Make serial submesh construction linear in the number of points

[haldaas]

Description

Submesh(mesh, comm=COMM_SELF) cost O(P^2) in the number of mesh points P.
On three ranks a UnitSquareMesh(181, 181) needed 8.9 seconds to build one
serial submesh. Four times more cells cost about ten times more time.

Cellwise BDDCPC pays this cost, because local_mesh builds one serial submesh per process.

The cost was in submesh_correct_entity_classes. A submesh on COMM_SELF has
no neighbour, so it has no ghost points and no owned points, and every
point is core. The function set that state one point at a time.
DMLabelSetValue moves the stratum into a hash set and destroys its index
set. The DMLabelHasPoint of the next iteration reads the hash set back,
sorts it, and rebuilds the index set and the bit array. Each point
therefore cost O(k log k) in the size k of the core stratum so far.

Set the three strata in bulk instead. This is the same fix as the one in
PR #5326 for the coarse and fine cell maps.

submesh_create also built a temporary label that marked every cell, and
passed it to DMPlexFilter. DMPlexFilter selects every cell by itself when
it gets no label, so the label was unnecessary. Submesh now leaves
label_name as None for a codim-0 submesh of the whole mesh. A codim-1
submesh still passes the "depth" label, because DMPlexFilter with no label
selects cells, not facets.

Measured on three ranks, for submesh_correct_entity_classes alone:

cells   before     after
  717    34 ms   0.12 ms
 2787   320 ms   0.43 ms
11059  3214 ms   1.85 ms
22023  8907 ms   3.80 ms

The whole submesh build at 11059 cells falls from 3256 ms to 71 ms.

Both paths produce the same submesh. On UnitSquareMesh(128, 128) with
three ranks, the submesh built with a label and the submesh built without
one have the same chart, the same subpoint index set, and the same
pyop2_core, pyop2_owned, pyop2_ghost and Face Sets strata.

Co-Authored-By: Claude Opus 5 noreply@anthropic.com

[connorjward]

Why did a lot of the code from fe68986 get removed? It looked relevant to the actual fix.

[pbrubeck]

Why did a lot of the code from fe68986 get removed? It looked relevant to the actual fix.

The majority of the old diff just moved a block of code into an if-statement in order to avoid passing a DMLabel to DMPlexFilter for a very minor performance win that did not extended well to codim != 0. That wasn't fixing the nonlinear cost, but gave a tiny speedup by making the constant in front of the linear term smaller.

[connorjward]

This is definitely better than before. I like having all the parsing live in one place.