refactor(readability): Wave D smoothing — mover dedup, renames, MPI helpers, package split (D-01..D-13)

.claude/skills/adaptive-meshing/SKILL.md

@@ -126,7 +126,7 @@ strictly-positive nodal values — evaluates to **NEGATIVE garbage** (even at it
 DOFs) → non-SPD → the mover wrecks the mesh. FIX (both):
 - **`8a9d2ff2`** (refresh `_nav_coords` + projected normals on every deform) —
   the real fix; makes `function.evaluate`/`points_in_domain` track deformation.
-- **Monotone RBF metric bake** (in `_winslow_mmpde`): Shepard-interpolate the
+- **Monotone RBF metric bake** (in `_mmpde_mover`, formerly `_winslow_mmpde`): Shepard-interpolate the
   metric from its **positive nodal values** — a convex average is guaranteed ≥0
   (monotone) + fast (no cell-location). Use RBF for the metric; it doesn't need
   high-precision eval.

src/underworld3/discretisation/remesh.py

@@ -226,7 +226,8 @@ def remesh_with_field_transfer(
     """Adapt-op contract: run a mover and transfer every registered var.
 
     ``do_move`` is a closure that performs the actual coordinate move —
-    typically the body of a ``_winslow_*`` mover, the OT step, or a
+    typically the body of one of the ``underworld3.meshing.smoothing``
+    package movers (spring / MA / OT / anisotropic / MMPDE) or a
     ``follow_metric`` mover. It is expected to call
     :meth:`Mesh._deform_mesh` one or more times and leave the mesh
     sitting at the final adapted positions. ``do_move`` MUST NOT touch

src/underworld3/meshing/_ot_adapt.py

@@ -5,7 +5,8 @@
 reusable library function. The public entry point is :meth:`Mesh.OT_adapt`
 (see ``discretisation/discretisation_mesh.py``); this module holds the
 algorithm and the boundary-slip helpers it shares with the OT mover
-(``_winslow_equidistribute`` in ``smoothing.py``).
+(``_ot_improvement_step`` in the ``underworld3.meshing.smoothing``
+package, ``smoothing/monge_ampere.py``).
 
 The algorithm, per adapt event: