Redistributed Submesh and MeshHierarchy

[pbrubeck]

Stack

This is PR 2 of 3: #5288 (adaptive-multigrid) -> this PR (mesh-redistribution) -> #5287 (assign-submesh-restricted).

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(mesh, redistribute=True) repartitions instead of inheriting the parent's parallel
  distribution, for both subdomain_id=None (the whole mesh, as needed by a redistributed
  MeshHierarchy) and a proper subdomain (co-dimension 0 only). The child records a
  submesh_point_sf pushing the parent's plex points onto its own; submesh_shares_distribution
  tells consumers (assembly, interpolation) whether two related meshes still share a distribution.
• Entity orientations are preserved across redistribution: the child inherits the parent's universal
  vertex numbering (dmcommon.submesh_vertex_numbering) and quadrilateral/hexahedral cell
  orientations (dmcommon.submesh_cell_orientations), so cell closures are ordered identically on
  both sides and RT/BDM/N1curl/RTCF/RTCE data transfers exactly instead of picking up sign/permutation
  flips.
• Assembling or interpolating across a redistributed mesh and its parent raises NotImplementedError,
  since entity maps are only defined when the two share a distribution; use Function.assign instead.
• MeshHierarchy (redistribute=True by default) and refine_marked_elements/HierarchyBase.adapt
  redistribute a refined/adapted mesh via Submesh whenever it would otherwise leave empty ranks.
  firedrake/mg/interface.py (prolong/restrict/inject) and firedrake/mg/utils.py
  (transfer_mesh, set_dm_refine_level, set_level) route transfers through the pre-redistribution
  mesh, then assign onto the redistributed one.

Testing

Redistribution round-trips exactly (<= 1e-16) for tri/quad/tet/hex x CG/DG/RT/BDM/N1curl/RTCF/RTCE on
1-3 ranks, including curved (P2) and periodic (DG1) coordinate fields
(tests/firedrake/submesh/test_submesh_assign.py). tests/firedrake/multigrid/test_redist_mesh.py
covers uniform and adaptive MeshHierarchy redistribution (2/3/4 ranks); test_submesh_assemble.py
covers the NotImplementedError paths. All pass at every process count their markers declare.

🤖 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.