cache visible_ranks on topology (#5183)

* cache on topology

* make private

Author: leo-collins

firedrake/mesh.py

@@ -1764,6 +1764,18 @@ def trans_mesh_entity_map(self, base_mesh, base_integral_type, base_subdomain_id
             composed_map, integral_type, _ = self.submesh_map_composed(base_mesh, base_integral_type, base_subset_points)
             return composed_map, integral_type
 
+    @cached_property
+    def _visible_ranks(self):
+        # Get parent mesh rank ownership information.
+        visible_ranks = np.empty(self.cell_set.total_size, dtype=IntType)
+        visible_ranks[:self.cell_set.size] = self.comm.rank
+        visible_ranks[self.cell_set.size:] = -1
+        # Halo exchange the visible ranks so that each rank knows which ranks can see each cell.
+        dmcommon.exchange_cell_orientations(
+            self.topology_dm, self._cell_numbering, visible_ranks
+        )
+        return visible_ranks
+
 
 class ExtrudedMeshTopology(MeshTopology):
     """Representation of an extruded mesh topology."""
@@ -4412,13 +4424,7 @@ def _parent_mesh_embedding(
         reference_coords = reference_coords[:, : parent_mesh.topological_dimension]
 
     # Get parent mesh rank ownership information.
-    visible_ranks = np.empty(parent_mesh.cell_set.total_size, dtype=IntType)
-    visible_ranks[:parent_mesh.cell_set.size] = parent_mesh.comm.rank
-    visible_ranks[parent_mesh.cell_set.size:] = -1
-    # Halo exchange the visible ranks so that each rank knows which ranks can see each cell.
-    dmcommon.exchange_cell_orientations(
-        parent_mesh.topology.topology_dm, parent_mesh.topology._cell_numbering, visible_ranks
-    )
+    visible_ranks = parent_mesh._visible_ranks
     locally_visible = parent_cell_nums != -1
 
     if parent_mesh.extruded: