Submesh: support tuple subdomain_id

firedrake/cython/dmcommon.pyx

@@ -2203,11 +2203,11 @@ def _get_expanded_dm_dg_coords(dm: PETSc.DM, ndofs: np.ndarray):
 
 def _get_periodicity(dm: PETSc.DM) -> tuple[tuple[bool, bool], ...]:
     """Return mesh periodicity information.
-    
+
     This function returns a 2-tuple of bools per dimension where the first entry indicates
     whether the mesh is periodic in that dimension, and the second indicates whether the
     mesh is single-cell periodic in that dimension.
-    
+
     """
     cdef:
         const PetscReal *maxCell, *L
@@ -4325,3 +4325,24 @@ def get_dm_cell_types(PETSc.DM dm):
     return tuple(
         polytope_type_enum for polytope_type_enum, found in enumerate(found_all) if found
     )
+
+
+def intersectIS(PETSc.IS i1, PETSc.IS i2):
+    """Return the intersection of two IS objects.
+
+    Parameters
+    ----------
+    i1 : PETSc.IS
+        The first IS.
+    i2 : PETSc.IS
+        The second IS.
+
+    Returns
+    -------
+    PETSc.IS
+        A PETSc.IS with the intersection.
+
+    """
+    cdef PETSc.IS iout = PETSc.IS()
+    CHKERR(ISIntersect(i1.iset, i2.iset, &iout.iset))
+    return iout

firedrake/cython/petschdr.pxi

@@ -142,6 +142,7 @@ cdef extern from "petscis.h" nogil:
     PetscErrorCode ISLocalToGlobalMappingGetBlockIndices(PETSc.PetscLGMap, const PetscInt**)
     PetscErrorCode ISLocalToGlobalMappingRestoreBlockIndices(PETSc.PetscLGMap, const PetscInt**)
     PetscErrorCode ISDestroy(PETSc.PetscIS*)
+    PetscErrorCode ISIntersect(PETSc.PetscIS, PETSc.PetscIS, PETSc.PetscIS*)
 
 cdef extern from "petscsf.h" nogil:
     struct PetscSFNode_:

firedrake/mesh.py

@@ -25,7 +25,7 @@
 from pyop2.mpi import (
     MPI, COMM_WORLD, temp_internal_comm
 )
-from functools import cached_property
+from functools import cached_property, reduce
 from pyop2.utils import as_tuple
 import petsctools
 from petsctools import OptionsManager, get_external_packages
@@ -4806,10 +4806,12 @@ def Submesh(mesh, subdim=None, subdomain_id=None, label_name=None, name=None, ig
     subdim : int | None
         Topological dimension of the submesh.
         Defaults to ``mesh.topological_dimension``.
-    subdomain_id : int | None
+    subdomain_id : int | Sequence | None
         Subdomain ID representing the submesh.
-        If `None` the submesh will cover the entire domain.
-        This is useful to obtain a codim-1 submesh over all facets or
+        If multiple subdomain IDs are provided, their union is taken.
+        If nested lists of subdomain IDs are provided, their intersection is taken.
+        If `None` the submesh will cover the entire domain,
+        this is useful to obtain a codim-1 submesh over all facets or
         a submesh over a different communicator.
     label_name : str | None
         Name of the label to search ``subdomain_id`` in.
@@ -4852,13 +4854,70 @@ def Submesh(mesh, subdim=None, subdomain_id=None, label_name=None, name=None, ig
     ridges to be contained in the quad mesh are shared by at most two
     facets to make the quad mesh orientation algorithm work.
 
+    Examples
+    --------
+    >>> mesh = UnitSquareMesh(4, 4)
+    >>> x, y = SpatialCoordinate(mesh)
+    >>> DG = FunctionSpace(mesh, "DG", 0)
+    >>> DGT = FunctionSpace(mesh, "DGT", 0)
+
+    Mark a cell subdomain and construct a codim-0 submesh from all cells in the subdomain
+
+    >>> cell_marker = assemble(interpolate(conditional(lt(x, 0.5), 1, 0), DG))
+    >>> mesh.mark_entities(cell_marker, 111)
+    >>> submesh = Submesh(mesh, subdomain_id=111)
+
+    Mark a facet subdomain and construct a codim-1 submesh from all facets in the subdomain
+
+    >>> facet_marker = assemble(interpolate(conditional(lt(abs(x-0.5), 1E-12), 1, 0), DGT))
+    >>> mesh.mark_entities(facet_marker, 222)
+    >>> submesh = Submesh(mesh, subdim=mesh.topological_dimension-1, subdomain_id=222)
+
+    Construct a codim-0 submesh of the union of multiple subdomains by passing a list
+
+    >>> mesh.mark_entities(assemble(interpolate(conditional(lt(x, 0.5), 1, 0), DG)), 1)
+    >>> mesh.mark_entities(assemble(interpolate(conditional(lt(y, 0.5), 1, 0), DG)), 2)
+    >>> submesh = Submesh(mesh, subdomain_id=[1, 2])
+
+    Construct a codim-0 submesh of the intersection of multiple subdomains by passing a nested list
+
+    >>> submesh = Submesh(mesh, subdomain_id=[(1, 2)])
+
+    Construct a codim-1 submesh of all the facets (the skeleton mesh)
+
+    >>> submesh = Submesh(mesh, subdim=1)
+
+    Construct a codim-1 submesh of the entire boundary
+
+    >>> submesh = Submesh(mesh, subdomain_id="on_boundary")
+
+    Construct a codim-1 submesh of the union of multiple boundaries
+
+    >>> submesh = Submesh(mesh, subdim=mesh.topological_dimension-1, subdomain_id=[1, 2, 3])
+
+    Construct a codim-0 submesh of the part of the mesh owned by each MPI rank
+
+    >>> submesh = Submesh(mesh, ignore_halo=True, comm=COMM_SELF)
+
     """
     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``")
+
+    if subdomain_id == "on_boundary":
+        if subdim is None:
+            subdim = mesh.topological_dimension - 1
+        elif subdim != mesh.topological_dimension - 1:
+            raise ValueError('subdomain_id="on_boundary" requires subdim=dim-1')
+        if label_name is None:
+            label_name = "exterior_facets"
+        elif label_name != "exterior_facets":
+            raise ValueError('subdomain_id="on_boundary" requires label_name="exterior_facets"')
+        subdomain_id = 1
+
     if subdim is None:
         subdim = mesh.topological_dimension
     plex = mesh.topology_dm
@@ -4876,15 +4935,53 @@ def Submesh(mesh, subdim=None, subdomain_id=None, label_name=None, name=None, ig
             label_name = dmcommon.CELL_SETS_LABEL
         elif subdim == dim - 1:
             label_name = dmcommon.FACE_SETS_LABEL
+
+    # Parse non-integer subdomain_id
+    if isinstance(subdomain_id, str):
+        raise ValueError(f"Submesh construction got invalid subdomain_id {subdomain_id}.")
+    elif isinstance(subdomain_id, Sequence):
+        label = plex.getLabel(label_name)
+        if subdim != dim:
+            plex.labelComplete(label)
+
+        def get_points(sub):
+            if sub == "on_boundary":
+                return plex.getStratumIS("exterior_facets", 1)
+            elif isinstance(sub, str):
+                raise ValueError(f"Submesh construction got invalid subdomain_id {sub}.")
+            else:
+                return label.getStratumIS(sub)
+
+        # Take the union of the labels in the list
+        iset = PETSc.IS().createGeneral([], comm=mesh.comm)
+        for sub in subdomain_id:
+            if isinstance(sub, Sequence) and not isinstance(sub, str):
+                # Take the intersection of the labels from nested lists
+                if len(sub) == 0:
+                    continue
+                cur = reduce(dmcommon.intersectIS, map(get_points, sub))
+            else:
+                cur = get_points(sub)
+            iset = iset.union(cur)
+        # Create a temporary label
+        label_name = "temp_label"
+        subdomain_id = 1
+        plex.createLabel(label_name)
+        label = plex.getLabel(label_name)
+        label.setStratumIS(subdomain_id, iset)
+
     subplex = dmcommon.submesh_create(plex, subdim, label_name, subdomain_id, ignore_halo, comm=comm)
 
+    if label_name == "temp_label":
+        plex.removeLabel(label_name)
+
     comm = comm or mesh.comm
     name = name or _generate_default_submesh_name(mesh.name)
     subplex.setName(_generate_default_mesh_topology_name(name))
     if subplex.getDimension() != subdim:
         raise RuntimeError(f"Found subplex dim ({subplex.getDimension()}) != expected ({subdim})")
     if reorder is None:
-        # Ideally we should set perm_is = mesh.dm_reordering[label_indices]
+        # Ideally we should set perm_is = mesh._dm_renumbering[label_indices]
         reorder = mesh._did_reordering
 
     submesh = Mesh(

tests/firedrake/submesh/test_submesh_interface.py

@@ -0,0 +1,107 @@
+import pytest
+import numpy as np
+from firedrake import *
+
+
+def test_submesh_subdomain_id_union():
+    mesh = UnitSquareMesh(4, 4)
+    x, y = SpatialCoordinate(mesh)
+    M = FunctionSpace(mesh, "DG", 0)
+    m1 = Function(M).interpolate(conditional(lt(x, 0.5), 1, 0))
+    m2 = Function(M).interpolate(conditional(lt(y, 0.5), 1, 0))
+    mesh.mark_entities(m1, 111)
+    mesh.mark_entities(m2, 222)
+
+    subdomain_id = [111, 222]
+    submesh1 = Submesh(mesh, mesh.topological_dimension, subdomain_id=subdomain_id)
+
+    m3 = Function(M).interpolate(m1 + m2 - m1 * m2)
+    expected = assemble(m3*dx)
+    assert abs(assemble(1*dx(domain=submesh1)) - expected) < 1E-12
+
+    mesh.mark_entities(m3, 333)
+    submesh2 = Submesh(mesh, mesh.topological_dimension, 333)
+    assert submesh2.cell_set.size == submesh1.cell_set.size
+    assert np.allclose(submesh2.coordinates.dat.data, submesh1.coordinates.dat.data)
+
+
+def test_submesh_subdomain_id_intersection():
+    mesh = UnitSquareMesh(4, 4)
+    x, y = SpatialCoordinate(mesh)
+    M = FunctionSpace(mesh, "DG", 0)
+    m1 = Function(M).interpolate(conditional(lt(x, 0.5), 1, 0))
+    m2 = Function(M).interpolate(conditional(lt(y, 0.5), 1, 0))
+    mesh.mark_entities(m1, 111)
+    mesh.mark_entities(m2, 222)
+
+    subdomain_id = [(111, 222)]
+    submesh1 = Submesh(mesh, mesh.topological_dimension, subdomain_id=subdomain_id)
+
+    m3 = Function(M).interpolate(m1 * m2)
+    expected = assemble(m3*dx)
+    assert abs(assemble(1*dx(domain=submesh1)) - expected) < 1E-12
+
+    mesh.mark_entities(m3, 333)
+    submesh2 = Submesh(mesh, mesh.topological_dimension, 333)
+    assert submesh2.cell_set.size == submesh1.cell_set.size
+    assert np.allclose(submesh2.coordinates.dat.data, submesh1.coordinates.dat.data)
+
+
+@pytest.mark.parametrize("subdomain_id", ["on_boundary", (1, 3, 6)])
+def test_submesh_facet_subdomain_id_union(subdomain_id):
+    mesh = UnitCubeMesh(2, 2, 2)
+    submesh1 = Submesh(mesh, mesh.topological_dimension - 1, subdomain_id=subdomain_id)
+    if subdomain_id == "on_boundary":
+        area = assemble(1*ds(domain=mesh))
+    else:
+        area = assemble(1*ds(subdomain_id, domain=mesh))
+    assert abs(assemble(1*dx(domain=submesh1)) - area) < 1E-12
+
+    DGT = FunctionSpace(mesh, "DGT", 0)
+    facet_function = Function(DGT)
+    DirichletBC(DGT, 1, subdomain_id).apply(facet_function)
+    facet_value = 999
+    rmesh = RelabeledMesh(mesh, [facet_function], [facet_value])
+    submesh2 = Submesh(rmesh, mesh.topological_dimension - 1, facet_value)
+    assert submesh2.cell_set.size == submesh1.cell_set.size
+    assert np.allclose(submesh2.coordinates.dat.data, submesh1.coordinates.dat.data)
+
+
+@pytest.mark.parametrize("sub", ["cell-cell", "cell-boundary"])
+def test_submesh_facet_subdomain_id_intersection(sub):
+    if sub == "cell-cell":
+        # (x <= 0.5) & (x >= 0.5)
+        subdomain_id = [(111, 222)]
+        expected = 1
+    elif sub == "cell-boundary":
+        # (x <= 0.5) & (x == 0 | y == 0 | y == 1)
+        subdomain_id = [(111, "on_boundary")]
+        expected = 2
+
+    mesh = UnitSquareMesh(4, 4)
+    x, y = SpatialCoordinate(mesh)
+    DG = FunctionSpace(mesh, "DG", 0)
+    DGT = FunctionSpace(mesh, "DGT", 0)
+    m1 = Function(DG).interpolate(conditional(lt(x, 0.5), 1, 0))
+    m2 = Function(DG).interpolate(conditional(lt(x, 0.5), 0, 1))
+    mesh.mark_entities(m1, 111)
+    mesh.mark_entities(m2, 222)
+
+    submesh1 = Submesh(mesh, mesh.topological_dimension - 1, subdomain_id=subdomain_id, label_name="Cell Sets")
+
+    assert abs(assemble(1*dx(domain=submesh1)) - expected) < 1E-12
+
+    facet_function = Function(DGT)
+    if sub == "cell-cell":
+        facet_function.interpolate(conditional(lt(abs(x-0.5), 1E-8), 1, 0))
+    elif sub == "cell-boundary":
+        facet_function.interpolate(conditional(lt(x, 0.5), 1, 0))
+        bnd = Function(DGT)
+        DirichletBC(DGT, 1, "on_boundary").apply(bnd)
+        facet_function.dat.data[:] *= bnd.dat.data_ro[:]
+
+    facet_value = 999
+    rmesh = RelabeledMesh(mesh, [facet_function], [facet_value])
+    submesh2 = Submesh(rmesh, mesh.topological_dimension - 1, facet_value)
+    assert submesh2.cell_set.size == submesh1.cell_set.size
+    assert np.allclose(submesh2.coordinates.dat.data, submesh1.coordinates.dat.data)