Redistributed Submesh and MeshHierarchy

[pbrubeck]

Summary

Mesh redistribution is now a Submesh of the mesh it was redistributed from, rather than an ad-hoc redist attribute bolted onto the mesh.

• Submesh(..., redistribute=True) repartitions instead of inheriting the parent's parallel distribution. It works both for subdomain_id=None (the whole mesh, which is what a redistributed MeshHierarchy needs) and for a proper subdomain. The child records a submesh_point_sf pushing the parent's plex points onto its own, so submesh_parent/submesh_ancestors make every consumer parent-aware.
• Entity orientations are preserved. The redistributed mesh inherits the parent's universal vertex numbering, and its cell orientations on quadrilaterals/hexahedra, so cell closures are ordered identically on both sides. Reference values therefore remain valid across the redistribution and RT/BDM/N1curl/RTCF/RTCE transfer exactly, instead of picking up sign and permutation flips.
• RedistributedMeshTransfer and firedrake/redist.py are gone. Data moves between the two DOF layouts through Function.assign, which composes the point SF with the two function spaces' PETSc sections into a section SF. This is the first step towards unifying non-matching DOF layouts — RestrictedFunctionSpace and same-distribution Submesh — on one mechanism; those two still go through the cell_node_map permutation for now.
• Assembling or interpolating a redistributed mesh alongside its parent raises NotImplementedError, since entity maps are only defined when the two share a distribution.

API

rmesh = Submesh(mesh, redistribute=True)            # whole mesh, repartitioned
rmesh.submesh_parent is mesh                        # True; mesh.has_empty_rank was why
Function(V_rmesh).assign(u)                         # parent -> redistributed
Function(V_mesh).assign(u_r, allow_missing_dofs=True)   # and back
assemble(inner(u, u) * dx(domain=rmesh))            # NotImplementedError

sub = Submesh(mesh, subdomain_id=1, redistribute=True)  # a proper subdomain too

mh = MeshHierarchy(base, 3)                         # redistribute=True by default
prolong(uc, uf)                                     # transfers on the parent, then assigns

Testing

Redistribution round-trips exactly (≤1e-16) for tri/quad/tet/hex × CG/DG/RT/BDM/N1curl/RTCF/RTCE on 1–3 ranks, including curved (P2) and periodic (DG1) coordinate fields. tests/firedrake/submesh and tests/firedrake/multigrid pass at 1, 2, 3 and 4 ranks.

RedistributedMeshTransfer, which this PR removes, was borrowed from @wence-'s unmerged branch main...wence/feature/redist-mg

🤖 Generated with Claude Code

[connorjward]

Is this ready for review? You seem to still be working on it.

[pbrubeck]

Is this ready for review? You seem to still be working on it.

It is ready you can review it, but ideally we should merge #5213 and #5215 first.

I'm adding the review suggestions from the meeting, and I have a genuine question: should we introduce a new redistribute kwarg or should we pass it through the distribution_parameters?

[pbrubeck]

Should we move this to Function.assign()? Maybe we can do it more generalically for Submesh, RestrictedFunctionSpace, and RestributedMesh

[connorjward]

Yes I think so.

[pbrubeck]

We now can redistribute a Mesh/Submesh. I am only adding support for assign across the submesh and its parent, which is what redistributed multigrid needs.

[pbrubeck]

we should only call _unoverlapped_dm on the base mesh