1, {IntTypeC} *cells, {IntTypeC} npoints, size_t ncells_ignore, int* cells_ignore)
{{
{IntTypeC} j = 0; /* index into x and X */
for({IntTypeC} i=0; i<npoints; i++) {{
/* i is the index into cells and ref_cell_dists_l1 */
/* The type definitions and arguments used here are defined as
statics in pointquery_utils.py */
struct ReferenceCoords temp_reference_coords, found_reference_coords;
/* to_reference_coords and to_reference_coords_xtr are defined in
pointquery_utils.py. If they contain python calls, this loop will
not run at c-loop speed. */
/* cells_ignore has shape (npoints, ncells_ignore) - find the ith row */
int *cells_ignore_i = cells_ignore + i*ncells_ignore;
cells[i] = locate_cell(f, &x[j], {self.geometric_dimension()}, &to_reference_coords, &to_reference_coords_xtr, &temp_reference_coords, &found_reference_coords, &ref_cell_dists_l1[i], ncells_ignore, cells_ignore_i);
for (int k = 0; k < {self.geometric_dimension()}; k++) {{
X[j] = found_reference_coords.X[k];
j++;
}}
}}
return 0;
}}
""")
libspatialindex_so = Path(rtree.core.rt._name).absolute()
lsi_runpath = f"-Wl,-rpath,{libspatialindex_so.parent}"
locator = compilation.load(
src, "c", "locator",
cppargs=[
f"-I{os.path.dirname(__file__)}",
f"-I{sys.prefix}/include",
f"-I{rtree.finder.get_include()}"
] + [f"-I{d}/include" for d in get_petsc_dir()],
ldargs=[
f"-L{sys.prefix}/lib",
str(libspatialindex_so),
f"-Wl,-rpath,{sys.prefix}/lib",
lsi_runpath
],
comm=self.comm
)
locator.argtypes = [ctypes.POINTER(function._CFunction),
ctypes.POINTER(ctypes.c_double),
ctypes.POINTER(ctypes.c_double),
ctypes.POINTER(ctypes.c_double),
ctypes.POINTER(ctypes.c_int),
ctypes.c_size_t,
ctypes.c_size_t,
np.ctypeslib.ndpointer(ctypes.c_int, flags="C_CONTIGUOUS")]
locator.restype = ctypes.c_int
return cache.setdefault(tolerance, locator)
@utils.cached_property # TODO: Recalculate if mesh moves. Extend this for regular meshes.
def input_ordering(self):
"""
Return the input ordering of the mesh vertices as a
:func:`~.VertexOnlyMesh` whilst preserving other information, such as
the global indices and parent mesh cell information.
Notes
-----
If ``redundant=True`` at mesh creation, all the vertices will
be returned on rank 0.
Any points that were not found in the original mesh when it was created
will still be present here in their originally supplied order.
"""
if not isinstance(self.topology, VertexOnlyMeshTopology):
raise AttributeError("Input ordering is only defined for vertex-only meshes.")
_input_ordering = make_vom_from_vom_topology(self.topology.input_ordering, self.name + "_input_ordering")
if _input_ordering:
_input_ordering._parent_mesh = self
_input_ordering.init()
return _input_ordering
[docs]
def cell_orientations(self):
"""Return the orientation of each cell in the mesh.
Use :meth:`.init_cell_orientations` to initialise."""
# View `_cell_orientations` (`CoordinatelessFunction`) as a property of
# `MeshGeometry` as opposed to one of `MeshTopology`, and treat it just like
# `_coordinates` (`CoordinatelessFunction`) so that we have:
# -- Regular MeshGeometry = MeshTopology + `_coordinates`,
# -- Immersed MeshGeometry = MeshTopology + `_coordinates` + `_cell_orientations`.
# Here, `_coordinates` and `_cell_orientations` both represent some geometric
# properties (i.e., "coordinates" and "cell normals").
#
# Two `MeshGeometry`s can share the same `MeshTopology` and `_coordinates` while
# having distinct definition of "cell normals"; they are then simply regarded as two
# distinct meshes as `dot(expr, cell_normal) * dx` in general gives different results.
#
# Storing `_cell_orientations` in `MeshTopology` would make the `MeshTopology`
# object only useful for specific definition of "cell normals".
if not hasattr(self, '_cell_orientations'):
raise CellOrientationsRuntimeError("No cell orientations found, did you forget to call init_cell_orientations?")
return self._cell_orientations
[docs]
@PETSc.Log.EventDecorator()
def init_cell_orientations(self, expr):
"""Compute and initialise meth:`cell_orientations` relative to a specified orientation.
:arg expr: a UFL expression evaluated to produce a
reference normal direction.
"""
import firedrake.function as function
import firedrake.functionspace as functionspace
if (self.ufl_cell().cellname(), self.geometric_dimension()) not in _supported_embedded_cell_types_and_gdims:
raise NotImplementedError('Only implemented for intervals embedded in 2d and triangles and quadrilaterals embedded in 3d')
if hasattr(self, '_cell_orientations'):
raise CellOrientationsRuntimeError("init_cell_orientations already called, did you mean to do so again?")
if not isinstance(expr, ufl.classes.Expr):
raise TypeError("UFL expression expected!")
if expr.ufl_shape != (self.geometric_dimension(), ):
raise ValueError(f"Mismatching shapes: expr.ufl_shape ({expr.ufl_shape}) != (self.geometric_dimension(), ) (({self.geometric_dimension}, ))")
fs = functionspace.FunctionSpace(self, 'DG', 0)
x = ufl.SpatialCoordinate(self)
f = function.Function(fs)
if self.topological_dimension() == 1:
normal = ufl.as_vector((-ReferenceGrad(x)[1, 0], ReferenceGrad(x)[0, 0]))
else: # self.topological_dimension() == 2
normal = ufl.cross(ReferenceGrad(x)[:, 0], ReferenceGrad(x)[:, 1])
f.interpolate(ufl.dot(expr, normal))
cell_orientations = function.Function(fs, name="cell_orientations", dtype=np.int32)
cell_orientations.dat.data[:] = (f.dat.data_ro < 0)
self._cell_orientations = cell_orientations.topological
def __getattr__(self, name):
val = getattr(self._topology, name)
setattr(self, name, val)
return val
def __dir__(self):
current = super(MeshGeometry, self).__dir__()
return list(OrderedDict.fromkeys(dir(self._topology) + current))
[docs]
def mark_entities(self, f, label_value, label_name=None):
"""Mark selected entities.
:arg f: The :class:`.Function` object that marks
selected entities as 1. f.function_space().ufl_element()
must be "DP" or "DQ" (degree 0) to mark cell entities and
"P" (degree 1) in 1D or "HDiv Trace" (degree 0) in 2D or 3D
to mark facet entities.
Can use "Q" (degree 2) functions for 3D hex meshes until
we support "HDiv Trace" elements on hex.
:arg lable_value: The value used in the label.
:arg label_name: The name of the label to store entity selections.
All entities must live on the same topological dimension. Currently,
one can only mark cell or facet entities.
"""
self.topology.mark_entities(f.topological, label_value, label_name)
@PETSc.Log.EventDecorator()
def make_mesh_from_coordinates(coordinates, name, tolerance=0.5):
"""Given a coordinate field build a new mesh, using said coordinate field.
Parameters
----------
coordinates : CoordinatelessFunction
The `CoordinatelessFunction` from which mesh is made.
name : str
The name of the mesh.
tolerance : numbers.Number
The tolerance; see `Mesh`.
comm: mpi4py.Intracomm
Communicator.
Returns
-------
MeshGeometry
The mesh.
"""
if hasattr(coordinates, '_as_mesh_geometry'):
mesh = coordinates._as_mesh_geometry()
if mesh is not None:
return mesh
V = coordinates.function_space()
element = coordinates.ufl_element()
if V.rank != 1 or len(element.reference_value_shape) != 1:
raise ValueError("Coordinates must be from a rank-1 FunctionSpace with rank-1 value_shape.")
assert V.mesh().ufl_cell().topological_dimension() <= V.value_size
mesh = MeshGeometry.__new__(MeshGeometry, element, coordinates.comm)
mesh.__init__(coordinates)
mesh.name = name
# Mark mesh as being made from coordinates
mesh._made_from_coordinates = True
mesh._tolerance = tolerance
return mesh
def make_mesh_from_mesh_topology(topology, name, tolerance=0.5):
"""Make mesh from tpology.
Parameters
----------
topology : MeshTopology
The `MeshTopology` from which mesh is made.
name : str
The name of the mesh.
tolerance : numbers.Number
The tolerance; see `Mesh`.
Returns
-------
MeshGeometry
The mesh.
"""
# Construct coordinate element
# TODO: meshfile might indicates higher-order coordinate element
cell = topology.ufl_cell()
geometric_dim = topology.topology_dm.getCoordinateDim()
if not topology.topology_dm.getCoordinatesLocalized():
element = finat.ufl.VectorElement("Lagrange", cell, 1, dim=geometric_dim)
else:
element = finat.ufl.VectorElement("DQ" if cell in [ufl.quadrilateral, ufl.hexahedron] else "DG", cell, 1, dim=geometric_dim, variant="equispaced")
# Create mesh object
mesh = MeshGeometry.__new__(MeshGeometry, element, topology.comm)
mesh._init_topology(topology)
mesh.name = name
mesh._tolerance = tolerance
return mesh
def make_vom_from_vom_topology(topology, name, tolerance=0.5):
"""Make `VertexOnlyMesh` from a mesh topology.
Parameters
----------
topology : VertexOnlyMeshTopology
The `VertexOnlyMeshTopology`.
name : str
The name of the mesh.
tolerance : numbers.Number
The tolerance; see `Mesh`.
Returns
-------
MeshGeometry
The mesh.
"""
import firedrake.functionspaceimpl as functionspaceimpl
import firedrake.functionspace as functionspace
import firedrake.function as function
gdim = topology.topology_dm.getCoordinateDim()
cell = topology.ufl_cell()
element = finat.ufl.VectorElement("DG", cell, 0, dim=gdim)
vmesh = MeshGeometry.__new__(MeshGeometry, element, topology.comm)
vmesh._init_topology(topology)
# Save vertex reference coordinate (within reference cell) in function
parent_tdim = topology._parent_mesh.ufl_cell().topological_dimension()
if parent_tdim > 0:
reference_coordinates_fs = functionspace.VectorFunctionSpace(topology, "DG", 0, dim=parent_tdim)
reference_coordinates_data = dmcommon.reordered_coords(topology.topology_dm, reference_coordinates_fs.dm.getDefaultSection(),
(topology.num_vertices(), parent_tdim),
reference_coord=True)
reference_coordinates = function.CoordinatelessFunction(reference_coordinates_fs,
val=reference_coordinates_data,
name=_generate_default_mesh_reference_coordinates_name(name))
refCoordV = functionspaceimpl.WithGeometry.create(reference_coordinates_fs, vmesh)
vmesh.reference_coordinates = function.Function(refCoordV, val=reference_coordinates)
else:
# We can't do this in 0D so leave it undefined.
vmesh.reference_coordinates = None
vmesh.name = name
vmesh._tolerance = tolerance
return vmesh
[docs]
@PETSc.Log.EventDecorator("CreateMesh")
def Mesh(meshfile, **kwargs):
"""Construct a mesh object.
Meshes may either be created by reading from a mesh file, or by
providing a PETSc DMPlex object defining the mesh topology.
:param meshfile: the mesh file name, a DMPlex object or a Netgen mesh object defining
mesh topology. See below for details on supported mesh
formats.
:param name: optional name of the mesh object.
:param dim: optional specification of the geometric dimension
of the mesh (ignored if not reading from mesh file).
If not supplied the geometric dimension is deduced from
the topological dimension of entities in the mesh.
:param reorder: optional flag indicating whether to reorder
meshes for better cache locality. If not supplied the
default value in ``parameters["reorder_meshes"]``
is used.
:param distribution_parameters: an optional dictionary of options for
parallel mesh distribution. Supported keys are:
- ``"partition"``: which may take the value ``None`` (use
the default choice), ``False`` (do not) ``True``
(do), or a 2-tuple that specifies a partitioning of
the cells (only really useful for debugging).
- ``"partitioner_type"``: which may take ``"chaco"``,
``"ptscotch"``, ``"parmetis"``, or ``"shell"``.
- ``"overlap_type"``: a 2-tuple indicating how to grow
the mesh overlap. The first entry should be a
:class:`DistributedMeshOverlapType` instance, the
second the number of levels of overlap.
:param distribution_name: the name of parallel distribution used
when checkpointing; if not given, the name is automatically
generated.
:param permutation_name: the name of entity permutation (reordering) used
when checkpointing; if not given, the name is automatically
generated.
:param comm: the communicator to use when creating the mesh. If
not supplied, then the mesh will be created on COMM_WORLD.
If ``meshfile`` is a DMPlex object then must be indentical
to or congruent with the DMPlex communicator.
:param tolerance: The relative tolerance (i.e. as defined on the reference
cell) for the distance a point can be from a cell and still be
considered to be in the cell. Defaults to 0.5. Increase
this if point at mesh boundaries (either rank local or global) are
reported as being outside the mesh, for example when creating a
:class:`VertexOnlyMesh`. Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear distance) so
will scale with the dimension of the mesh.
:param netgen_flags: The dictionary of flags to be passed to ngsPETSc.
When the mesh is read from a file the following mesh formats
are supported (determined, case insensitively, from the
filename extension):
* GMSH: with extension `.msh`
* Exodus: with extension `.e`, `.exo`
* CGNS: with extension `.cgns`
* Triangle: with extension `.node`
* HDF5: with extension `.h5`, `.hdf5`
(Can only load HDF5 files created by
:meth:`~.CheckpointFile.save_mesh` method.)
.. note::
When the mesh is created directly from a DMPlex object or a Netgen
mesh object, the ``dim`` parameter is ignored (the DMPlex already
knows its geometric and topological dimensions).
"""
import firedrake.function as function
user_comm = kwargs.get("comm", COMM_WORLD)
name = kwargs.get("name", DEFAULT_MESH_NAME)
reorder = kwargs.get("reorder", None)
if reorder is None:
reorder = parameters["reorder_meshes"]
distribution_parameters = kwargs.get("distribution_parameters", None)
if distribution_parameters is None:
distribution_parameters = {}
if isinstance(meshfile, str) and \
any(meshfile.lower().endswith(ext) for ext in ['.h5', '.hdf5']):
from firedrake.output import CheckpointFile
with CheckpointFile(meshfile, 'r', comm=user_comm) as afile:
return afile.load_mesh(name=name, reorder=reorder,
distribution_parameters=distribution_parameters)
elif isinstance(meshfile, function.Function):
coordinates = meshfile.topological
elif isinstance(meshfile, function.CoordinatelessFunction):
coordinates = meshfile
else:
coordinates = None
if coordinates is not None:
return make_mesh_from_coordinates(coordinates, name)
tolerance = kwargs.get("tolerance", 0.5)
utils._init()
# We don't need to worry about using a user comm in these cases as
# they all immediately call a petsc4py which in turn uses a PETSc
# internal comm
geometric_dim = kwargs.get("dim", None)
if isinstance(meshfile, PETSc.DMPlex):
plex = meshfile
if MPI.Comm.Compare(user_comm, plex.comm.tompi4py()) not in {MPI.CONGRUENT, MPI.IDENT}:
raise ValueError("Communicator used to create `plex` must be at least congruent to the communicator used to create the mesh")
elif netgen and isinstance(meshfile, netgen.libngpy._meshing.Mesh):
try:
from ngsPETSc import FiredrakeMesh
except ImportError:
raise ImportError("Unable to import ngsPETSc. Please ensure that ngsolve is installed and available to Firedrake.")
from firedrake_citations import Citations
Citations().register("Betteridge2024")
netgen_flags = kwargs.get("netgen_flags", {"quad": False, "transform": None, "purify_to_tets": False})
netgen_firedrake_mesh = FiredrakeMesh(meshfile, netgen_flags, user_comm)
plex = netgen_firedrake_mesh.meshMap.petscPlex
else:
basename, ext = os.path.splitext(meshfile)
if ext.lower() in ['.e', '.exo']:
plex = _from_exodus(meshfile, user_comm)
elif ext.lower() == '.cgns':
plex = _from_cgns(meshfile, user_comm)
elif ext.lower() == '.msh':
if geometric_dim is not None:
opts = {"dm_plex_gmsh_spacedim": geometric_dim}
else:
opts = {}
opts = OptionsManager(opts, "")
with opts.inserted_options():
plex = _from_gmsh(meshfile, user_comm)
elif ext.lower() == '.node':
plex = _from_triangle(meshfile, geometric_dim, user_comm)
else:
raise RuntimeError("Mesh file %s has unknown format '%s'."
% (meshfile, ext[1:]))
plex.setName(_generate_default_mesh_topology_name(name))
# Create mesh topology
topology = MeshTopology(plex, name=plex.getName(), reorder=reorder,
distribution_parameters=distribution_parameters,
distribution_name=kwargs.get("distribution_name"),
permutation_name=kwargs.get("permutation_name"),
comm=user_comm)
mesh = make_mesh_from_mesh_topology(topology, name)
if netgen and isinstance(meshfile, netgen.libngpy._meshing.Mesh):
netgen_firedrake_mesh.createFromTopology(topology, name=plex.getName(), comm=user_comm)
mesh = netgen_firedrake_mesh.firedrakeMesh
mesh._tolerance = tolerance
return mesh
[docs]
@PETSc.Log.EventDecorator("CreateExtMesh")
def ExtrudedMesh(mesh, layers, layer_height=None, extrusion_type='uniform', periodic=False, kernel=None, gdim=None, name=None, tolerance=0.5):
"""Build an extruded mesh from an input mesh
:arg mesh: the unstructured base mesh
:arg layers: number of extruded cell layers in the "vertical"
direction. One may also pass an array of
shape (cells, 2) to specify a variable number
of layers. In this case, each entry is a pair
``[a, b]`` where ``a`` indicates the starting
cell layer of the column and ``b`` the number
of cell layers in that column.
:arg layer_height: the layer height. A scalar value will result in
evenly-spaced layers, whereas an array of values
will vary the layer height through the extrusion.
If this is omitted, the value defaults to
1/layers (i.e. the extruded mesh has total height 1.0)
unless a custom kernel is used. Must be
provided if using a variable number of layers.
:arg extrusion_type: the algorithm to employ to calculate the extruded
coordinates. One of "uniform", "radial",
"radial_hedgehog" or "custom". See below.
:arg periodic: the flag for periodic extrusion; if True, only constant layer extrusion is allowed.
Can be used with any "extrusion_type" to make annulus, torus, etc.
:arg kernel: a ``pyop2.Kernel`` to produce coordinates for
the extruded mesh. See :func:`~.make_extruded_coords`
for more details.
:arg gdim: number of spatial dimensions of the
resulting mesh (this is only used if a
custom kernel is provided)
:arg name: optional name for the extruded mesh.
:kwarg tolerance: The relative tolerance (i.e. as defined on the
reference cell) for the distance a point can be from a
cell and still be considered to be in the cell.
Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear
distance) so will scale with the dimension of the
mesh.
The various values of ``extrusion_type`` have the following meanings:
``"uniform"``
the extruded mesh has an extra spatial
dimension compared to the base mesh. The layers exist
in this dimension only.
``"radial"``
the extruded mesh has the same number of
spatial dimensions as the base mesh; the cells are
radially extruded outwards from the origin. This
requires the base mesh to have topological dimension
strictly smaller than geometric dimension.
``"radial_hedgehog"``
similar to `radial`, but the cells
are extruded in the direction of the outward-pointing
cell normal (this produces a P1dgxP1 coordinate field).
In this case, a radially extruded coordinate field
(generated with ``extrusion_type="radial"``) is
available in the ``radial_coordinates`` attribute.
``"custom"``
use a custom kernel to generate the extruded coordinates
For more details see the :doc:`manual section on extruded meshes <extruded-meshes>`.
"""
import firedrake.functionspace as functionspace
import firedrake.function as function
if name is not None and name == mesh.name:
raise ValueError("Extruded mesh and base mesh can not have the same name")
name = name if name is not None else mesh.name + "_extruded"
mesh.init()
layers = np.asarray(layers, dtype=IntType)
if layers.shape:
if periodic:
raise ValueError("Must provide constant layer for periodic extrusion")
if layers.shape != (mesh.cell_set.total_size, 2):
raise ValueError("Must provide single layer number or array of shape (%d, 2), not %s",
mesh.cell_set.total_size, layers.shape)
if layer_height is None:
raise ValueError("Must provide layer height for variable layers")
# variable-height layers need to be present for the maximum number
# of extruded layers
num_layers = layers.sum(axis=1).max() if mesh.cell_set.total_size else 0
num_layers = mesh._comm.allreduce(num_layers, op=MPI.MAX)
# Convert to internal representation
layers[:, 1] += 1 + layers[:, 0]
else:
if layer_height is None:
# Default to unit
layer_height = 1 / layers
num_layers = layers
# All internal logic works with layers of base mesh (not layers of cells)
layers = layers + 1
try:
assert num_layers == len(layer_height)
except TypeError:
# layer_height is a scalar; equi-distant layers are fine
pass
topology = ExtrudedMeshTopology(mesh.topology, layers, periodic=periodic)
if extrusion_type == "uniform":
pass
elif extrusion_type in ("radial", "radial_hedgehog"):
# do not allow radial extrusion if tdim = gdim
if mesh.geometric_dimension() == mesh.topological_dimension():
raise RuntimeError("Cannot radially-extrude a mesh with equal geometric and topological dimension")
else:
# check for kernel
if kernel is None:
raise RuntimeError("If the custom extrusion_type is used, a kernel must be provided")
# otherwise, use the gdim that was passed in
if gdim is None:
raise RuntimeError("The geometric dimension of the mesh must be specified if a custom extrusion kernel is used")
helement = mesh._coordinates.ufl_element().sub_elements[0]
if extrusion_type == 'radial_hedgehog':
helement = helement.reconstruct(family="DG", variant="equispaced")
if periodic:
velement = finat.ufl.FiniteElement("DP", ufl.interval, 1, variant="equispaced")
else:
velement = finat.ufl.FiniteElement("Lagrange", ufl.interval, 1)
element = finat.ufl.TensorProductElement(helement, velement)
if gdim is None:
gdim = mesh.geometric_dimension() + (extrusion_type == "uniform")
coordinates_fs = functionspace.VectorFunctionSpace(topology, element, dim=gdim)
coordinates = function.CoordinatelessFunction(coordinates_fs, name=_generate_default_mesh_coordinates_name(name))
eutils.make_extruded_coords(topology, mesh._coordinates, coordinates,
layer_height, extrusion_type=extrusion_type, kernel=kernel)
self = make_mesh_from_coordinates(coordinates, name)
self._base_mesh = mesh
if extrusion_type == "radial_hedgehog":
helement = mesh._coordinates.ufl_element().sub_elements[0].reconstruct(family="CG")
element = finat.ufl.TensorProductElement(helement, velement)
fs = functionspace.VectorFunctionSpace(self, element, dim=gdim)
self.radial_coordinates = function.Function(fs, name=name + "_radial_coordinates")
eutils.make_extruded_coords(topology, mesh._coordinates, self.radial_coordinates,
layer_height, extrusion_type="radial", kernel=kernel)
self._tolerance = tolerance
return self
class MissingPointsBehaviour(enum.Enum):
IGNORE = None
ERROR = "error"
WARN = "warn"
[docs]
class VertexOnlyMeshMissingPointsError(Exception):
"""Exception raised when 1 or more points are not found by a
:func:`~.VertexOnlyMesh` in its parent mesh.
Attributes
----------
n_missing_points : int
The number of points which were not found in the parent mesh.
"""
def __init__(self, n_missing_points):
self.n_missing_points = n_missing_points
def __str__(self):
return (
f"{self.n_missing_points} vertices are outside the mesh and have "
"been removed from the VertexOnlyMesh."
)
[docs]
@PETSc.Log.EventDecorator()
def VertexOnlyMesh(mesh, vertexcoords, reorder=None, missing_points_behaviour='error',
tolerance=None, redundant=True, name=None):
"""
Create a vertex only mesh, immersed in a given mesh, with vertices defined
by a list of coordinates.
:arg mesh: The unstructured mesh in which to immerse the vertex only mesh.
:arg vertexcoords: A list of coordinate tuples which defines the vertices.
:kwarg reorder: optional flag indicating whether to reorder
meshes for better cache locality. If not supplied the
default value in ``parameters["reorder_meshes"]``
is used.
:kwarg missing_points_behaviour: optional string argument for what to do
when vertices which are outside of the mesh are discarded. If
``'warn'``, will print a warning. If ``'error'`` will raise a
:class:`~.VertexOnlyMeshMissingPointsError`.
:kwarg tolerance: The relative tolerance (i.e. as defined on the reference
cell) for the distance a point can be from a mesh cell and still be
considered to be in the cell. Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear distance) so
will scale with the dimension of the mesh. The default is the parent
mesh's ``tolerance`` property. Changing this from default will
cause the parent mesh's spatial index to be rebuilt which can take some
time.
:kwarg redundant: If True, the mesh will be built using just the vertices
which are specified on rank 0. If False, the mesh will be built using
the vertices specified by each rank. Care must be taken when using
``redundant = False``: see the note below for more information.
:kwarg name: Optional name for the new ``VertexOnlyMesh``. If none is
specified a name will be generated from the parent mesh name.
.. note::
The vertex only mesh uses the same communicator as the input ``mesh``.
.. note::
Extruded meshes with variable extrusion layers are not yet supported.
See note below about ``VertexOnlyMesh`` as input.
.. note::
When running in parallel with ``redundant = False``, ``vertexcoords``
will redistribute to the mesh partition where they are located. This
means that if rank A has ``vertexcoords`` {X} that are not found in the
mesh cells owned by rank A but are found in the mesh cells owned by
rank B, then they will be moved to rank B.
.. note::
If the same coordinates are supplied more than once, they are always
assumed to be a new vertex.
"""
from firedrake_citations import Citations
Citations().register("nixonhill2023consistent")
if tolerance is None:
tolerance = mesh.tolerance
else:
mesh.tolerance = tolerance
mesh.init()
vertexcoords = np.asarray(vertexcoords, dtype=RealType)
if reorder is None:
reorder = parameters["reorder_meshes"]
gdim = mesh.geometric_dimension()
_, pdim = vertexcoords.shape
if not np.isclose(np.sum(abs(vertexcoords.imag)), 0):
raise ValueError("Point coordinates must have zero imaginary part")
# Bendy meshes require a smarter bounding box algorithm at partition and
# (especially) cell level. Projecting coordinates to Bernstein may be
# sufficient.
if np.any(np.asarray(mesh.coordinates.function_space().ufl_element().degree()) > 1):
raise NotImplementedError("Only straight edged meshes are supported")
# Currently we take responsibility for locating the mesh cells in which the
# vertices lie.
#
# In the future we hope to update the coordinates field correctly so that
# the DMSwarm PIC can immerse itself in the DMPlex. We can also hopefully
# provide a callback for PETSc to use to find the parent cell id. We would
# add `DMLocatePoints` as an `op` to `DMShell` types and do
# `DMSwarmSetCellDM(yourdmshell)` which has `DMLocatePoints_Shell`
# implemented. Whether one or both of these is needed is unclear.
if pdim != gdim:
raise ValueError(f"Mesh geometric dimension {gdim} must match point list dimension {pdim}")
swarm, input_ordering_swarm, n_missing_points = _pic_swarm_in_mesh(
mesh, vertexcoords, tolerance=tolerance, redundant=redundant, exclude_halos=False
)
missing_points_behaviour = MissingPointsBehaviour(missing_points_behaviour)
if missing_points_behaviour != MissingPointsBehaviour.IGNORE:
if n_missing_points:
error = VertexOnlyMeshMissingPointsError(n_missing_points)
if missing_points_behaviour == MissingPointsBehaviour.ERROR:
raise error
elif missing_points_behaviour == MissingPointsBehaviour.WARN:
from warnings import warn
warn(str(error))
else:
raise ValueError("missing_points_behaviour must be IGNORE, ERROR or WARN")
name = name if name is not None else mesh.name + "_immersed_vom"
swarm.setName(_generate_default_mesh_topology_name(name))
input_ordering_swarm.setName(_generate_default_mesh_topology_name(name) + "_input_ordering")
topology = VertexOnlyMeshTopology(
swarm,
mesh.topology,
name=swarm.getName(),
reorder=reorder,
input_ordering_swarm=input_ordering_swarm,
)
vmesh_out = make_vom_from_vom_topology(topology, name, tolerance)
vmesh_out._parent_mesh = mesh
vmesh_out.init()
return vmesh_out
class FiredrakeDMSwarm(PETSc.DMSwarm):
"""A DMSwarm with a saved list of added fields"""
def __init__(self, *args, **kwargs):
super().__init__(*args, **kwargs)
self._fields = None
self._default_fields = None
self._default_extra_fields = None
self._other_fields = None
@property
def fields(self):
return self._fields
@fields.setter
def fields(self, fields):
if self._fields:
raise ValueError("Fields have already been set")
self._fields = fields
@property
def default_fields(self):
return self._default_fields
@default_fields.setter
def default_fields(self, fields):
if self._default_fields:
raise ValueError("Default fields have already been set")
self._default_fields = fields
@property
def default_extra_fields(self):
return self._default_extra_fields
@default_extra_fields.setter
def default_extra_fields(self, fields):
if self._default_extra_fields:
raise ValueError("Default extra fields have already been set")
self._default_extra_fields = fields
@property
def other_fields(self):
return self._other_fields
@other_fields.setter
def other_fields(self, fields):
if self._other_fields:
raise ValueError("Other fields have already been set")
self._other_fields = fields
def _pic_swarm_in_mesh(
parent_mesh,
coords,
fields=None,
tolerance=None,
redundant=True,
exclude_halos=True,
):
"""Create a Particle In Cell (PIC) DMSwarm immersed in a Mesh
This should only by used for meshes with straight edges. If not, the
particles may be placed in the wrong cells.
:arg parent_mesh: the :class:`Mesh` within with the DMSwarm should be
immersed.
:arg coords: an ``ndarray`` of (npoints, coordsdim) shape.
:kwarg fields: An optional list of named data which can be stored for each
point in the DMSwarm. The format should be::
[(fieldname1, blocksize1, dtype1),
...,
(fieldnameN, blocksizeN, dtypeN)]
For example, the swarm coordinates themselves are stored in a field
named ``DMSwarmPIC_coor`` which, were it not created automatically,
would be initialised with ``fields = [("DMSwarmPIC_coor", coordsdim,
RealType)]``. All fields must have the same number of points. For more
information see `the DMSWARM API reference
<https://www.mcs.anl.gov/petsc/petsc-current/manualpages/DMSWARM/DMSWARM.html>_.
:kwarg tolerance: The relative tolerance (i.e. as defined on the reference
cell) for the distance a point can be from a cell and still be
considered to be in the cell. Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear distance) so
will scale with the dimension of the mesh. The default is the parent
mesh's ``tolerance`` property. Changing this from default will
cause the parent mesh's spatial index to be rebuilt which can take some
time.
:kwarg redundant: If True, the DMSwarm will be created using only the
points specified on MPI rank 0.
:kwarg exclude_halos: If True, the DMSwarm will not contain any points in
the mesh halos. If False, it will but the global index of the points
in the halos will match a global index of a point which is not in the
halo.
:returns: (swarm, input_ordering_swarm, n_missing_points)
- swarm: the immersed DMSwarm
- input_ordering_swarm: a DMSwarm with points in the same order and with the
same rank decomposition as the supplied ``coords`` argument. This
includes any points which are not found in the parent mesh! Note
that if ``redundant=True``, all points in the generated DMSwarm
will be found on rank 0 since that was where they were taken from.
- n_missing_points: the number of points in the supplied ``coords``
argument which were not found in the parent mesh.
.. note::
The created DMSwarm uses the communicator of the input Mesh.
.. note::
In complex mode the "DMSwarmPIC_coor" field is still saved as a real
number unlike the coordinates of a DMPlex which become complex (though
usually with zeroed imaginary parts).
.. note::
When running in parallel with ``redundant = False``, ``coords``
will redistribute to the mesh partition where they are located. This
means that if rank A has ``coords`` {X} that are not found in the
mesh cells owned by rank A but are found in the mesh cells owned by
rank B, **and rank B has not been supplied with those**, then they will
be moved to rank B.
.. note::
If the same coordinates are supplied more than once, they are always
assumed to be a new vertex.
.. note::
Three DMSwarm fields are created automatically here:
#. ``parentcellnum`` which contains the firedrake cell number of the
immersed vertex and
#. ``refcoord`` which contains the reference coordinate of the immersed
vertex in the parent mesh cell.
#. ``globalindex`` which contains a unique ID for each DMSwarm point -
here this is the index into the ``coords`` array if ``redundant`` is
``True``, otherwise it's an index in rank order, so if rank 0 has 10
points, rank 1 has 20 points, and rank 3 has 5 points, then rank 0's
points will be numbered 0-9, rank 1's points will be numbered 10-29,
and rank 3's points will be numbered 30-34. Note that this ought to
be ``DMSwarmField_pid`` but a bug in petsc4py means that this field
cannot be set.
#. ``inputrank`` which contains the MPI rank at which the ``coords``
argument was specified. For ``redundant=True`` this is always 0.
#. ``inputindex`` which contains the index of the point in the
originally supplied ``coords`` array after it has been redistributed
to the correct rank. For ``redundant=True`` this is always the same
as ``globalindex`` since we only use the points on rank 0.
If the parent mesh is extruded, two more fields are created:
#. ``parentcellbasenum`` which contains the firedrake cell number of the
base cell of the immersed vertex and
#. ``parentcellextrusionheight`` which contains the extrusion height of
the immersed vertex in the parent mesh cell.
Another three are required for proper functioning of the DMSwarm:
#. ``DMSwarmPIC_coor`` which contains the coordinates of the point.
#. ``DMSwarm_cellid`` the DMPlex cell within which the DMSwarm point is
located.
#. ``DMSwarm_rank``: the MPI rank which owns the DMSwarm point.
.. note::
All PIC DMSwarm have an associated "Cell DM", if one wishes to interact
directly with PETSc's DMSwarm API. For the ``swarm`` output, this is
the parent mesh's topology DM (in most cases a DMPlex). For the
``input_ordering_swarm`` output, this is the ``swarm`` itself.
"""
if tolerance is None:
tolerance = parent_mesh.tolerance
else:
parent_mesh.tolerance = tolerance
# Check coords
coords = np.asarray(coords, dtype=RealType)
plex = parent_mesh.topology.topology_dm
tdim = parent_mesh.topological_dimension()
gdim = parent_mesh.geometric_dimension()
(
coords_local,
global_idxs_local,
reference_coords_local,
parent_cell_nums_local,
owned_ranks_local,
input_ranks_local,
input_coords_idxs_local,
missing_global_idxs,
) = _parent_mesh_embedding(
parent_mesh,
coords,
tolerance,
redundant,
exclude_halos,
remove_missing_points=False,
)
visible_idxs = parent_cell_nums_local != -1
if parent_mesh.extruded:
# need to store the base parent cell number and the height to be able
# to map point coordinates back to the parent mesh
if parent_mesh.variable_layers:
raise NotImplementedError(
"Cannot create a DMSwarm in an ExtrudedMesh with variable layers."
)
base_parent_cell_nums, extrusion_heights = _parent_extrusion_numbering(
parent_cell_nums_local, parent_mesh.layers
)
# mesh.topology.cell_closure[:, -1] maps Firedrake cell numbers to plex
# numbers.
plex_parent_cell_nums = parent_mesh.topology.cell_closure[
base_parent_cell_nums, -1
]
base_parent_cell_nums_visible = base_parent_cell_nums[visible_idxs]
extrusion_heights_visible = extrusion_heights[visible_idxs]
else:
plex_parent_cell_nums = parent_mesh.topology.cell_closure[
parent_cell_nums_local, -1
]
base_parent_cell_nums_visible = None
extrusion_heights_visible = None
n_missing_points = len(missing_global_idxs)
# Exclude the invisible points at this stage
swarm = _dmswarm_create(
fields,
parent_mesh.comm,
plex,
coords_local[visible_idxs],
plex_parent_cell_nums[visible_idxs],
global_idxs_local[visible_idxs],
reference_coords_local[visible_idxs],
parent_cell_nums_local[visible_idxs],
owned_ranks_local[visible_idxs],
input_ranks_local[visible_idxs],
input_coords_idxs_local[visible_idxs],
base_parent_cell_nums_visible,
extrusion_heights_visible,
parent_mesh.extruded,
tdim,
gdim,
)
# Note when getting original ordering for extruded meshes we recalculate
# the base_parent_cell_nums and extrusion_heights - note this could
# be an SF operation
if redundant and parent_mesh.comm.rank != 0:
original_ordering_swarm_coords = np.empty(shape=(0, coords.shape[1]))
else:
original_ordering_swarm_coords = coords
# Set pointSF
# In the below, n merely defines the local size of an array, local_points_reduced,
# that works as "broker". The set of indices of local_points_reduced is the target of
# inputindex; see _make_input_ordering_sf. All points in local_points are leaves.
# Then, local_points[halo_indices] = -1, local_points_reduced.fill(-1), and MPI.MAX ensure that local_points_reduced has
# the swarm local point numbers of the owning ranks after reduce. local_points_reduced[j] = -1
# if j corresponds to a missing point. Then, broadcast updates
# local_points[halo_indices] (it also updates local_points[~halo_indices]`, not changing any values there).
# If some index of local_points_reduced corresponds to a missing point, local_points_reduced[index] is not updated
# when we reduce and it does not update any leaf data, i.e., local_points, when we bcast.
owners = swarm.getField("DMSwarm_rank").ravel()
halo_indices, = np.where(owners != parent_mesh.comm.rank)
halo_indices = halo_indices.astype(IntType)
n = coords.shape[0]
m = owners.shape[0]
_swarm_input_ordering_sf = VertexOnlyMeshTopology._make_input_ordering_sf(swarm, n, None) # sf: swarm local point <- (inputrank, inputindex)
local_points_reduced = np.empty(n, dtype=utils.IntType)
local_points_reduced.fill(-1)
local_points = np.arange(m, dtype=utils.IntType) # swarm local point numbers
local_points[halo_indices] = -1
unit = MPI._typedict[np.dtype(utils.IntType).char]
_swarm_input_ordering_sf.reduceBegin(unit, local_points, local_points_reduced, MPI.MAX)
_swarm_input_ordering_sf.reduceEnd(unit, local_points, local_points_reduced, MPI.MAX)
_swarm_input_ordering_sf.bcastBegin(unit, local_points_reduced, local_points, MPI.REPLACE)
_swarm_input_ordering_sf.bcastEnd(unit, local_points_reduced, local_points, MPI.REPLACE)
if np.any(local_points < 0):
raise RuntimeError("Unable to make swarm pointSF due to inconsistent data")
# Interleave each rank and index into (rank, index) pairs for use as remote
# in the SF
remote_ranks_and_idxs = np.empty(2 * len(halo_indices), dtype=IntType)
remote_ranks_and_idxs[0::2] = owners[halo_indices]
remote_ranks_and_idxs[1::2] = local_points[halo_indices]
swarm.restoreField("DMSwarm_rank")
sf = swarm.getPointSF()
sf.setGraph(m, halo_indices, remote_ranks_and_idxs)
swarm.setPointSF(sf)
original_ordering_swarm = _swarm_original_ordering_preserve(
parent_mesh.comm,
swarm,
original_ordering_swarm_coords,
plex_parent_cell_nums,
global_idxs_local,
reference_coords_local,
parent_cell_nums_local,
owned_ranks_local,
input_ranks_local, # This is just an array of 0s for redundant, and comm.rank otherwise. But I need to pass it in to get the correct ordering
input_coords_idxs_local,
parent_mesh.extruded,
parent_mesh.layers,
)
# no halos here
sf = original_ordering_swarm.getPointSF()
nroots = original_ordering_swarm.getLocalSize()
sf.setGraph(nroots, None, [])
original_ordering_swarm.setPointSF(sf)
return swarm, original_ordering_swarm, n_missing_points
def _dmswarm_create(
fields,
comm,
plex,
coords,
plex_parent_cell_nums,
coords_idxs,
reference_coords,
parent_cell_nums,
ranks,
input_ranks,
input_coords_idxs,
base_parent_cell_nums,
extrusion_heights,
extruded,
tdim,
gdim,
):
"""
Create a PIC DMSwarm (or DMSwarm that looks like it's a PIC DMSwarm) using
the given data.
Parameters
----------
fields : list of tuples
List of tuples of the form (name, number of components, type) for any
additional fields to be added to the DMSwarm. The default fields are
automatically added and do not need to be specified here. Can be an
empty list if no additional fields are required.
comm : MPI communicator
The MPI communicator to use when creating the DMSwarm.
plex : PETSc DM
The DM to set as the "CellDM" of the DMSwarm - i.e. the DMPlex or
DMSwarm of the parent mesh.
coords : numpy array of RealType with shape (npoints, gdim)
The coordinates of the particles in the DMSwarm.
plex_parent_cell_nums : numpy array of IntType with shape (npoints,)
Array to be used as the "parentcellnum" field of the DMSwarm.
coords_idxs : numpy array of IntType with shape (npoints,)
Array to be used as the "globalindex" field of the DMSwarm.
reference_coords : numpy array of RealType with shape (npoints, tdim)
Array to be used as the "refcoord" field of the DMSwarm.
parent_cell_nums : numpy array of IntType with shape (npoints,)
Array to be used as the "parentcellnum" field of the DMSwarm.
ranks : numpy array of IntType with shape (npoints,)
Array to be used as the "DMSwarm_rank" field of the DMSwarm.
input_ranks : numpy array of IntType with shape (npoints,)
Array to be used as the "inputrank" field of the DMSwarm.
input_coords_idxs : numpy array of IntType with shape (npoints,)
Array to be used as the "inputindex" field of the DMSwarm.
base_parent_cell_nums : numpy array of IntType with shape (npoints,) (or None)
Optional array to be used as the "parentcellbasenum" field of the
DMSwarm. Must be provided if extruded=True.
extrusion_heights : numpy array of IntType with shape (npoints,) (or None)
Optional array to be used as the "parentcellextrusionheight" field of
the DMSwarm. Must be provided if extruded=True.
extruded : bool
Whether the parent mesh is extruded.
tdim : int
The topological dimension of the parent mesh.
gdim : int
The geometric dimension of the parent mesh.
Returns
-------
swarm : PETSc DMSwarm
The created DMSwarm.
Notes
-----
When the `plex` is a DMSwarm, the created DMSwarm isn't actually a PIC
DMSwarm, but it has all the associated fields of a PIC DMSwarm. This is
because PIC DMSwarms cannot have their "CellDM" set to a DMSwarm, so we
fake it!
"""
# These are created by default for a PIC DMSwarm
default_fields = [
("DMSwarmPIC_coor", gdim, RealType),
("DMSwarm_cellid", 1, IntType),
("DMSwarm_rank", 1, IntType),
]
default_extra_fields = [
("parentcellnum", 1, IntType),
("refcoord", tdim, RealType),
("globalindex", 1, IntType),
("inputrank", 1, IntType),
("inputindex", 1, IntType),
]
if extruded:
default_extra_fields += [
("parentcellbasenum", 1, IntType),
("parentcellextrusionheight", 1, IntType),
]
other_fields = fields
if other_fields is None:
other_fields = []
_, coordsdim = coords.shape
# Create a DMSWARM
swarm = FiredrakeDMSwarm().create(comm=comm)
# save the fields on the swarm
swarm.fields = default_fields + default_extra_fields + other_fields
swarm.default_fields = default_fields
swarm.default_extra_fields = default_extra_fields
swarm.other_fields = other_fields
plexdim = plex.getDimension()
if plexdim != tdim or plexdim != gdim:
# This is a Firedrake extruded or immersed mesh, so we need to use the
# mesh geometric dimension when we create the swarm. In this
# case DMSwarmMigate() will not work.
swarmdim = gdim
else:
swarmdim = plexdim
# Set swarm DM dimension to match DMPlex dimension
# NB: Unlike a DMPlex, this does not correspond to the topological
# dimension of a mesh (which would be 0). In all PETSc examples
# the dimension of the DMSwarm is set to match that of the
# DMPlex used with swarm.setCellDM. As noted above, for an
# extruded mesh this will stop DMSwarmMigrate() from working.
swarm.setDimension(swarmdim)
# Set coordinates dimension
swarm.setCoordinateDim(coordsdim)
# Link to DMPlex cells information for when swarm.migrate() is used
swarm.setCellDM(plex)
# Set to Particle In Cell (PIC) type
if not isinstance(plex, PETSc.DMSwarm):
swarm.setType(PETSc.DMSwarm.Type.PIC)
else:
# This doesn't work where we embed a DMSwarm in a DMSwarm, instead
# we register some default fields manually
for name, size, dtype in default_fields:
if name == "DMSwarmPIC_coor" or name == "DMSwarm_cellid":
swarm.registerField(name, size, dtype=dtype)
# Register any fields
for name, size, dtype in swarm.default_extra_fields + swarm.other_fields:
swarm.registerField(name, size, dtype=dtype)
swarm.finalizeFieldRegister()
# Note that no new fields can now be associated with the DMSWARM.
num_vertices = len(coords)
swarm.setLocalSizes(num_vertices, -1)
# Add point coordinates. This amounts to our own implementation of
# DMSwarmSetPointCoordinates because Firedrake's mesh coordinate model
# doesn't always exactly coincide with that of DMPlex: in most cases the
# plex_parent_cell_nums (DMSwarm_cellid field) and parent_cell_nums
# (parentcellnum field), the latter being the numbering used by firedrake,
# refer fundamentally to the same cells. For extruded meshes the DMPlex
# dimension is based on the topological dimension of the base mesh.
# NOTE ensure that swarm.restoreField is called for each field too!
swarm_coords = swarm.getField("DMSwarmPIC_coor").reshape((num_vertices, gdim))
swarm_parent_cell_nums = swarm.getField("DMSwarm_cellid").ravel()
field_parent_cell_nums = swarm.getField("parentcellnum").ravel()
field_reference_coords = swarm.getField("refcoord").reshape((num_vertices, tdim))
field_global_index = swarm.getField("globalindex").ravel()
field_rank = swarm.getField("DMSwarm_rank").ravel()
field_input_rank = swarm.getField("inputrank").ravel()
field_input_index = swarm.getField("inputindex").ravel()
swarm_coords[...] = coords
swarm_parent_cell_nums[...] = plex_parent_cell_nums
field_parent_cell_nums[...] = parent_cell_nums
field_reference_coords[...] = reference_coords
field_global_index[...] = coords_idxs
field_rank[...] = ranks
field_input_rank[...] = input_ranks
field_input_index[...] = input_coords_idxs
# have to restore fields once accessed to allow access again
swarm.restoreField("inputindex")
swarm.restoreField("inputrank")
swarm.restoreField("DMSwarm_rank")
swarm.restoreField("globalindex")
swarm.restoreField("refcoord")
swarm.restoreField("parentcellnum")
swarm.restoreField("DMSwarmPIC_coor")
swarm.restoreField("DMSwarm_cellid")
if extruded:
field_base_parent_cell_nums = swarm.getField("parentcellbasenum").ravel()
field_extrusion_heights = swarm.getField("parentcellextrusionheight").ravel()
field_base_parent_cell_nums[...] = base_parent_cell_nums
field_extrusion_heights[...] = extrusion_heights
swarm.restoreField("parentcellbasenum")
swarm.restoreField("parentcellextrusionheight")
return swarm
def _parent_extrusion_numbering(parent_cell_nums, parent_layers):
"""
Given a list of Firedrake cell numbers (e.g. from mesh.locate_cell) and
number of layers, get the base parent cell numbers and extrusion heights.
Parameters
----------
parent_cell_nums : ``np.ndarray``
Firedrake cell numbers (e.g. from mesh.locate_cell)
parent_layers : ``int``
Number of layers in the extruded mesh
Returns
-------
base_parent_cell_nums : ``np.ndarray``
The base parent cell numbers
extrusion_heights : ``np.ndarray``
The extrusion heights
Notes
-----
Only works for meshes without variable layers.
"""
# Extruded mesh parent_cell_nums goes from bottom to top. So for
# mx = ExtrudedMesh(UnitIntervalMesh(2), 3) we have
# mx.layers = 4
# and
# -------------------layer 4-------------------
# | parent_cell_num = 2 | parent_cell_num = 5 |
# | extrusion_height = 2 | extrusion_height = 2 |
# -------------------layer 3-------------------
# | parent_cell_num = 1 | parent_cell_num = 4 |
# | extrusion_height = 1 | extrusion_height = 1 |
# -------------------layer 2-------------------
# | parent_cell_num = 0 | parent_cell_num = 3 |
# | extrusion_height = 0 | extrusion_height = 0 |
# -------------------layer 1-------------------
# base_cell_num = 0 base_cell_num = 1
# The base_cell_num is the cell number in the base mesh which, in this
# case, is a UnitIntervalMesh with two cells.
base_parent_cell_nums = parent_cell_nums // (parent_layers - 1)
extrusion_heights = parent_cell_nums % (parent_layers - 1)
return base_parent_cell_nums, extrusion_heights
def _mpi_array_lexicographic_min(x, y, datatype):
"""MPI operator for lexicographic minimum of arrays.
This compares two arrays of shape (N, 2) lexicographically, i.e. first
comparing the two arrays by their first column, returning the element-wise
minimum, with ties broken by comparing the second column element wise.
Parameters
----------
x : ``np.ndarray``
The first array to compare of shape (N, 2).
y : ``np.ndarray``
The second array to compare of shape (N, 2).
datatype : ``MPI.Datatype``
The datatype of the arrays.
Returns
-------
``np.ndarray``
The lexicographically lowest array of shape (N, 2).
"""
# Check the first column
min_idxs = np.where(x[:, 0] < y[:, 0])[0]
result = np.copy(y)
result[min_idxs, :] = x[min_idxs, :]
# if necessary, check the second column
eq_idxs = np.where(x[:, 0] == y[:, 0])[0]
if len(eq_idxs):
# We only check where we have equal values to avoid unnecessary work
min_idxs = np.where(x[eq_idxs, 1] < y[eq_idxs, 1])[0]
result[eq_idxs[min_idxs], :] = x[eq_idxs[min_idxs], :]
return result
array_lexicographic_mpi_op = MPI.Op.Create(_mpi_array_lexicographic_min, commute=True)
def _parent_mesh_embedding(
parent_mesh, coords, tolerance, redundant, exclude_halos, remove_missing_points
):
"""Find the parent mesh cells containing the given coordinates.
Parameters
----------
parent_mesh : ``Mesh``
The parent mesh to embed in.
coords : ``np.ndarray``
The coordinates to embed of (npoints, coordsdim) shape.
tolerance : ``float``
The relative tolerance (i.e. as defined on the reference cell) for the
distance a point can be from a cell and still be considered to be in
the cell. Note that this tolerance uses an L1
distance (aka 'manhattan', 'taxicab' or rectilinear distance) so
will scale with the dimension of the mesh. The default is the parent
mesh's ``tolerance`` property. Changing this from default will
cause the parent mesh's spatial index to be rebuilt which can take some
time.
redundant : ``bool``
If True, the embedding will be done using only the points specified on
MPI rank 0.
exclude_halos : ``bool``
If True, the embedding will be done using only the points specified on
the locally owned mesh partition.
remove_missing_points : ``bool``
If True, any points which are not found in the mesh will be removed
from the output arrays. If False, they will be kept on the MPI rank
which owns them but will be marked as not being not found in the mesh
by setting their associated cell numbers to -1 and their reference
coordinates to NaNs. This does not effect the behaviour of
``missing_global_idxs``.
Returns
-------
coords_embedded : ``np.ndarray``
The coordinates of the points that were embedded on this rank. If
``remove_missing_points`` is False then this will include points that
were specified on this rank but not found in the mesh.
global_idxs : ``np.ndarray``
The global indices of the points on this rank.
reference_coords : ``np.ndarray``
The reference coordinates of the points that were embedded as given by
the local mesh partition. If ``remove_missing_points`` is False then
the missing point reference coordinates will be NaNs.
parent_cell_nums : ``np.ndarray``
The parent cell indices (as given by ``locate_cell``) of the global
coordinates that were embedded in the local mesh partition. If
``remove_missing_points`` is False then the missing point numbers
will be -1.
owned_ranks : ``np.ndarray``
The MPI rank of the process that owns the parent cell of each point.
By "owns" we mean the mesh partition where the parent cell is not in
the halo. If a point is not found in the mesh then the rank is
``parent_mesh.comm.size + 1``.
input_ranks : ``np.ndarray``
The MPI rank of the process that specified the input ``coords``.
input_coords_idx : ``np.ndarray``
The indices of the points in the input ``coords`` array that were
embedded. If ``remove_missing_points`` is False then this will include
points that were specified on this rank but not found in the mesh.
missing_global_idxs : ``np.ndarray``
The indices of the points in the input coords array that were not
embedded on any rank.
.. note::
Where we have ``exclude_halos == True`` and ``remove_missing_points ==
False``, and we run in parallel, the points are ordered such that the
halo points follow the owned points. Any missing points will be at the
end of the array. This is to ensure that dat views work as expected -
in general it is always assumed that halo points follow owned points.
"""
if isinstance(parent_mesh.topology, VertexOnlyMeshTopology):
raise NotImplementedError(
"VertexOnlyMeshes don't have a working locate_cells_ref_coords_and_dists method"
)
import firedrake.functionspace as functionspace
import firedrake.constant as constant
import firedrake.interpolation as interpolation
import firedrake.assemble as assemble
# In parallel, we need to make sure we know which point is which and save
# it.
if redundant:
# rank 0 broadcasts coords to all ranks
coords_local = parent_mesh._comm.bcast(coords, root=0)
ncoords_local = coords_local.shape[0]
coords_global = coords_local
ncoords_global = coords_global.shape[0]
global_idxs_global = np.arange(coords_global.shape[0])
input_coords_idxs_local = np.arange(ncoords_local)
input_coords_idxs_global = input_coords_idxs_local
input_ranks_local = np.zeros(ncoords_local, dtype=int)
input_ranks_global = input_ranks_local
else:
# Here, we have to assume that all points we can see are unique.
# We therefore gather all points on all ranks in rank order: if rank 0
# has 10 points, rank 1 has 20 points, and rank 3 has 5 points, then
# rank 0's points have global numbering 0-9, rank 1's points have
# global numbering 10-29, and rank 3's points have global numbering
# 30-34.
coords_local = coords
ncoords_local = coords.shape[0]
ncoords_local_allranks = parent_mesh._comm.allgather(ncoords_local)
ncoords_global = sum(ncoords_local_allranks)
# The below code looks complicated but it's just an allgather of the
# (variable length) coords_local array such that they are concatenated.
coords_local_size = np.array(coords_local.size)
coords_local_sizes = np.empty(parent_mesh._comm.size, dtype=int)
parent_mesh._comm.Allgatherv(coords_local_size, coords_local_sizes)
coords_global = np.empty(
(ncoords_global, coords.shape[1]), dtype=coords_local.dtype
)
parent_mesh._comm.Allgatherv(coords_local, (coords_global, coords_local_sizes))
# # ncoords_local_allranks is in rank order so we can just sum up the
# # previous ranks to get the starting index for the global numbering.
# # For rank 0 we make use of the fact that sum([]) = 0.
# startidx = sum(ncoords_local_allranks[:parent_mesh._comm.rank])
# endidx = startidx + ncoords_local
# global_idxs_global = np.arange(startidx, endidx)
global_idxs_global = np.arange(coords_global.shape[0])
input_coords_idxs_local = np.arange(ncoords_local)
input_coords_idxs_global = np.empty(ncoords_global, dtype=int)
parent_mesh._comm.Allgatherv(
input_coords_idxs_local, (input_coords_idxs_global, ncoords_local_allranks)
)
input_ranks_local = np.full(ncoords_local, parent_mesh._comm.rank, dtype=int)
input_ranks_global = np.empty(ncoords_global, dtype=int)
parent_mesh._comm.Allgatherv(
input_ranks_local, (input_ranks_global, ncoords_local_allranks)
)
# Get parent mesh rank ownership information:
# Interpolating Constant(parent_mesh.comm.rank) into P0DG cleverly creates
# a Function whose dat contains rank ownership information in an ordering
# that is accessible using Firedrake's cell numbering. This is because, on
# each rank, parent_mesh.comm.rank creates a Constant with the local rank
# number, and halo exchange ensures that this information is visible, as
# nessesary, to other processes.
P0DG = functionspace.FunctionSpace(parent_mesh, "DG", 0)
with stop_annotating():
visible_ranks = interpolation.Interpolate(
constant.Constant(parent_mesh.comm.rank), P0DG
)
visible_ranks = assemble(visible_ranks).dat.data_ro_with_halos.real
locally_visible = np.full(ncoords_global, False)
# See below for why np.inf is used here.
ranks = np.full(ncoords_global, np.inf)
(
parent_cell_nums,
reference_coords,
ref_cell_dists_l1,
) = parent_mesh.locate_cells_ref_coords_and_dists(coords_global, tolerance)
assert len(parent_cell_nums) == ncoords_global
assert len(reference_coords) == ncoords_global
assert len(ref_cell_dists_l1) == ncoords_global
if parent_mesh.geometric_dimension() > parent_mesh.topological_dimension():
# The reference coordinates contain an extra unnecessary dimension
# which we can safely delete
reference_coords = reference_coords[:, : parent_mesh.topological_dimension()]
locally_visible[:] = parent_cell_nums != -1
ranks[locally_visible] = visible_ranks[parent_cell_nums[locally_visible]]
# see below for why np.inf is used here.
ref_cell_dists_l1[~locally_visible] = np.inf
# ensure that points which a rank thinks it owns are always chosen in a tie
# break by setting the rank to be negative. If multiple ranks think they
# own a point then the one with the highest rank will be chosen.
on_this_rank = ranks == parent_mesh.comm.rank
ranks[on_this_rank] = -parent_mesh.comm.rank
ref_cell_dists_l1_and_ranks = np.stack((ref_cell_dists_l1, ranks), axis=1)
# In parallel there will regularly be disagreements about which cell owns a
# point when those points are close to mesh partition boundaries.
# We now have the reference cell l1 distance and ranks being np.inf for any
# point which is not locally visible. By collectively taking the minimum
# of the reference cell l1 distance, which is tied to the rank via
# ref_cell_dists_l1_and_ranks, we both check which cell the coordinate is
# closest to and find out which rank owns that cell.
# In cases where the reference cell l1 distance is the same for a
# particular coordinate, we break the tie by choosing the lowest rank.
# This turns out to be a lexicographic row-wise minimum of the
# ref_cell_dists_l1_and_ranks array: we minimise the distance first and
# break ties by choosing the lowest rank.
owned_ref_cell_dists_l1_and_ranks = parent_mesh.comm.allreduce(
ref_cell_dists_l1_and_ranks, op=array_lexicographic_mpi_op
)
# switch ranks back to positive
owned_ref_cell_dists_l1_and_ranks[:, 1] = np.abs(
owned_ref_cell_dists_l1_and_ranks[:, 1]
)
ref_cell_dists_l1_and_ranks[:, 1] = np.abs(ref_cell_dists_l1_and_ranks[:, 1])
ranks = np.abs(ranks)
owned_ref_cell_dists_l1 = owned_ref_cell_dists_l1_and_ranks[:, 0]
owned_ranks = owned_ref_cell_dists_l1_and_ranks[:, 1]
changed_ref_cell_dists_l1 = owned_ref_cell_dists_l1 != ref_cell_dists_l1
changed_ranks = owned_ranks != ranks
# If distance has changed the the point is not in local mesh partition
# since some other cell on another rank is closer.
locally_visible[changed_ref_cell_dists_l1] = False
parent_cell_nums[changed_ref_cell_dists_l1] = -1
# If the rank has changed but the distance hasn't then there was a tie
# break and we need to search for the point again, this time disallowing
# the previously identified cell: if we match the identified owned_rank AND
# the distance is the same then we have found the correct cell. If we
# cannot make a match to owned_rank and distance then we can't see the
# point.
changed_ranks_tied = changed_ranks & ~changed_ref_cell_dists_l1
if any(changed_ranks_tied):
cells_ignore_T = np.asarray([np.copy(parent_cell_nums)])
while any(changed_ranks_tied):
(
parent_cell_nums[changed_ranks_tied],
new_reference_coords,
ref_cell_dists_l1[changed_ranks_tied],
) = parent_mesh.locate_cells_ref_coords_and_dists(
coords_global[changed_ranks_tied],
tolerance,
cells_ignore=cells_ignore_T.T[changed_ranks_tied, :],
)
# delete extra dimension if necessary
if parent_mesh.geometric_dimension() > parent_mesh.topological_dimension():
new_reference_coords = new_reference_coords[:, : parent_mesh.topological_dimension()]
reference_coords[changed_ranks_tied, :] = new_reference_coords
# remove newly lost points
locally_visible[changed_ranks_tied] = (
parent_cell_nums[changed_ranks_tied] != -1
)
changed_ranks_tied &= locally_visible
# if new ref_cell_dists_l1 > owned_ref_cell_dists_l1 then we should
# disregard the point.
locally_visible[changed_ranks_tied] &= (
ref_cell_dists_l1[changed_ranks_tied]
<= owned_ref_cell_dists_l1[changed_ranks_tied]
)
changed_ranks_tied &= locally_visible
# update the identified rank
ranks[changed_ranks_tied] = visible_ranks[
parent_cell_nums[changed_ranks_tied]
]
# if the rank now matches then we have found the correct cell
locally_visible[changed_ranks_tied] &= (
owned_ranks[changed_ranks_tied] == ranks[changed_ranks_tied]
)
# remove these rank matches from changed_ranks_tied
changed_ranks_tied &= ~locally_visible
# add more cells to ignore
cells_ignore_T = np.vstack((
cells_ignore_T,
parent_cell_nums)
)
# Any ranks which are still np.inf are not in the mesh
missing_global_idxs = np.where(owned_ranks == np.inf)[0]
if not remove_missing_points:
missing_coords_idxs_on_rank = np.where(
(owned_ranks == np.inf) & (input_ranks_global == parent_mesh.comm.rank)
)[0]
locally_visible[missing_coords_idxs_on_rank] = True
parent_cell_nums[missing_coords_idxs_on_rank] = -1
reference_coords[missing_coords_idxs_on_rank, :] = np.nan
owned_ranks[missing_coords_idxs_on_rank] = parent_mesh.comm.size + 1
if exclude_halos and parent_mesh.comm.size > 1:
off_rank_coords_idxs = np.where(
(owned_ranks != parent_mesh.comm.rank)
& (owned_ranks != parent_mesh.comm.size + 1)
)[0]
locally_visible[off_rank_coords_idxs] = False
coords_embedded = np.compress(locally_visible, coords_global, axis=0)
global_idxs = np.compress(locally_visible, global_idxs_global, axis=0)
reference_coords = np.compress(locally_visible, reference_coords, axis=0)
parent_cell_nums = np.compress(locally_visible, parent_cell_nums, axis=0)
owned_ranks = np.compress(locally_visible, owned_ranks, axis=0).astype(int)
input_ranks = np.compress(locally_visible, input_ranks_global, axis=0)
input_coords_idxs = np.compress(locally_visible, input_coords_idxs_global, axis=0)
return (
coords_embedded,
global_idxs,
reference_coords,
parent_cell_nums,
owned_ranks,
input_ranks,
input_coords_idxs,
missing_global_idxs,
)
def _swarm_original_ordering_preserve(
comm,
swarm,
original_ordering_coords_local,
plex_parent_cell_nums_local,
global_idxs_local,
reference_coords_local,
parent_cell_nums_local,
ranks_local,
input_ranks_local,
input_idxs_local,
extruded,
layers,
):
"""
Create a DMSwarm with the original ordering of the coordinates in a vertex
only mesh embedded using ``_parent_mesh_embedding`` whilst preserving the
values of all other DMSwarm fields except any added fields.
"""
ncoords_local = len(reference_coords_local)
gdim = original_ordering_coords_local.shape[1]
tdim = reference_coords_local.shape[1]
# Gather everything except original_ordering_coords_local from all mpi
# ranks
ncoords_local_allranks = comm.allgather(ncoords_local)
ncoords_global = sum(ncoords_local_allranks)
parent_cell_nums_global = np.empty(
ncoords_global, dtype=parent_cell_nums_local.dtype
)
comm.Allgatherv(
parent_cell_nums_local, (parent_cell_nums_global, ncoords_local_allranks)
)
plex_parent_cell_nums_global = np.empty(
ncoords_global, dtype=plex_parent_cell_nums_local.dtype
)
comm.Allgatherv(
plex_parent_cell_nums_local,
(plex_parent_cell_nums_global, ncoords_local_allranks),
)
reference_coords_local_size = np.array(reference_coords_local.size)
reference_coords_local_sizes = np.empty(comm.size, dtype=int)
comm.Allgatherv(reference_coords_local_size, reference_coords_local_sizes)
reference_coords_global = np.empty(
(ncoords_global, reference_coords_local.shape[1]),
dtype=reference_coords_local.dtype,
)
comm.Allgatherv(
reference_coords_local, (reference_coords_global, reference_coords_local_sizes)
)
global_idxs_global = np.empty(ncoords_global, dtype=global_idxs_local.dtype)
comm.Allgatherv(global_idxs_local, (global_idxs_global, ncoords_local_allranks))
ranks_global = np.empty(ncoords_global, dtype=ranks_local.dtype)
comm.Allgatherv(ranks_local, (ranks_global, ncoords_local_allranks))
input_ranks_global = np.empty(ncoords_global, dtype=input_ranks_local.dtype)
comm.Allgatherv(input_ranks_local, (input_ranks_global, ncoords_local_allranks))
input_idxs_global = np.empty(ncoords_global, dtype=input_idxs_local.dtype)
comm.Allgatherv(input_idxs_local, (input_idxs_global, ncoords_local_allranks))
# Sort by global index, which will be in rank order (they probably already
# are but we can't rely on that)
global_idxs_global_order = np.argsort(global_idxs_global)
sorted_parent_cell_nums_global = parent_cell_nums_global[global_idxs_global_order]
sorted_plex_parent_cell_nums_global = plex_parent_cell_nums_global[
global_idxs_global_order
]
sorted_reference_coords_global = reference_coords_global[
global_idxs_global_order, :
]
sorted_global_idxs_global = global_idxs_global[global_idxs_global_order]
sorted_ranks_global = ranks_global[global_idxs_global_order]
sorted_input_ranks_global = input_ranks_global[global_idxs_global_order]
sorted_input_idxs_global = input_idxs_global[global_idxs_global_order]
# Check order is correct - we can probably remove this eventually since it's
# quite expensive
if not np.all(sorted_input_ranks_global[1:] >= sorted_input_ranks_global[:-1]):
raise ValueError("Global indexing has not ordered the ranks as expected")
# get rid of any duplicated global indices (i.e. points in halos)
unique_global_idxs, unique_idxs = np.unique(
sorted_global_idxs_global, return_index=True
)
unique_parent_cell_nums_global = sorted_parent_cell_nums_global[unique_idxs]
unique_plex_parent_cell_nums_global = sorted_plex_parent_cell_nums_global[
unique_idxs
]
unique_reference_coords_global = sorted_reference_coords_global[unique_idxs, :]
unique_ranks_global = sorted_ranks_global[unique_idxs]
unique_input_ranks_global = sorted_input_ranks_global[unique_idxs]
unique_input_idxs_global = sorted_input_idxs_global[unique_idxs]
# save the points on this rank which match the input rank ready for output
input_ranks_match = unique_input_ranks_global == comm.rank
output_global_idxs = unique_global_idxs[input_ranks_match]
output_parent_cell_nums = unique_parent_cell_nums_global[input_ranks_match]
output_plex_parent_cell_nums = unique_plex_parent_cell_nums_global[
input_ranks_match
]
output_reference_coords = unique_reference_coords_global[input_ranks_match, :]
output_ranks = unique_ranks_global[input_ranks_match]
output_input_ranks = unique_input_ranks_global[input_ranks_match]
output_input_idxs = unique_input_idxs_global[input_ranks_match]
if extruded:
(
output_base_parent_cell_nums,
output_extrusion_heights,
) = _parent_extrusion_numbering(output_parent_cell_nums, layers)
else:
output_base_parent_cell_nums = None
output_extrusion_heights = None
# check if the input indices are in order from zero - this can also probably
# be removed eventually because, again, it's expensive.
if not np.array_equal(output_input_idxs, np.arange(output_input_idxs.size)):
raise ValueError(
"Global indexing has not ordered the input indices as expected."
)
if len(output_global_idxs) != len(original_ordering_coords_local):
raise ValueError(
"The number of local global indices which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_parent_cell_nums) != len(original_ordering_coords_local):
raise ValueError(
"The number of local parent cell numbers which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_plex_parent_cell_nums) != len(original_ordering_coords_local):
raise ValueError(
"The number of local plex parent cell numbers which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_reference_coords) != len(original_ordering_coords_local):
raise ValueError(
"The number of local reference coordinates which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_ranks) != len(original_ordering_coords_local):
raise ValueError(
"The number of local rank numbers which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_input_ranks) != len(original_ordering_coords_local):
raise ValueError(
"The number of local input rank numbers which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_input_idxs) != len(original_ordering_coords_local):
raise ValueError(
"The number of local input indices which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if extruded:
if len(output_base_parent_cell_nums) != len(original_ordering_coords_local):
raise ValueError(
"The number of local base parent cell numbers which will be used to make the swarm do not match the input number of original ordering coordinates."
)
if len(output_extrusion_heights) != len(original_ordering_coords_local):
raise ValueError(
"The number of local extrusion heights which will be used to make the swarm do not match the input number of original ordering coordinates."
)
return _dmswarm_create(
[],
comm,
swarm,
original_ordering_coords_local,
output_plex_parent_cell_nums,
output_global_idxs,
output_reference_coords,
output_parent_cell_nums,
output_ranks,
output_input_ranks,
output_input_idxs,
output_base_parent_cell_nums,
output_extrusion_heights,
extruded,
tdim,
gdim,
)
[docs]
def RelabeledMesh(mesh, indicator_functions, subdomain_ids, **kwargs):
"""Construct a new mesh that has new subdomain ids.
:arg mesh: base :class:`~.MeshGeometry` object using which the
new one is constructed.
:arg indicator_functions: list of indicator functions that mark
selected entities (cells or facets) as 1; must use
"DP"/"DQ" (degree 0) functions to mark cell entities and
"P" (degree 1) functions in 1D or "HDiv Trace" (degree 0) functions
in 2D or 3D to mark facet entities.
Can use "Q" (degree 2) functions for 3D hex meshes until
we support "HDiv Trace" elements on hex.
:arg subdomain_ids: list of subdomain ids associated with
the indicator functions in indicator_functions; thus,
must have the same length as indicator_functions.
:kwarg name: optional name of the output mesh object.
"""
import firedrake.function as function
if not isinstance(mesh, MeshGeometry):
raise TypeError(f"mesh must be a MeshGeometry, not a {type(mesh)}")
tmesh = mesh.topology
if isinstance(tmesh, VertexOnlyMeshTopology):
raise NotImplementedError("Currently does not work with VertexOnlyMesh")
elif isinstance(tmesh, ExtrudedMeshTopology):
raise NotImplementedError("Currently does not work with ExtrudedMesh; use RelabeledMesh() on the base mesh and then extrude")
if not isinstance(indicator_functions, Sequence) or \
not isinstance(subdomain_ids, Sequence):
raise ValueError("indicator_functions and subdomain_ids must be `list`s or `tuple`s of the same length")
if len(indicator_functions) != len(subdomain_ids):
raise ValueError("indicator_functions and subdomain_ids must be `list`s or `tuple`s of the same length")
if len(indicator_functions) == 0:
raise RuntimeError("At least one indicator function must be given")
for f in indicator_functions:
if not isinstance(f, function.Function):
raise TypeError(f"indicator functions must be instances of function.Function: got {type(f)}")
if f.function_space().mesh() is not mesh:
raise ValueError(f"indicator functions must be defined on {mesh}")
for subid in subdomain_ids:
if not isinstance(subid, numbers.Integral):
raise TypeError(f"subdomain id must be an integer: got {subid}")
name1 = kwargs.get("name", DEFAULT_MESH_NAME)
plex = tmesh.topology_dm
# Clone plex: plex1 will share topology with plex.
plex1 = plex.clone()
plex1.setName(_generate_default_mesh_topology_name(name1))
# Remove pyop2 labels.
plex1.removeLabel("pyop2_core")
plex1.removeLabel("pyop2_owned")
plex1.removeLabel("pyop2_ghost")
# Do not remove "exterior_facets" and "interior_facets" labels;
# those should be reused as the mesh has already been distributed (if size > 1).
for label_name in [dmcommon.CELL_SETS_LABEL, dmcommon.FACE_SETS_LABEL]:
if not plex1.hasLabel(label_name):
plex1.createLabel(label_name)
for f, subid in zip(indicator_functions, subdomain_ids):
elem = f.topological.function_space().ufl_element()
if elem.reference_value_shape != ():
raise RuntimeError(f"indicator functions must be scalar: got {elem.reference_value_shape} != ()")
if elem.family() in {"Discontinuous Lagrange", "DQ"} and elem.degree() == 0:
# cells
height = 0
dmlabel_name = dmcommon.CELL_SETS_LABEL
elif (elem.family() == "HDiv Trace" and elem.degree() == 0 and mesh.topological_dimension() > 1) or \
(elem.family() == "Lagrange" and elem.degree() == 1 and mesh.topological_dimension() == 1) or \
(elem.family() == "Q" and elem.degree() == 2 and mesh.topology.ufl_cell().cellname() == "hexahedron"):
# facets
height = 1
dmlabel_name = dmcommon.FACE_SETS_LABEL
else:
raise ValueError(f"indicator functions must be 'DP' or 'DQ' (degree 0) to mark cells and 'P' (degree 1) in 1D or 'HDiv Trace' (degree 0) in 2D or 3D to mark facets: got (family, degree) = ({elem.family()}, {elem.degree()})")
# Clear label stratum; this is a copy, so safe to change.
plex1.clearLabelStratum(dmlabel_name, subid)
dmlabel = plex1.getLabel(dmlabel_name)
section = f.topological.function_space().dm.getSection()
dmcommon.mark_points_with_function_array(plex, section, height, f.dat.data_ro_with_halos.real.astype(IntType), dmlabel, subid)
distribution_parameters_noop = {"partition": False,
"overlap_type": (DistributedMeshOverlapType.NONE, 0)}
reorder_noop = None
tmesh1 = MeshTopology(plex1, name=plex1.getName(), reorder=reorder_noop,
distribution_parameters=distribution_parameters_noop,
perm_is=tmesh._dm_renumbering,
distribution_name=tmesh._distribution_name,
permutation_name=tmesh._permutation_name,
comm=tmesh.comm)
return make_mesh_from_mesh_topology(tmesh1, name1)
[docs]
@PETSc.Log.EventDecorator()
def SubDomainData(geometric_expr):
"""Creates a subdomain data object from a boolean-valued UFL expression.
The result can be attached as the subdomain_data field of a
:class:`ufl.Measure`. For example:
.. code-block:: python3
x = mesh.coordinates
sd = SubDomainData(x[0] < 0.5)
assemble(f*dx(subdomain_data=sd))
"""
import firedrake.functionspace as functionspace
import firedrake.projection as projection
# Find domain from expression
m = extract_unique_domain(geometric_expr)
# Find selected cells
fs = functionspace.FunctionSpace(m, 'DG', 0)
f = projection.project(ufl.conditional(geometric_expr, 1, 0), fs)
# Create cell subset
indices, = np.nonzero(f.dat.data_ro_with_halos > 0.5)
return op2.Subset(m.cell_set, indices)
[docs]
def Submesh(mesh, subdim, subdomain_id, label_name=None, name=None):
"""Construct a submesh from a given mesh.
Parameters
----------
mesh : MeshGeometry
Parent mesh (`MeshGeometry`).
subdim : int
Topological dimension of the submesh.
subdomain_id : int
Subdomain ID representing the submesh.
label_name : str
Name of the label to search ``subdomain_id`` in.
name : str
Name of the submesh.
Returns
-------
MeshGeometry
Submesh.
Notes
-----
Currently, one can only make submeshes that have the same
topological dimension as the parent mesh.
Examples
--------
.. code-block:: python3
dim = 2
mesh = RectangleMesh(2, 1, 2., 1., quadrilateral=True)
x, y = SpatialCoordinate(mesh)
DQ0 = FunctionSpace(mesh, "DQ", 0)
indicator_function = Function(DQ0).interpolate(conditional(x > 1., 1, 0))
mesh.mark_entities(indicator_function, 999)
mesh = RelabeledMesh(mesh, [indicator_function], [999])
subm = Submesh(mesh, dim, 999)
V0 = FunctionSpace(mesh, "CG", 1)
V1 = FunctionSpace(subm, "CG", 1)
V = V0 * V1
u = TrialFunction(V)
v = TestFunction(V)
u0, u1 = split(u)
v0, v1 = split(v)
dx0 = Measure("dx", domain=mesh)
dx1 = Measure("dx", domain=subm)
a = inner(u1, v0) * dx0(999) + inner(u0, v1) * dx1
A = assemble(a)
"""
if not isinstance(mesh, MeshGeometry):
raise TypeError("Parent mesh must be a `MeshGeometry`")
if isinstance(mesh.topology, ExtrudedMeshTopology):
raise NotImplementedError("Can not create a submesh of an ``ExtrudedMesh``")
elif isinstance(mesh.topology, VertexOnlyMeshTopology):
raise NotImplementedError("Can not create a submesh of a ``VertexOnlyMesh``")
mesh.topology.init()
plex = mesh.topology_dm
dim = plex.getDimension()
if subdim != dim:
raise NotImplementedError(f"Found submesh dim ({subdim}) != parent dim ({dim})")
if label_name is None:
label_name = dmcommon.CELL_SETS_LABEL
name = name or _generate_default_submesh_name(mesh.name)
subplex = dmcommon.submesh_create(plex, label_name, subdomain_id)
subplex.setName(_generate_default_mesh_topology_name(name))
if subplex.getDimension() != subdim:
raise RuntimeError(f"Found subplex dim ({subplex.getDimension()}) != expected ({subdim})")
submesh = Mesh(subplex, name=name, distribution_parameters={"partition": False,
"overlap_type": (DistributedMeshOverlapType.NONE, 0)})
submesh.topology.submesh_parent = mesh.topology
submesh.submesh_parent = mesh
submesh.init()
return submesh
