[pbrubeck]

Stacked on #5541; review only the last four commits.

Summary

dS and mesh.interior_facets now work on extruded meshes, so FDM no longer needs extrude_interior_facet_maps.

Form compilation splits dS before TSFC:

 compile_form(form)
   for each split form f
+    if a mesh of f is extruded
+      replace each dS integral by dS_v + dS_h
     TSFCKernel(f)

On an extruded mesh, the interior facets are one entity set with one component per stratum:

mesh.interior_facets                       # op3.Slice with two components
├── interior_facet_vert
└── interior_facet_horiz
V.interior_facet_node_list                 # op3.Dat.from_components(vert map, horiz map)
mesh.interior_facet_local_facet_indices    # horizontal facets numbered after the vertical ones

op3.Dat.from_components is new. It builds a Dat on a set with several components from one Dat per component, in the layout of the axes. Owned entries of all components come first, so [:nfacets] still selects the owned facets.

FDM reads the interior facet maps of every mesh in the same way:

-index_facet, local_facet_data, nfacets = extrude_interior_facet_maps(V)
-index_coef, _, _ = extrude_interior_facet_maps(Gq_facet or Gq)
+nfacets = mesh.interior_facets.owned.local_size
+index_facet = V.interior_facet_node_list
+index_coef = coefficient.function_space().interior_facet_node_list
+local_facet_data = mesh.interior_facet_local_facet_indices.data_ro.reshape((-1, 2))

Evidence

• Before: assemble(Constant(1)*dS(domain=extruded_mesh)) raises ValueError: interior_facet integral cannot be used with a TensorProductCell. mesh.interior_facets raises TypeError on extruded meshes.
  After: test_interior_facet_dS_extr gets an interior facet area of 3.0 on the unit cube with 2x2x2 cells. test_interior_facet_maps_extr checks that, on every rank, the node list and the local facet numbers describe the same owned facets, and that the ranks together own the 10 interior facets once. Both pass at 1 and 3 ranks. The maps test fails at 3 ranks if the subset Dats are concatenated instead of laid out by pyop3.
• tests/pyop3/expr/tensor/test_dat.py::test_from_components checks that owned entries of all components are stored before the ghost entries.
• tests/firedrake/extrusion/ and the facet regression tests (test_facet_*.py, test_facets.py, test_interior_facets.py, test_mixed_interior_facets.py): 586 passed at 1 rank, 54 passed at 3 ranks, 0 failed.
• test_fdm.py::test_ipdg_direct_solver passes for cg/dg/rt-Box and dg/rt-Rectangle.

Merge Danger

Door: two-way

Blast Radius: mesh

_entity_axes_by_name builds every named entity set, so a regression would show up in facet assembly on all meshes. On extruded meshes, V.interior_facet_node_list returns only owned rows, while on other meshes it also returns ghost rows.

This PR was prepared with Claude Code.

🤖 Generated with Claude Code