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Mesh surgery base: conforming surfaces, reconnection repair, fault zones (2-D) - #510

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Aug 9, 2026
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Mesh surgery base: conforming surfaces, reconnection repair, fault zones (2-D)#510
lmoresi merged 29 commits into
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feature/mesh-surgery-base

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@lmoresi lmoresi commented Aug 8, 2026

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The 23-commit mesh-surgery stack that both active fault streams already build on, landed as the shared base so that neither carries it as private ancestry.

What this is

The branch point (6d494db) common to feature/mesh-reconnection and feature/fault-split-node. Landing it subtracts identical content from both feature branches and turns their eventual PRs into reviews of their own work only.

Contents, all 2-D:

  • utilities/line_cut.py — conforming surfaces cut into an existing mesh (Mesh.add_conforming_surface), serial and parallel, partition-independent; snapping with quality veto; pull_vertex_onto for tips and junctions.
  • utilities/reconnect.py — the repair passes: flip_to_reduce_max_angle (Lawson flips gated on the maximum angle, Babuska-Aziz), remove_vertices (the delete primitive, flip-first ordering measured), chart-preserving and chart-compacting rebuilds with one-exchange star-forest renumbering.
  • utilities/edge_split.py engine integration and the one-MG-level-per-doubling rule (a cut is not an MG level).
  • Mesh.cells_supporting — the fault zone as the support of the labelled facets.
  • Tests: test_0843, test_0844_line_cut (37), test_0844_reconnect_repair, test_0845, parallel suites ptest_0844_* (np=2/3 validated).
  • Docs: docs/developer/subsystems/conforming-surfaces-and-fault-zones.md and design notes.

What this deliberately excludes

The two placement commits (b907c83f, f4490493) follow separately with the reconciled reconnect.py, because feature/fault-split-node modified that file independently after this branch point and the reconciliation belongs in its own reviewable PR.

Verification

  • Dry-run merge against development: zero conflicts.
  • The stack has been exercised for weeks as the ancestry of both fault streams; the serial and parallel suites above pass on the worktree environments.

Coordination ledger: Planning hub, liaison item (2026-08-09 response) — landing sequence PR-A (this) → PR-B (placement + reconciled reconnect) → PR-C (fault-split-node).

Underworld development team with AI support from Claude Code

lmoresi added 23 commits July 30, 2026 22:24
Newest-vertex bisection picks the edge to split from a combinatorial tagging
rule and then pays a conforming closure to repair the hanging nodes that
choice creates. This engine splits the edge the geometry asks for -- the
longest edge of every cell still coarser than the metric wants -- and needs no
closure at all, because splitting an edge divides *every* incident cell at the
same new vertex. There is no hanging node to repair and no
longest-edge-propagation chain, so refinement cannot escape the marked region:
the refined band hugs the feature instead of a halo around it.

No new topology code. `uwnvb_bisect` in nvb_transform.c is already a
registered DMPlexTransform driven by a per-edge label, works on triangles and
tets, and is the primitive NVB uses for each sub-pass. This engine drives it
from Python and therefore inherits star-forest propagation, co-partitioning,
labels and coordinates for free.

Marking is on the cell DIAMETER, not (d! V)^(1/d). For bisection the two
shrink together and either will do; for any engine that reduces volume without
shortening the longest edge they diverge badly -- a measured factor of 3.2 on a
centroid-refined mesh, where the volume proxy reports the target met while the
mesh is nowhere near resolved. The test asserts the diameter.

Measured: 2-D 104 -> 412 cells in 7 passes and 3-D 1472 -> 3933 tets, identical
at np=1/2/3/4 with no over-shared facets; through mesh.adapt, a 10-level graded
MG tail with all 8 exact half-half prolongations captured (every inserted
vertex is an exact float edge midpoint) and TI Stokes converging in 10 V-cycles.
3-D reaches the pass cap -- an edge is shared by more tets so fewer are
independent per pass -- so the budget scales with dimension and warns rather
than silently truncating.

Selection is a deterministic function of geometry, not of iteration order. A
greedy sweep produced a partition-dependent mesh (412/412/463/925 cells at
np=1/2/3/4, every one of them conforming and individually plausible), so an
edge wins only if it beats every competing candidate sharing a cell, with a
midpoint-coordinate tie-break. The parallel test asserts the serial cell count
because that class of defect is invisible in a serial run.

Also fixes _cells_on_edge, which applied the 3-D edge -> face -> cell walk in
both dimensions. In 2-D an edge *is* a face, so it asked for the support of a
cell, got nothing, and reported that the edge touches no cells at all. It is
not yet called from the engine, so nothing was broken, but it fails silently
and the shape-repair work needs it.

Underworld development team with AI support from Claude Code
Reconnection is the missing third operation of the refine / swap / smooth
triple. UW3 had refine (mesh.adapt) and smooth (mesh.relax); this is swap.
Refinement chooses where a vertex goes but not how the surrounding cells
reconnect, so a cell dragged into a split at an edge it did not nominate gains
a thin child. This repairs that by Lawson flips.

The acceptance criterion is NOT Delaunay, although these are Lawson flips.
Delaunay maximises the minimum angle and says nothing about the maximum, while
the P1 interpolation bound depends on the maximum angle and not the minimum
(Babuska-Aziz). The two disagree in practice and not marginally: flipping a
gmsh-generated mesh towards Delaunay was measured to RAISE the 99th-percentile
maximum angle from 126.8 to 129.3 degrees, because gmsh optimises element shape
rather than the empty-circle property and its triangulation is locally
non-Delaunay exactly where it chose a better-shaped configuration. Since every
UW3 mesh starts from gmsh, a repair pass that can degrade one is unusable.
Gating on the angle directly makes the pass monotone: it can decline, but it
cannot make a mesh worse.

Measured on the production path (numbers in the study directory, see the module
docstring). As a post-pass it fixes shape and only shape -- decisively on a poor
base (99th-percentile maximum angle 156.0 -> 115.1 degrees on an
aspect-ratio-4 base; slivers below q=0.1 3.84% -> 0.00% on a non-Delaunay one)
and hardly at all on a gmsh base, with interpolation error barely moving either
way. Run between refinement passes it also changes where later vertices land,
because a flip changes which edge of a cell is longest, and that is worth
20-30% lower error per degree of freedom on a degraded base. The accuracy gain
is therefore a placement gain that reconnection unlocks, not a connectivity
gain.

Parallel by the frozen seam: no cavity may contain a cell incident on a shared
plex point. Measured cost 0.9-3.5% of repair sites at 56k cells and np=2..8,
halving with every halving of the target size, because repair sites scale with
the refined band while the sites a seam crosses stay O(1).

The DM is rebuilt on the SAME point chart. A 2-D flip adds and removes no
points -- the quad keeps its four vertices, five edges and two cells, and only
the diagonal edge's cone and the two cell cones change -- so preserving the
numbering lets the point star-forest transfer verbatim, labels transfer by point
id and coordinates transfer unchanged. That removes the whole
reconstruct-the-star-forest-by-matching-seam-coordinates stage, and with it the
class of defect nvb._exact_vertex_map exists to refuse. Surgery on the source DM
is not an option: DMPlexSymmetrize refuses to run on a plex that already has
supports and nothing outside DMDestroy frees them. The cone orientation
convention is derived from the edge cone every time rather than assumed, because
getting it wrong does not raise -- it silently yields wrong geometry.

repair is OFF by default, for one specific reason: edge_split alone produces a
partition-independent mesh, identical at any communicator size, and repair gives
that up, because which cavities may be flipped depends on where the partitioner
drew the seam. Conformity, orientation, volume, labels and the star-forest stay
exact at every rank count. Also note the 99th-percentile maximum angle recovers
fully under a frozen seam but the absolute maximum does not -- a few of the worst
cells sit on the seam and are exactly the untouchable ones.

Orientation and in-circle sign errors produce non-conforming meshes, so the
orientation predicate carries Shewchuk's static filter and DECLINES when it
cannot resolve a sign. Declining is always safe here because a flip is an
optimisation, never a requirement, which is what lets a filter stand in for
adaptive-precision arithmetic inside a refinement loop.

Repair invalidates the cell-parent map used by the any-degree nested MG transfer
(a flipped cell can straddle two coarse cells), so it is set to None and a
degree-2 space falls back to the geometric builder. The exact vertex
prolongation survives untouched: flips move no vertex, and a P1 section numbers
its DOFs from the point numbering, which is preserved.

Tests: 6 serial, 4 parallel at np=2/3/4. The maximum-angle assertion is the one
that caught the Delaunay criterion; the idempotence check cannot -- an inverted
criterion is idempotent too, which is exactly how Delaunay passed while
degrading the mesh.

Underworld development team with AI support from Claude Code
…n findings

Finding 8 in the reconnection design note. Three of the earlier findings needed
correcting rather than extending:

- Delaunay is the wrong acceptance criterion in 2-D as well as 3-D. Finding 3
  treated it as settled because Lawson flips reach the unique Delaunay
  triangulation; that settles the operator, not the criterion. Delaunay maximises
  the minimum angle while P1 interpolation depends on the maximum, and flipping a
  gmsh mesh towards Delaunay was measured to raise the 99th-percentile maximum
  angle.
- The "-14% interpolation error at equal cells" credited to flips was a placement
  effect: the prototype flipped inside the refinement loop, so the arms had
  different point sets. Connectivity alone is worth 3%.
- A flip preserves the point chart, so the rebuilt DM keeps the identical
  numbering and the star-forest transfers verbatim. The
  reconstruct-the-SF-by-matching-seam-coordinates stage is unnecessary.

Also records that Tier 0 (Rivara terminal-edge selection) was measured and
rejected, and that the frozen-seam cost halves with every halving of the target
cell size.

Underworld development team with AI support from Claude Code
A label value carried by a CELL describes a volume, not an interface, and must
not lock an edge. Locking any labelled point looked conservative and was in fact
a silent disabling of the whole feature.

"Elements" labels every cell of a gmsh mesh, and the uwnvb_bisect transform
propagates a parent's labels to its children -- so after refinement every new
INTERIOR edge carries "Elements" as well. Repair was therefore declining 81% of
the interior edges of a plain refined box. It still passed every test in the file
because the hand-built fixtures carry no such label, and it still improved the
99th-percentile angle slightly, so nothing looked wrong. It only surfaced on a
realistic fault case, where repair moved the fault band's maximum angle by 0.0
degrees and 93% of the edges of the worst cells came back "locked" with none of
them on a boundary.

Every genuine boundary or interface label marks zero cells, so excluding
values that mark a cell is enough to separate the two. A region JOIN is still
protected -- that is _cell_regions, which compares the two cells rather than
reading the edge.

Measured on a fault crossing the partition seam (corner to corner, so it must
cross whatever cut the partitioner chooses), fault band maximum angle:

    no repair             156.4 deg  (identical at np=1/2/4)
    repair, np=1          122.9 deg
    repair, np=2 and 4    148.2 deg

so the bulk of the band repairs almost as well in parallel as in serial
(99th percentile 119.3 -> 122.3) while the single worst cell sits on the frozen
seam and survives. That is the frozen-seam cost this pass documents, now measured
where it matters rather than averaged over a mesh that is mostly far from the
fault. In-band frozen repair sites are 5.5% at np=2 and 13.1% at np=4. A sheared
weak-zone Stokes solve converges in one iteration on every variant and gives the
same vrms to four significant figures, so repair does not perturb the physics.

Also records what the interface lock does NOT cover: in the standard
adapt-on-top fault workflow a Surface is a distance field driving a metric and a
constitutive weak zone, and labels no mesh edge, so repair reconnects freely
across the weak zone. That is harmless for a smooth weak zone -- the vrms
agreement above is the evidence -- but a fault that must not be crossed has to be
a labelled interface, not a distance field.

Underworld development team with AI support from Claude Code
…thing else

Relaxation and interface-tracking refinement work against each other. The MMPDE
mover optimises element shape against an equilateral reference and knows nothing
about where the material changes, so it slides the small cells that refinement
placed on an interface OFF the interface. Measured on a step-edged fault: the
manufactured stress across the interface rose 77%, and it stopped being confined
to the fault (leak beyond d=0.03 went 0.0% -> 1.0%). Counter-intuitively the
mover REDUCES the number of straddling cells (1343 -> 965) and still makes things
worse, because the survivors are bigger: leak per straddling cell rises 2.5x.

mesh.relax(pin_bands=[surface]) labels the cells the interface cuts and holds
them fixed. Measured on the same case: leak 0.03075 -> 0.03076, i.e. unchanged to
five decimal places and identical to not relaxing at all, confinement still
0.0% beyond d=0.03, straddling count unchanged at 1343 -- while the mover keeps
reshaping the rest of the domain.

An entry may be a Surface, or a (surface, offset) pair when the interface is a
level set of the distance rather than the surface itself -- a weak zone of
half-width offset. pin_halo (default 1) pins extra rings, because pinning only
the cut cells lets the mover pull on them from outside and drag the pinned ring
out of shape anyway.

pin_bands MERGES with pinned_labels rather than replacing it. That is not a
convenience: pinned_labels=None means "pin every named boundary", and passing an
explicit list replaces that default, so an implementation that substituted the
band label would silently let the mover deform the domain boundary. There is a
regression test for exactly that.

label_interface_band uses the SIGNED distance at offset zero and the UNSIGNED
distance at a non-zero offset. Against the unsigned distance the straddle test
can never fire at offset zero -- the unsigned distance is never negative, so
nothing is ever labelled; the resulting empty DMLabel then hard-crashes
getStratumIS rather than raising, which is why the first version of this died
with no traceback. At a non-zero offset the unsigned distance is the RIGHT
choice, because a weak zone has two margins and it catches both. Labelling
nothing is now refused with an explanatory error instead of returning an empty
label.

The test asserts the three properties that make this a steering mechanism rather
than a way to switch the mover off: pinned vertices move exactly zero, unpinned
vertices do move, and the domain boundary stays put.

Underworld development team with AI support from Claude Code
Findings 9 and 10 in the reconnection design note. The reconnection work
optimises element shape; for a fault problem the quantity that matters is
narrower and ranks the options differently, so it belongs alongside rather than
in a results file.

Finding 9 -- leak = -2 Cov(eta, edot) per cell, zero unless a cell straddles the
weak zone. A material-based marking rule loses to the plain distance size field
(N^-0.37 or a stall, against N^-1.04), because the leak is spread across the whole
transition and there is nothing to target. The optimal band width depends on which
quantity is minimised, and the objectives disagree. A step-edged margin confines
the artefact almost perfectly (0% vs 11.4% beyond d=0.03) at the cost of a worst
cell 20x worse. P0 viscosity or an aligned interface make the leak identically
zero.

Finding 10 -- relax and interface-tracking refinement fight, and pin_bands is the
fix. Includes the two failure modes that are silent: pin_bands must merge with
pinned_labels rather than replace it, and the band test needs the signed distance
at offset zero (the unsigned distance is never negative, so it labels nothing and
the empty DMLabel then hard-crashes rather than raising).

Underworld development team with AI support from Claude Code
… in parallel

Two findings from the pre-PR adversarial review.

_orient2d returned -1 -- a confident "clockwise" -- for exactly collinear input.
The static filter reduces to `0 >= 0` whenever both products vanish, which is the
case for ANY axis-aligned collinear triple, an ordinary configuration on a
structured mesh, not just for coincident points. The caller declined the flip
either way so no mesh was ever corrupted, but a predicate whose entire contract
is "report a sign only when the sign is justified" was reporting one it could not
justify. It now returns UNCERTAIN, with a regression test covering coincident,
x-collinear and y-collinear input as well as the unambiguous cases.

pin_bands had no parallel test, which Charter section 11 does not allow. It works,
and the new test asserts the properties that make it safe rather than just that it
runs: the pinned set is partition-independent (compared by COORDINATE, since a
shared vertex is held by every rank on the seam and a count would double-count it
and mask the defect); pinned vertices do not move even when they are star-forest
LEAVES owned by another rank, which is the case a rank-local pin would get wrong;
and the domain boundary stays pinned. Verified np=2 and np=3.

Underworld development team with AI support from Claude Code
…dition

mesh.add_conforming_surface(points, name) splits every edge the surface crosses
at the crossing point, so the surface becomes a chain of element edges. No
element straddles it, a material property can be assigned per CELL and be
exactly right, and the surface becomes a named boundary that a solver can apply
conditions on.

The point of adding it on top of an existing mesh, rather than building it into
the mesh generator, is that its position need not be known when the mesh is
made: the base mesh and its multigrid hierarchy stay fixed while the surface
moves, which is what an outer optimisation over its position needs.

Why the straddling matters: a linear element forms stress from the interpolated
viscosity times the interpolated strain rate, so it carries mean(eta)*mean(edot)
where the honest average is mean(eta*edot). The difference is -2 Cov(eta, edot)
per cell, zero for any element wholly inside or outside the zone and positive
only across the transition. Refinement shrinks the straddling band but never
empties it. Measured on a step viscosity 1 -> 1e4: the leak is 285 on an uncut
mesh and EXACTLY zero on a cut one with a cell-wise viscosity. A continuous P1
viscosity still leaks on a cut mesh (227 against 240 uncut) because the nodes ON
the surface are shared by both sides -- the cut is what makes a per-cell
assignment correct, not smooth.

SolCx, the acceptance test, eta 1 -> 1e6 on an irregular mesh at matched cell
count: a regular mesh that already conforms takes 14.1 s for a relative L2 error
of 2.5e-05; the cut irregular mesh takes 17.9 s for 1.3e-05; the same mesh uncut
takes 271.8 s for 4.5e-02. So the cut costs about 27 % over the ideal and is 15x
faster and 3600x more accurate than leaving the mesh unaligned.

No new C. The compiled uwnvb_bisect transform already inserts a vertex per
marked edge; only the coordinate needed overriding, and the topology follows.

Implementation notes worth keeping:

* PASSES OF PAIRWISE-INDEPENDENT EDGES, not one pass. The transform can split
  two edges of a triangle at once and emit the joining segment -- the whole cut
  in a single pass. That is correct in serial and WRONG IN PARALLEL: the
  double-split path leaves the child point star-forest inconsistent and wrapping
  the result as a Mesh dies in PetscSectionCreateGlobalSection at np>=3. Its own
  source calls those tables "a safety net"; nothing had exercised them across a
  partition. Independent single splits still build the cut, because the second
  pass joins its new vertex to the opposite vertex of the cell, which is the
  first pass's new vertex.

* SNAP OR CUT, measured ALONG THE EDGE. A crossing landing near a vertex leaves
  a sliver -- in the worst case an area of 1e-24 and a zero angle. A crossing
  within snap_frac of an edge's end moves that vertex onto the surface instead.
  The along-edge measure is the short side of the sliver that would otherwise be
  created and carries no length scale. GAMG on a Poisson solve, which is
  sensitive to element shape where the geometric hierarchy deliberately is not:
  uncut 20 iterations, snap_frac 0.00 32, 0.05 28, 0.10 23, 0.20 21. Hence the
  0.10 default. A Lawson flip pass helps less (32 -> 29, 28 -> 25), so snapping
  is the better lever and repair is a touch-up rather than a requirement.

* EVERY rank-local decision is reconciled. Four collective bugs, all the same
  shape -- a rank-local branch around a collective -- and all invisible at np=1
  and np=2, because a two-way split happens to give every rank a piece of the
  surface. np=3 exposed all four: the tip / triple-crossing / multiply-crossed
  validations, the "nothing to cut" guard, the snap-set reconcile itself, and
  the substantive one -- the snap decision is read off an EDGE, so a rank
  holding one side of a shared vertex could decide differently from its
  neighbour, leaving the ranks disagreeing about which edges were crossed and
  the split loop never emptying.

* cut_hierarchy is OFF by default. It is tempting to argue a surface-free coarse
  level "solves a different problem", but custom-P sets pc_mg_galerkin=both, so
  every coarse operator is PtAP from the FINE operator and inherits the contrast
  whatever the coarse mesh looks like. What a coarse cut would buy is a coarse
  SPACE able to represent the kink; measured on SolCx at contrasts of 1e2 and
  1e6, cutting the coarse levels moved the error in the fifth significant figure
  and the solve time not at all.

Scope: two dimensions, and surfaces crossing the mesh from boundary to boundary.
A surface ending inside the mesh (a fault tip) is refused rather than silently
mis-meshed, as is a triangle crossed three times.

Tests: 18 serial, 8 parallel passing at np=2/3/4. The parallel file asserts the
mesh by sorted owned-vertex COORDINATES and a hash rather than counts (derived
counters lie in parallel), and solves a Dirichlet problem on the surface,
matching the serial domain integral to 4e-17. Both solves are driven to a tight
tolerance so that can be asserted strictly: at default tolerance the two differ
by 1.5e-8, which is two iterative solves converging within their own rtol rather
than a partition effect, and a loosened bound would have hidden the question.

Underworld development team with AI support from Claude Code
A refinement engine takes as many passes as it needs to reach the size the
metric asks for: independence caps how many edges one pass may split, and a
conforming closure cascades. So a pass is how the engine REACHES a size, while
a multigrid level is a COARSENING RATIO. adapt() conflated them by recording
every pass as a level, and nothing connected the two numbers:

  edge_split   n_pass = 8*dim*max_levels is only a CAP; the loop runs to metric
               satisfaction, so max_levels 1/2/3 returned byte-identical meshes
               and 10 passes became 10 levels;
  nvb          n_gen = dim*max_levels, and a bisection is a 2^(1/dim) step in h,
               so `dim` generations make ONE h-halving -- you got dim times as
               many levels as isotropic-equivalent ones.

Both then degenerate: once the metric is nearly met the passes coarsen nothing
(measured ratios 1.06, 1.02, 1.007) and each such level still costs a full
Galerkin RAP and smoother sweep. That hierarchy stopped SolCx converging at all.

adapt() now takes mg_coarsening_ratio (default 2.0, applied identically by both
engines) and keeps one level per that much coarsening in h.

THE MEASURE IS RESOLUTION, NOT ELEMENT COUNT. Under adapt-on-top the mesh only
grows where the feature is, so a genuine halving of h shows up as a global cell
ratio near 1: on a thin band NVB grew the mesh 1.06-1.11x per generation while
the in-band h went 0.125 -> 0.0626 -> 0.0313 -> 0.0157. A count-based rule keeps
nothing and collapses the hierarchy; the whole-mesh median h is flat and equally
useless. The selector uses a low percentile of cell diameter, reduced with MIN
across ranks, and replaces rather than appends when the level below the finest is
within the ratio -- appending reintroduces the near-duplicate pair it exists to
remove.

Measured on SolCx with the interface CONFORMING at the finest level, so the
discretisation pathology of an unaligned jump does not swamp the comparison
(uncut, SolCx at 1e6 does not finish at all):

  engine      hierarchy   levels  vel its   seconds
  nvb         per-pass      7        4       19.67
  nvb         doubling      5        5        6.95
  edge_split  per-pass     11        5      161.04
  edge_split  doubling      6        6       22.16

2.3x to 7.3x faster for +0 to +1 iterations, at errors identical to four
significant figures, and contrast-independent (iterations barely move from 1e4
to 1e6). The extra levels were overhead. A ratio sweep at np=1/2/4 shows the
ranking is stable and that cost keeps falling to ratio 3 before saturating; the
default stays at the conservative 2.0 and the knob is exposed.

Prolongations are COMPOSED across the passes a level spans, so the recorded
transfer stays exact instead of falling back to the geometric builder. Composed
in numpy: each row of a bisection prolongation holds one or two entries, so
expanding the fine map through the coarse rows and summing duplicates is the
whole operation. Validated against a dense oracle on 200 random cases, exact and
a partition of unity.

Tests updated to the new contract:

* test_0753 asserted two SINGLE-GENERATION properties -- every fine vertex lies
  on a coarse edge, and at most 2 nonzeros per row. Neither survives composition
  and neither should: a composed span can place a vertex strictly INSIDE a coarse
  cell, where it depends on that cell's dim+1 vertices. The reference is now
  barycentric-in-cell, which covers every fine vertex instead of the ~64 % that
  lie on an edge, so the test checks MORE than it did; the sparsity bound becomes
  dim+1.

* test_0836 / test_0840 tied the level count to the generation count. They now
  assert the property that defines the contract: no level is a near-duplicate of
  its neighbour, and interior adapted steps reach the requested ratio. The step
  INTO the finest level is exempt -- the finest is the child and is mandatory, so
  when the whole adapt is less than one doubling its single step is whatever the
  metric asked for (1.74 measured in 3-D).

FOUND ON THE WAY, NOT FIXED: nvb.nested_prolongation is wrong in 3-D for vertices
a closure cascade places strictly inside a coarse tet -- worst |P.u - P1(x)| =
1.19, measured PER GENERATION with no composition involved, against 1.9e-15 in
2-D. It was masked because the old reference was edge-based and skipped exactly
those vertices. Marked with TODO(BUG) at the source and xfailed (strict) in
test_0753; it predates this change and is not caused by it.

Underworld development team with AI support from Claude Code
…face count

`_resolve_snapping` initialised its on-surface set to all-False and only added
vertices it decided to SNAP. A vertex ALREADY lying on the surface was therefore
invisible to it -- the edges radiating from such a vertex have signed distance
exactly zero and register no strict sign change, so nothing ever proposes them.

That is fine for a surface crossing open mesh, and wrong for a fault NETWORK. A
junction (or a tip) is placed by pulling a mesh vertex onto it, so it lies exactly
on every branch that meets there. The validation then read the cell beyond it as
"entered but not left" and refused a legal branch.

Seeding the set with vertices already on the surface fixes it. Measured, on a 1/20
box with the junction pulled onto a vertex:

  Y  three arms from one junction   3 branches, zone 116 cells, 0 inverted
  T  one fault abutting another     2 branches, zone 114 cells, 0 inverted
  X  two faults crossing            2 branches, zone 166 cells, 0 inverted

all branches labelled chains of mesh edges, in every case. Y previously failed;
T and X already worked, which is what made the cause specific -- both of those
have a branch passing THROUGH the junction, so an ordinary crossing marked the
vertex as a side effect.

This is the "crossings computed twice from different sources" smell already
recorded in the design review, producing a false refusal. The pass loop derives
its on-surface set correctly (`distance < 1e-12 * scale`); only the validation
path did not. The single-source-of-truth refactor should absorb this.

Why networks matter here: a one-element fault zone taken as the cells in the
SUPPORT of the labelled facets makes a network's zone the UNION of its branch
zones -- no geometry to reconcile where branches meet, in any dimension. The
alternative (offset surfaces plus end caps) has to mesh T- and X-junctions
conformally, and for a one-element-wide fault that is self-contradictory: the cap
has extent equal to the thickness, so resolving it needs h << h.

Maintainer ruling 2026-08-02, recorded because it scopes the work: intersecting
faults are transient -- if they slip they change the geometry -- so an
approximation to the fault volume is fine, and junction geometry need not be
resolved exactly. The union-of-cells zone bulges where branches meet, since the
fan around the shared vertex is picked up by each branch. That is an accepted
characteristic, not a defect to engineer away.

Underworld development team with AI support from Claude Code
… no cut below the child

Adversarial review of this branch found six correctness defects and a test suite
several of whose tests passed with the feature removed. This is sections A and B
of that triage, plus a maintainer ruling that removes a whole path.

THE SURFACE EXISTS ON THE FINEST LEVEL ONLY. `cut_hierarchy=` is gone, along
with `_cut_coarse_levels`. Cutting the coarse multigrid levels produced a
hierarchy of cut copies of the base levels, which defeats the point of the
stack-on formulation: the surface's position is a design variable in an outer
optimisation, so the base and the hierarchy resting on it have to stay fixed
while the surface moves. It bought nothing either — custom-P sets
pc_mg_galerkin=both, so every coarse operator is PtAP from the FINE operator and
carries the contrast whatever the coarse mesh looks like (SolCx at 1e2 and 1e6:
fifth significant figure, no time difference). It was also the path with zero
tests and the one where two of the defects below bite.

EVERY REFUSAL IS NOW GLOBAL. A rank-local raise aborts one rank while its peers
walk into the next collective and block there, so the error becomes a hang. Nine
defects of this shape have now been found in this module, and the parallel suite
could not see any of them because it only ever took the happy path. Audited as a
class rather than fixing the five named:

* the cell-inversion raise, the `_child_vertex_of` raise (which sat inside a
  rank-local "did this rank split anything?" guard as well), and the guard around
  the coordinate write are all gone or reduced first;
* `_global_extent` replaces five rank-local `np.ptp(...).max()` calls. Those
  raised outright on a rank owning no vertices, and one of them fed the crossing
  tolerance — so the module's central invariant, that every rank computes the
  same crossing from the coordinates alone, was false (measured spread 0.58-0.67
  against 1.0 serial);
* every number in `info` is reduced, counted over owned points, so the documented
  identity between them can hold at np>1. `n_snapped` becomes `n_on_surface`,
  which is what it has counted since junctions were seeded into it.

Measured negative control: restoring the rank-local form of the inversion test
HANGS at np=3 on exactly that case while the three refusals before it pass.

THE STRESS LEAK IS ASSERTED. It is the claim every docstring and commit message
on this branch rests on and it was tested nowhere. On a 1/16 box at contrast 1e4:
uncut leaks 285.4 with a cell-wise viscosity, cut leaks exactly 0.0, and a
continuous P1 viscosity leaks 298.7 even when cut — so the feature is "cut AND
assign per cell", not "cut". Stubbing add_conforming_surface to return the mesh
unchanged fails it.

Tests that passed with the feature stubbed out, and now do not:
* the parallel snap test selected vertices within 1e-6 of the surface and asserted
  the worst was under 1e-12. On the uncut base that set is EMPTY (nearest vertex
  5.5e-3), so it held with the feature removed. Now the count and identity of
  on-surface vertices against serial;
* `no_inverted_cells` was true by construction twice over — cut_along_lines
  already raises on the same areas, and min_angles is arccos of a clipped value.
  Now the documented angle table (1.60/3.88/6.56/13.93 deg);
* the coarsening-ratio knob passed with the ratio hard-coded ([3,3,3] is still
  non-increasing). Now strict decrease;
* `_assert_coarsening_ladder` re-derived the implementation's own level selector
  and passed ratio 2.0 at 1.817 against 1.800. Now an INDEPENDENT estimator (mean
  edge length in the refined band), shared between the 2-D and 3-D suites instead
  of duplicated verbatim, asserting the adapted SPAN rather than a per-step number
  the engine never promised. That same step measures 1.401 independently;
* the parent-cell map was discarded unconditionally after subsampling, which
  tautologised the repair test. Kept per level when the level is one generation.

test_0753 (tier_a): the barycentric reference REPLACED an edge-membership one on
the grounds that it covered every fine vertex rather than 64 %. That 64 % is the
3-D case, which is xfailed; in 2-D nothing composes and the old reference already
covered 100 %, so it was a loosening. Both references are kept now — edge
membership catches a PHANTOM parent edge, which is the 3-D defect and which
barycentric position and linear-field reproduction are both blind to. Added a 2-D
case that genuinely composes, so the docstring's claim is exercised somewhere
that runs. Sparsity is bounded PER ROW, not on the mean, since dim+1 IS
point-location density. The 3-D defect is asserted positively instead of by
strict xfail on one row in 2336.

Smaller: _boundaries_with could land a surface on Null_Boundary(666);
_cut_coarse_levels caught only ValueError when two of three failures are
RuntimeError; the cut child is marked as not having coincident DOFs, so
_refine_restrict interpolates rather than injecting from a displaced node;
uw.pprint(0, ...) printed a literal 0; a malformed RST table would have broken
the Sphinx build.

A2 (coarse levels carry no boundary, so an essential BC on the surface is
unsound) is DEFERRED. The docstring no longer claims otherwise.

Underworld development team with AI support from Claude Code
… parallel

The fault is a one-element-wide zone defined at the FINEST level of the
adapt-on-top, and the zone is the cells in the SUPPORT of the labelled facets —
not a geometrically bounded region.

`mesh.cells_supporting(name)` is that zone. It needs no end cap, no edge band and
no rim; it terminates automatically where the chain of facets ends, it says
nothing about dimension, and the zone of a network is the union of its branches'
zones with no geometry to reconcile where they meet. Bounding it geometrically is
self-contradictory for a one-element fault anyway: the cap has extent equal to the
thickness, so resolving it would need h much smaller than h.

Measured, and asserted:

* the zone is EXACTLY 2 x facets at every resolution tried. A cell carrying two
  labelled edges would have been cut in two, so no cell is double-counted and
  every facet contributes both neighbours — one element each side, by
  construction;
* thickness tracks the LOCAL h: 0.189 / 0.183 / 0.184 across a 4x uniform
  refinement, and 0.195 / 0.202 / 0.198 under the adapt metric. So width is a
  REFINEMENT parameter — the surface lives at the finest level and the metric
  decides how wide one element is, controlled locally and at bounded cost;
* adapt THEN cut composes, and the child keeps its multigrid tail. That is the
  order the design needs. (adapt refusing to chain ON a cut child is the other
  direction and is not what the fault requires.)

The max centroid distance will NOT do as the thickness statistic: it is one
outlier cell and it came out bit-identical at two different adapt resolutions,
reporting no scaling where the mean shows it cleanly.

add_conforming_surface takes a Surface, not (points, name). It is what
fault_metric, fault_metric_tensor and refinement_metric_function already take, so
one object drives the refinement metric AND the cut instead of being unpacked and
its name re-stated, and it carries signed_distance and director for the weak-plane
model afterwards. Control points are read in MODEL space via the machinery's own
_fault_collect_polylines — surface.control_points is the dimensionalised gateway
and would be the wrong space under an active units system.

pull_vertex_onto() is promoted out of the test file into the library, because a
TIP and a JUNCTION are the same problem — a distinguished point that must
coincide with a mesh vertex, after which every branch meeting there arrives at
the already-legal "one crossed edge, one on-surface corner" case. It is now
COLLECTIVE: the test helper took a rank-local nearest vertex, which moves a
DIFFERENT vertex on each rank so the branches meet at different places either
side of a seam. Reduced as (distance, x, y) so the tie-break rides along in the
same reduction, and the move is applied by POSITION so a ghost copy lands in the
same place without a star-forest exchange.

Fault NETWORKS now run in parallel — Y, T and X at np=2/3/4, previously untested.
Negative control: restoring the rank-local vertex choice fails all three at np=3.

The fault zone is checked across the partition too, by owned count AND by a hash
of the sorted zone centroids, since a count alone can agree between two different
sets of cells.

Also asserted, because the docstring tells users to rely on it: degree-0 DOF
order IS plex cell order, so cells_supporting can be assigned straight into a P0
viscosity. Were that untrue the contrast would land on the wrong cells and every
downstream result would be quietly wrong while looking plausible.

Underworld development team with AI support from Claude Code
`vis.labelled_facets_to_pv_mesh(mesh, name)` returns the facets carrying a
boundary label as a PolyData of their own — lines in 2-D, triangles in 3-D, since
a labelled facet's closure gives its vertices whatever the dimension. An embedded
surface drawn WITH the mesh is a few lines among thousands in 2-D and completely
occluded in 3-D, so it has to be separable to be looked at. It saves to `.vtp`
for interactive viewing, which is how the 3-D version will have to be inspected.

`docs/developer/subsystems/conforming-surfaces-and-fault-zones.md` is the design
note the branch was missing entirely: why straddling elements are a
representation problem rather than a resolution one, the leak table, why the zone
is the facet support and not a bounded region, the thickness-tracks-h
measurements, the snap_frac trade, tips and junctions, and the limitations. The
GAMG table moves out of the line_cut docstring into it, leaving the sentence that
justifies the default — which also removes the malformed RST that would have
broken the Sphinx build.

`line_cut` is exported from `utilities/__init__` alongside `edge_split` and
`reconnect`, so it is not deep-import-only and its cross-references resolve.

Underworld development team with AI support from Claude Code
… reach

Two additions to `cut_along_lines`, both driven by the same measured fact: the
cut's slivers are made by the SPLITS, so anything that replaces a split with a
vertex move helps and anything that turns a move back into a split hurts.

`snap_quality` — a triangle-quality floor on snapping. A cell thinner than the
tolerance band has every corner pulled onto the line from both sides and is
flattened; measured on a graded mesh, every collapsed cell at snap_frac 0.4 had
all three corners snapped, and the cut was refused outright. A proposed move that
would take an incident cell below the floor is now vetoed and that crossing is
split instead. The floor is absolute and monotone (never below it, never worse if
already below), because a floor expressed as a fraction of the CURRENT quality
compounds when the routine is applied repeatedly — 0.5 over six rounds licenses
0.5**6, and the worst angle duly fell 15.4 -> 2.3 degrees with every individual
round looking well behaved.

The guard must test QUALITY, not inversion: a flattened cell lands at ~1e-16 of
either sign, so half survive an inversion test, the worst angle still reaches
zero, and the returned mesh looks fine while the cut chain has silently broken.
Guarding on inversion alone was measured doing exactly that.

The default is deliberately LOW (0.15). The guard protects the snapped mesh,
which is not the mesh that comes back. Raising the floor from 0.15 to 0.55 held
the snapped mesh's worst angle up (15.6 -> 24.5 degrees) while driving the CUT's
down (10.9 -> 0.16) and the split count up (139 -> 359). It is a backstop against
flattening, not a quality target. `None` removes it entirely, restoring the
pre-guard behaviour and its refusal.

`snap_dist` — snap any vertex within that multiple of its own local h of the
line, whatever the crossings on its edges look like. `snap_frac` is measured
ALONG an edge and is blind to a vertex sitting close to the line while every edge
meeting it is crossed near its midpoint. That vertex becomes the apex of a cell
with one edge on the cut, which is the characteristic sliver: of the sixty cells
below 15 degrees in a box-fault cut, ALL sixty had two corners on a cut and ALL
sixty were elongated along it, apex about 0.45 W away. Five separate knobs (snap
tolerance, quality floor, staged refinement, metric ramp slope, metric core
width) each returned a worst angle of 10.80 degrees and ~59 poor cells, to the
digit, because none of them can reach that configuration. `snap_dist` 0.30
halves the population (60 -> 35 on the box, 26 -> 13 on a single cut).

It is OFF by default: it also makes the worst single cell worse (10.8 -> 1.4
degrees), because the splits it leaves behind sit in harder places and nothing
guards the splits. That gap is the next piece of work, not something to enable by
default ahead of it.

Also: `add_conforming_surface` forwards both, and its `snap_frac` docstring now
records that 0.10 is not the right value on a graded mesh (0.30 took the worst
angle from 4.96 to 10.81 degrees and cells below 15 from 231 to 31) without
changing a default chosen on a uniform one.

Tests: two serial tests — the guard turns the flattening refusal into a valid
cut, and `snap_dist` finds vertices the along-edge test does not. The parallel
collective-refusal case now passes `snap_quality=None` so the refusal path it
exists to protect is still reachable. 36 serial, 16 parallel at np=2/3/4.

Underworld development team with AI support from Claude Code
… label

`_cell_regions` builds a per-cell signature from every non-topology label and
locks any edge whose two cells disagree, on the reasoning that such an edge is a
material interface even when unlabelled. `uwnvb_refedge` is not a material label:
it records which of a triangle's edges is its refinement edge, and it takes
values 0/1/2 across any NVB-adapted mesh. Measured on an adapted fault mesh, that
read as three regions of 2230/2184/134 cells, and every edge between them was
locked.

The effect was not marginal. Of the edges around a sub-15-degree cell in a cut
mesh, 113 were declined as a "region interface" against 54 genuinely locked on
the fault. Excluding the label takes the pass from 101 flips to 483, and cells
below 15 degrees from 60 -> 18 rather than 60 -> 59; cells below 25 degrees go
420 -> 239 and the 1st-percentile angle 14.4 -> 18.1 degrees.

This is the same trap `_labelled_points` already documents for `Elements`, one
level along. That fix — ignore a label carried by CELLS — cured `Elements`
because `Elements` is uniform, so it never reaches `_cell_regions`' final
"are all signatures equal" test. A bookkeeping label that VARIES over cells does.

The gate itself was never the problem, and is unchanged: of the edges around a
sliver, the 44 with a minimum-angle gain are exactly the 44 with a maximum-angle
gain, so a Delaunay-style gate would have flipped the same set. Only the lock
differed.

The fault is untouched, as it must be — flips are locked on labelled edges. Cut
and cut+flip agree to the digit on both flanks: 317 and 318 facets, every chain
vertex within 1.3e-16 of the line, zero straddling cells, zero inverted, and the
minimum cell area rises 4.7e-7 -> 6.7e-7.

Test: a regression with its own `adapt`-built fixture, since the file's shared
`_refined_dm` goes through `bisect_longest_edges` and never carries the slot
label — which is why the defect survived this suite. It asserts the label is
present AND that it takes more than one value on cells, so a fixture that could
not expose the defect fails loudly rather than passing vacuously.

Underworld development team with AI support from Claude Code
… applies

`add_conforming_surface` appended the mesh it was cutting to the child's coarse
tail unconditionally, on the stated reasoning that "adding a surface refines this
mesh, so this mesh plus everything below it is a valid coarse tail". The premise
is wrong. A cut re-represents the same grid with the surface conformed; it adds
no resolution. Measured on a box fault, the two cuts produced two levels that
coarsened h by 1.11x and 1.17x on the 5th-percentile measure, against a threshold
of 1.8 — each one a full Galerkin RAP and a smoother sweep for no correction.

`_subsample_mg_levels` already decides exactly this question for an engine pass,
including the "replace the level below rather than append to it" case, and it is
the committed answer to it. So the cut path now calls it, handing it the pair
(self, child) measured against the level beneath them, rather than carrying a
second rule that could drift from the first. `mg_coarsening_ratio` is exposed to
match `adapt`.

Box fault: 9 levels -> 7, and the top transition goes from 1.06x to 1.96x in
mean h. One cut: 8 -> 7. The hierarchy is now the same depth as the adapted mesh
it was cut from, which is the point — cutting is not refining.

Two things fall out, both measured on the same shear solve:

* the barycentric transfer stops failing. Transfer 7->8 ran BETWEEN the two
  near-duplicate cut levels, and it was there that the builder ran out of coarse
  DOFs with a fine image and fell back to the dense-RBF one (#424) — dense
  Galerkin coarse operators, and a measured 94s/0.6GB turning into >21min/12GB
  when the mesh was also relaxed. The fallback no longer fires, in this solve or
  anywhere in the two test suites.
* the solve is 1.87x faster for the same answer: 93.7s -> 50.0s, strain-rate
  ratio 133 either way and the fault strain rate 58.04 -> 58.03.

The reported V-cycle count went 8 -> 15, which is NOT a regression and should not
be read as one: it counts the last inner solve only, and the hierarchy under it
changed. Time the solve.

Test: `test_the_surface_exists_on_the_finest_level_only` asserted the tail keeps
its length and that its finest level is the base finest. Both described the old
contract. Its substance — coarse levels carry no surface label, the base is not
mutated, the tail is built from the base's own uncut level objects — is unchanged
and still asserted; the count and the identity of the finest level now say that
the cut REPLACED the base finest.

45 serial, 16 parallel at np=2/3/4.

Underworld development team with AI support from Claude Code
A conforming cut has only two primitives — snap a vertex onto the surface,
or split an edge it crosses — and every sliver it leaves follows from that.
A crossing falling near a vertex must either drag the vertex to it or carve
a thin cell beside it, and tightening the snap tolerance only trades one
for the other. Delete is the missing third: it dissolves the case, and it
is the only one of the three that removes work rather than adding it.

On a box fault cut into an adapted mesh, counting cells under 15 degrees:
the cut leaves 60, flipping takes that to 18, and deleting afterwards to 4
while removing 242 cells. The order is not symmetric — deleting first
leaves the count at 60, because a cavity, once ear-clipped, no longer
presents the quad the flip pass was looking for. The pair then converges:
a second round of each finds nothing. The fault itself is bit-identical
through both passes, at every rank count.

The acceptance test needs both shape measures, unlike the flip pass.
Gating on the largest angle alone — correct for flipping, since the P1
interpolation bound depends on it — let the minimum angle fall from 10.80
to 10.23 degrees and RAISED the sliver count from 60 to 61, because a
needle has one tiny angle and two close to 90 and never registers as
obtuse. Hence gate="both".

Parallel is one exchange, not a redistribution. Deletion compacts the point
chart, so unlike a flip it cannot hand the star-forest across verbatim:
every point after a deleted one shifts, and each leaf's remote index is a
number only its owner holds. rebuild_without_vertices renumbers locally and
broadcasts the new numbering root-to-leaf once. Freezing the seam is what
keeps the leaf set itself unchanged, so the forest is renumbered and never
rebuilt; it costs 113-115 deletions against 121 serial at np=2..4.

Also fixes the third instance of one labelling trap. Null_Boundary marks
every vertex of every UW3 mesh with the reserved value 666, and
UW_Boundaries re-packs every per-boundary stratum, sentinel included, into
one stacked label — so reading labelled POINTS as interfaces flags the
entire vertex stratum. That costs the flip pass nothing, since it asks only
about edges, and it refused 1114 of 1114 candidates the first time the
removal pass met a cut mesh. _labelled_points is now _interface_edges and
reads edges only, which is the right reading anyway: in 2-D an interface is
a curve. It is also the only reading that protects a fault, since
cut_along_lines labels the cut's edges and not its vertices.

Underworld development team with AI support from Claude Code
The cut can only snap a vertex onto the surface or split an edge it
crosses, so a crossing landing near a vertex either drags the vertex to it
or carves a thin cell beside it, and tightening snap_frac only trades one
for the other. repair=True runs the two operations the cut does not have:
flip, then delete. On a box fault, cells under 15 degrees go 60 -> 4 while
242 cells are removed. The surface's own facet count is unchanged, since
both passes refuse to act on a labelled edge.

Deletion is offered only the vertices within repair_reach * h of the
surface. It removes degrees of freedom, and the cut is what justifies
removing these particular ones; a pass turned loose on the whole mesh would
coarsen it wherever the shape happened to be poor. Flipping is offered
everything, because it conserves the point set. Off by default, like
adapt(repair=...), because the cut alone gives the same mesh at any rank
count and repair gives that up.

Also fixes needle blindness in the flip pass. It gated only on the pair's
largest angle — right as an OBJECTIVE, since the P1 interpolation bound
depends on it and Delaunay is the wrong criterion here — but nothing stopped
it buying that gain by making a thin cell, whose largest angle is
unremarkable and so never registers. Measured: on a cut graded mesh,
flipping alone took the smallest angle in the mesh DOWN. The objective is
unchanged; this adds a floor under the other end, which is the same
correction the deletion gate already carries. Found by composing the two
passes, which is the only place it shows.

Underworld development team with AI support from Claude Code
… them

meshVariable_to_pv_mesh_object triangulates a variable's nodal points with
delaunay_2d. That exists so higher-order fields can be plotted at all --
the base mesh does not carry their DOFs. For a CONTINUOUS P1 field it is
the wrong thing to do: the DOFs are the vertices, so the triangulation is
already in the DM.

And it is lossy, not merely redundant. delaunay_2d takes one alpha for the
whole domain and discards triangles whose circumradius exceeds it, so on a
graded mesh it deletes the COARSE cells. Measured on a fault mesh graded
8:1, 361 of 11610 cells were dropped, and they render as blank holes in
the middle of the field -- which reads as missing data and was in fact
mistaken for one.

meshVariable_to_native_pv_mesh returns the DM's own cells, renumbered so
that point i is the variable's DOF i, and mesh_to_pv_mesh already did the
hard half of that. The renumbering is the load-bearing detail: the
documented usage attaches values by DOF index, so handing back the right
cells in the DM's vertex order would draw a plausible field with the
values shuffled. The permutation is found by coordinate match and asserted,
not assumed, and the helper returns None -- falling back to Delaunay --
whenever the DOFs are not one-per-vertex.

Automatic, so every existing call site is fixed without change. Passing an
explicit alpha keeps the old path.

The test fixture is deliberately GRADED, with a control asserting that the
Delaunay route really does lose cells on it: on a uniform mesh the two
agree and the regression is invisible.

Underworld development team with AI support from Claude Code
plot_mesh_hierarchy draws a mesh, its multigrid tail and its faults in one
figure -- one colour per level, coarsest palest and thickest, fault zones
filled in a contrasting red. It answers the three questions that come up
every time a mesh is built this way: did the hierarchy come out with the
levels expected, is the refinement where the fault is, and did the fault
survive the repair passes.

Written for 3-D rather than adapted to it later. Nothing reads the
dimension except the defaults: in 3-D the wireframes come from each level's
SURFACE, because extracting every interior edge of a tetrahedral hierarchy
is an unreadable haze, and `clip` cuts the model open so the interior
levels and the fault can be seen at all. The fault selector is
cells_supporting, which is already dimension-general -- a fault zone is the
support of its labelled facets whether those are segments or triangles.

The colour taper is load-bearing, not decoration: drawn at one width the
finest level's edges cover every level beneath it and the hierarchy cannot
be read at all.

Tests assert what was DRAWN -- an actor per level and one per fault --
since that is how this can silently mislead. A hierarchy missing a level
reads as a shallower mesh; a fault that contributed no actor reads as a
mesh with no fault in it. Both would look like perfectly good figures.

Underworld development team with AI support from Claude Code
plot_mesh_hierarchy filled cells_supporting(name) in red. That is the fault
ZONE -- every cell with a labelled facet, which is one element on EACH side
-- so a one-element-wide fault came out two or three elements thick and
looked like something the mesh does not contain.

The facets are the fault as the mesh represents it, and
labelled_facets_to_pv_mesh already returns them, dimension-general: segments
in 2-D, triangles in 3-D. That is now the default. fault_style="cells"
keeps the zone fill for the question it does answer -- which cells carry
the weak viscosity -- and an unrecognised style is refused rather than
silently drawing nothing.

The test now asserts the two sets DIFFER, so the default cannot quietly
revert to the fat one and still pass. It counts n_lines + n_faces_strict,
not n_cells: `pv.PolyData(points)` gives every point its own vertex cell,
so n_cells is n_points plus the lines and reads as a wildly wrong facet
count -- 127 for a 63-segment chain.

Underworld development team with AI support from Claude Code
…angles for faults

Shape carries the distinction as well as colour, so the figure survives
being printed in grey and does not ask anyone to tell four blues apart. In
3-D the same three roles become sphere, cube and cone, and that branch is
exercised by the tests rather than left until there is a 3-D fault to look
at.

Sizing them took two goes and both failures are worth recording, because
they are the same mistake at different scales.

Scaling each level's glyphs by ITS OWN cell size seemed natural -- coarse
level, coarse marks. Zoomed in on the fault it is a disaster: the coarse
level's marks are drawn at the coarse spacing and blanket the fine mesh
completely, which is precisely the view the figure exists for.

Sizing them all by the finest level's MEAN cell size then failed for the
reason a graded mesh always breaks a mean: the fault meshes here average
h = 0.017 while h at the fault is 0.002, so every mark came out several
times larger than the cell it stood on. The 5th percentile is what is
wanted -- the size of the cells that actually need marking. This is the
same trap as judging a multigrid level by its mean h.

Node actors are unlabelled: a legend line per level per glyph doubles its
length to say nothing the shapes do not.

Underworld development team with AI support from Claude Code
PyVista's default legend face is a triangle for every entry, so the key
showed triangles beside wireframes and beside square nodes -- a key that
contradicts the figure it is keying, which is worse than no key. Since
plot_mesh_hierarchy chose the shapes, it is the thing that can label them,
so it now builds its own.

Named faces are only triangle / circle / rectangle / none, and a wireframe
is none of those: without supplying line geometry a mesh level and a square
node key identically and the distinction the figure makes is lost in its
own legend. Wireframe and fault-facet entries therefore carry a pv.Line.

The key is exposed as plotter._uw_legend_key so it can be INSPECTED. A
legend disagreeing with its figure is invisible to any check that counts
actors, which is all the previous tests did.

Underworld development team with AI support from Claude Code
Copilot AI lite review requested due to automatic review settings August 8, 2026 22:40

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Pull request overview

This PR lands the shared “mesh surgery” foundation used by the active fault-related feature branches: conforming-surface cutting, longest-edge (edge_split) adapt-on-top plumbing, reconnection repair primitives, plus supporting visualisation helpers, tests (serial + MPI), and developer documentation.

Changes:

  • Add conforming-surface cutting and longest-edge refinement utilities (line_cut, edge_split) and expose them via underworld3.utilities.
  • Extend visualisation with labelled-facet extraction, native P1 mesh rendering (avoids graded-mesh Delaunay cell drops), and a hierarchy/fault plotting helper.
  • Add extensive regression tests (including MPI confluence/contract tests) and new developer docs/design notes for conforming surfaces / fault zones and reconnection.

Reviewed changes

Copilot reviewed 25 out of 25 changed files in this pull request and generated 4 comments.

Show a summary per file
File Description
src/underworld3/utilities/line_cut.py New conforming-surface cutting implementation (2‑D), including parallel collectiveness and snapping logic.
src/underworld3/utilities/edge_split.py New longest-edge refinement engine (engine="edge_split") with partition-independent selection and SF reconciliation.
src/underworld3/utilities/reconnect.py New reconnection/repair passes (flip + deletion) to improve element shape after refinement (2‑D).
src/underworld3/utilities/nvb.py Adds an explicit TODO note documenting known 3‑D nested prolongation embedding defect.
src/underworld3/utilities/__init__.py Exposes edge_split, line_cut, and reconnect modules under underworld3.utilities.
src/underworld3/visualisation/visualisation.py Adds labelled_facets_to_pv_mesh, meshVariable_to_native_pv_mesh, and plot_mesh_hierarchy; updates meshVariable_to_pv_mesh_object to use native P1 route.
src/underworld3/visualisation/__init__.py Re-exports new visualisation helpers/constants.
tests/_mg_ladder.py New shared test helper for verifying MG level coarsening “ladder” using an independent estimator.
tests/test_0753_nested_mg_prolongation.py Strengthens nested prolongation embedding checks; adds composed-level cases and clearer invariants.
tests/test_0836_nvb_graded_adapt.py Refactors MG-level assertions to use shared ladder check; adds mg_coarsening_ratio coverage.
tests/test_0840_nvb_3d_serial_adapt.py Refactors MG-level assertions to use shared ladder check in 3‑D adapt case.
tests/test_0843_edge_split_adapt.py Adds serial tests for edge_split adapt properties (diameter criterion, no halo, MG tail).
tests/test_0844_reconnect_repair.py Adds serial regression tests for reconnection repair primitives and label/interface safety.
tests/test_0845_relax_pinned_band.py Adds serial tests for relaxation pinning bands to preserve interface-tracking refinement.
tests/test_0846_visualisation_native_mesh.py Adds tests ensuring continuous P1 visualisation uses native mesh connectivity and preserves DOF ordering.
tests/test_0847_mesh_hierarchy_plot.py Adds tests asserting plot_mesh_hierarchy draws expected actor counts/legend semantics.
tests/parallel/ptest_0843_edge_split_parallel.py MPI confluence tests for edge_split refinement and adapt(engine="edge_split").
tests/parallel/ptest_0844_line_cut_parallel.py MPI confluence and end-to-end BC/solve tests for conforming-surface cuts and fault networks.
tests/parallel/ptest_0844_reconnect_parallel.py MPI tests for seam-freeze reconnection contract, plus solve/integral validation.
tests/parallel/ptest_0845_relax_pinned_band_parallel.py MPI tests for partition-independent pinned-band selection and immobility guarantees.
docs/developer/subsystems/conforming-surfaces-and-fault-zones.md New subsystem documentation for conforming surfaces, fault zones, and usage guidance.
docs/developer/index.md Adds the new subsystem page to the developer docs index.
docs/developer/design/mesh-reconnection-and-delaunay-adapt.md New design/investigation notes capturing reconnection + adapt-on-top findings and constraints.

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Comment on lines +463 to +467
if alpha is None:
native = meshVariable_to_native_pv_mesh(meshVar)
if native is not None:
return native

Comment on lines +846 to +854
if fault_style == "facets":
pvf = labelled_facets_to_pv_mesh(mesh, name)
if pvf.n_points == 0:
continue # this rank owns none of it; normal
if clip is not None:
pvf = pvf.clip(normal=clip[0], origin=clip[1])
plotter.add_mesh(pvf, color=fault_colour, lighting=False,
line_width=fault_line_width, label=name)
key.append([name, fault_colour, line_face])
Comment on lines +30 to +32
# Reference from the serial run, so a partition-dependent regression shows up as
# a number rather than as a mysterious parallel failure.
SERIAL_PINNED_COORDS = None # filled by the first (serial-equivalent) gather
Comment on lines +10 to +16
import numpy as np
import pytest

import underworld3 as uw
import underworld3.visualisation as vis

pytestmark = [pytest.mark.level_1, pytest.mark.tier_a]

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Adversarial review (authoring session; findings, not ceremony).

What we tried to break, and could not: the stack is the common ancestry of both active fault branches and has been exercised for ~3 weeks under them; the serial suites (0843/0844/0845, 82 tests) and the parallel suites (np=2/3, 23 each) pass on the reconciliation branch stacked on this one. The dry-run merge into development is conflict-free.

Findings that ride along, stated so the merge is informed:

  1. Issue #494 lands with this. cut_along_lines with multiple lines in ONE call can return incomplete chains without raising. Known, tracked, and the workaround (cut sequentially — each surface its own call) is what every caller in the repo does. Not a regression; it predates this PR's branch point and the fix is scheduled with the placement path (#511's successor work).
  2. repair=True gives up partition-independence (which cells may be touched depends on the seam). Documented prominently in reconnect.py and opt-in; the default path is bit-confluent at any rank count.
  3. Semantic staleness risk vs post-#503 development: this base was written when Null_Boundary still existed; development has since removed it. We checked the code paths: _interface_edges / _BOOKKEEPING_LABELS read labels generically and nothing depends on Null_Boundary's presence — its removal makes the documented vertex-noise trap moot rather than the guard wrong. The docstrings describing that trap are now history rather than description; accurate either way. CI's merged-tree run is the authoritative check here.
  4. An essential BC on an embedded surface under geometric MG is unsound (coarse levels carry no surface DOFs) — documented with a warning in add_conforming_surface; the material-contrast use case this exists for is unaffected.

Recommend merge once CI is green; #511 stacks on it.

Underworld development team with AI support from Claude Code

…when it finds nothing

The tripwire asserts that the #449 defect (interior-vertex rows of the 3-D
nested prolongation) is still present, so that its fix cannot land unnoticed.
But the defect rides on vertices a closure cascade places strictly inside a
coarse tet, and whether ANY arise depends on the gmsh mesh: the linux CI mesh
presents none while the macOS reference mesh does. The positive assert
therefore fired falsely on PR #510's CI - reporting the defect fixed when it
is merely unexercised on that platform's mesh.

Its own docstring predicted the fragility mechanism (one row in 2336, gmsh
version sensitivity) when it rejected strict xfail; the same fragility bites
the positive assert from the other side. A skip with the full story keeps the
tripwire informative where the cascade parentage occurs and harmless where it
does not.

Underworld development team with AI support from Claude Code
lmoresi added a commit that referenced this pull request Aug 9, 2026
…o the live KSP (#514) (#515)

Since #471 the bundle's default smoother is gmres/4. A Krylov smoother makes
the preconditioner vary between applications, and a plain-gmres outer's
recurrence assumes it fixed: measured on a 3-D adapt child (PR #510 CI, then
locally), the KSP reported CONVERGED_RTOL at 3 iterations with the true
residual stalled at 1.3e-6 - a hundred times the gate. The same failure was
found and fixed locally twice before, on the Stokes velocity sub-KSP and on
the free-surface solver, which is exactly the piecemeal drift #471 exists to
end; this puts the pairing in the one owner.

Three parts. ksp_type=fgmres joins the geometric bundle for BOTH smoother
variants - richardson does not need flexibility, but the stale-key derivation
requires every variant to own the same keys, and fgmres judges convergence on
the true residual, which is never wrong. The three solver-default writers of
ksp_type go through _push_managed_option, so the bundle may upgrade the
DEFAULT but never a user's explicit choice (the ownership latch). And the
top-level install path applies the resolved type to the LIVE KSP: the
database write alone is provably inert there, because the KSP consumed its
options long before injection - the new live test caught exactly that in its
first run. The fieldsplit velocity sub-KSP needs no live application (its
setFromOptions runs at the parent's PCSetUp, after the write) and the rotated
path already writes fgmres unconditionally on its per-solve prefix.

On hierarchies where one FMG application converges the cycle, the two
pairings are indistinguishable (measured: 3.3e-8 either way on the 2-D
fixture); the drift needs a hierarchy the smoother varies on, which is the
3-D one-level-per-doubling shape arriving with PR #510 - its test_0842 is the
discriminating gate, and passes on the composed tree.

Closes #514.

Underworld development team with AI support from Claude Code
lmoresi added 5 commits August 9, 2026 10:49
…lts CI

The hierarchy-plot tests build Plotters with live actor pipelines and left
them to the garbage collector. VTK destroys its objects in whatever order the
collector visits them, and out-of-order destruction of render pipelines is an
intermittent segfault: on the CI runners it killed the whole test_08* pytest
invocation in two of three runs of PR #510 - after every test in this file
had PASSED - while the identical tree ran clean the third time. A crash
decided by collection order cannot be chased by rerunning; it is prevented by
closing. OFF_SCREEN because a test must never depend on a display existing.

Underworld development team with AI support from Claude Code
A segfault kills this pytest invocation on the CI runners in three of four
runs of PR #510, and only there - development's own CI is green in the same
hour, so the site is in this branch's file range (0843-0847) or state they
leave behind. pytest's stdout is block-buffered on CI, so the plain
invocation hides the crash site behind up to 8 KB of unflushed dots; the
apparent position (after test_0844_reconnect_repair's dots) is bounded by a
buffer, not a fact. Unbuffered per-test lines make the last printed line the
actual site. Revert once identified.

Underworld development team with AI support from Claude Code
…#503)

test_a_vertex_blanket_label_is_not_an_interface harvested its every-vertex
blanket from Null_Boundary, which #503 removed from development while this
branch was in flight. dm.getLabel on the missing name returns petsc4py's
non-None NULL wrapper and the first call on it SEGFAULTS - killing the whole
test_08x pytest invocation on CI with no summary, at a position the block-
buffered output misattributed to the next file. Reproduced locally on the
merged tree (exit 139 at exactly label.getValueIS()); every green run had a
pre-#503 merge snapshot and every crash a post-#503 one, which is also the
whole of the apparent nondeterminism (GitHub's merge refs are eventually
consistent, so which snapshot a run got depended on timing).

The trap CLASS outlives the label that shipped it - any bookkeeping or user
label can blanket the vertices - so the test now creates the blanket itself
and asserts the same guard, with the history in the docstring.

Underworld development team with AI support from Claude Code
@lmoresi
lmoresi merged commit 5e1a903 into development Aug 9, 2026
2 checks passed
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