Forward-from-nodes history; semi-Lagrangian schemes named by trace and launch; every history equals serial in parallel

[lmoresi]

Stacked on #795.

What changes

One entry point for the semi-Lagrangian histories. uw.systems.ddt.SemiLagrangian(mesh, psi_fn, V_fn, vtype, trace=, launch=) selects one of four schemes:

trace	launch	class (former name)
backward	nodes (default)	BackwardNodesSemiLagrangian (SemiLagrangian)
backward	integration_points	BackwardIntegrationPointsSemiLagrangian (IntegrationPointSemiLagrangian)
forward	integration_points	ForwardIntegrationPointsSemiLagrangian (ForwardSemiLagrangian)
forward	nodes	ForwardNodesSemiLagrangian (new)

A keyword the chosen scheme does not take is a TypeError. The former class names and the former stress_transport strings (semi_lagrangian, integration_point, forward) still work, with a FutureWarning. stress_transport takes backward_nodes (default), backward_integration_points, forward_integration_points, forward_nodes, lagrangian, eulerian; AdvDiffusionSLCN(transport=...) chooses its value history among the four semi-Lagrangian schemes.

Forward from nodes. The history launches its values from the field's nodes and from a lattice inside every element (the discontinuous basis two degrees up), carries them one step forward, fits the arrivals in each cell at the field's degree, and projects the per-cell fits onto the continuous store. A cell with too few arrivals takes a linear fit to its own arrivals, or their mean; an arrival on a shared face is fitted in every cell that contains it. A stress is committed by L2 projection onto the store and launched from that field. Rotating diffusing Gaussian, P2, SLCN solver, integral error:

	half turn, disc	half turn, box	full turn, disc
forward from nodes	1.78e-2	6.57e-2	8.14e-2
backward from nodes	2.52e-2	6.43e-2	8.94e-2

The box, where the flow crosses every wall, is slightly worse than the backward scheme. A serial-only version that let thin cells borrow arrivals from their neighbours reached 1.68e-2 and 6.32e-2; that borrowing depends on the partition and was removed. First order; a fixed mesh.

Every history gives the serial answer in parallel. tests/parallel/test_1066 holds the six stress histories (turned-over Maxwell box) and the four semi-Lagrangian value histories (rotating Gaussian with inflow) to 1e-6 of their serial values at np >= 3; verified at np 3, 4 and 6. Five sources of partition dependence were removed:

1. History projections were solved at the projection default tolerance (1e-4) with an aggregating multigrid; they are now CG with Jacobi to 1e-12 from a zero start (the warm start also made a restart differ from a straight run).
2. The nodal and integration-point histories recorded the current field by evaluating it at nudged nodes (serial) or by copying it (parallel, and only when handed the variable itself); a field that is a mesh variable is now always copied.
3. Behaviour change of the default scheme: the nodal trace-back took its start velocity at the node nudged 0.1% toward "the closest cell's" centroid. A seam node was nudged differently on each rank, and a node on a no-slip wall was given a velocity. The trace now starts at the node. Serial answers near walls change; all 388 tests in the transport, Navier-Stokes and viscoelastic set pass unchanged.
4. global_evaluate: a point that the swarm migration handed to a rank whose cells do not contain it was given the nearest-centroid rbf extrapolation (3e-2 at a steep stress, np 4). The rank whose cell contains it now evaluates it with the FE interpolant. This runs only where the cell hint is authoritative (no DMLocatePoints collective inside), and a finite rbf value is kept where the FE value is NaN.
5. Cell tie-breaks in the forward fits, described above.

Open

• Particle (Lagrangian) stress history differs from serial by 1.2e-5 at np >= 4 #797: the particle history differs from serial by 1.2e-5 at np 4 and 6 (np 3 matches); marked xfail.
• evaluate(..., evalf=True) flags every point as extrapolated #798, evaluate() is off by up to 4e-5 for a field the P2 space holds exactly, at points near a node #799: a false "not located" warning from evalf=True, and serial evaluate off by up to 4e-5 near nodes for an exactly represented P2 field.
• SLCN trace-back gives a partition-dependent answer (1.6% at np=8 on a 128x128 level set) #682 (SLCN level-set volume depends on the rank count) is probably the same set of causes; not rerun.
• TODO(DESIGN): face arrivals are offered to every rank, not only across seams; the two forward schemes use different rules for an arrival exactly on a face.
• Not yet offered for the Navier-Stokes velocity history.

Tests

tests/parallel/test_1066 (new), test_1062 tightened to 1e-6, test_1102 (new, forward from nodes against hard baselines), test_1063 covers forward_nodes, test_1059 covers selection, renamed strings and the Maxwell box for every history. Serial transport/NS/VE set: 388 passed. Parallel np 3/4/6: 10 passed, 1 xfail at np >= 4.

🤖 Generated with Claude Code

https://claude.ai/code/session_017kSkAq7oJ5J3XisuvLBovo

[lmoresi]

Adversarial review

Two review passes before the push (on c434d8a and on b20c992). Findings and disposition:

Fixed

• The SemiLagrangian entry point passed positional arguments to schemes whose positional order differs (varsymbol=2, order=True silently); now keyword-only after vtype, and an argument the scheme does not take is a TypeError.
• Forward from nodes kept the pre-solve fit for a cell with no arrivals, so an empty inlet cell read back the stress from before the solve; the fallback is now the field the cell launched, and nothing is carried between steps.
• Forward-from-nodes inflow detection used the per-rank points_in_domain, which treats partition faces as boundary: every seam node would have taken the inflow value. Now the global restore test the other flavours use.
• The global_evaluate containment round overwrote a finite rbf value with NaN for a located-but-NaN point (the case the fallback exists for), and could meet a DMLocatePoints collective on non-authoritative meshes through the interpolation cache. Now keeps finite values and runs only where the hint is authoritative.
• The owned-node mask relied on a write-then-read-back through the ghost update (wrong inside a deferred update); now read from the global section.
• A strictly-inside arrival could also be kept by a neighbour whose tolerance band it touched (partition-dependent); now only its own cell.
• containing_cells could miss the containing cell beyond the k nearest centroids; now falls back to the locator. Quadrilateral centroids used the simplex formula.
• History projections warm-started from a state a restart does not restore (restart test failed at 1e-12); now zero-start CG/Jacobi to 1e-12.
• test_1102 windows could not see a default change (+-10%); now 1e-4. test_1066 resets the model per case, asserts the seam exchange ran, runs the inflow path; test_1063 covers forward_nodes.

Deferred (TODO(DESIGN) in the code)

• Face arrivals are allgathered to every rank, including faces interior to a partition (no-slip wall nodes each step).
• The forward integration-point exchange gives a face arrival to one cell; forward from nodes to every containing cell.

Filed: #797 (particle history, np >= 4), #798 (evalf extrapolation flag), #799 (serial evaluate near nodes).

Underworld development team with AI support from Claude Code

[lmoresi]

Added (28314aa):

• SLCN trace-back gives a partition-dependent answer (1.6% at np=8 on a 128x128 level set) #682 fixed. global_evaluate now applies the monotone clamp on the rank that evaluates each point, not on the rank that asked. The level-set volume at np 1/2/4/8 is 0.0706771442/415/438/412; np 8 was 1.6% off. Serial results are unchanged.
• NavierStokesSLCN(velocity_transport=...). The velocity history can use any of the four semi-Lagrangian schemes, built by the same helper as AdvDiffusionSLCN(transport=...). test_1103 runs a lid-driven cavity at Re 100: the three schemes that accept P2 agree to 0.2%, and forward from integration points refuses a P2 velocity. test_1066 adds the cavity, which equals serial at np 3/4/6.
• Test runs. The whole tests/parallel suite at np 4: 168 passed, 1 xfailed (Particle (Lagrangian) stress history differs from serial by 1.2e-5 at np >= 4 #797), 1 failed. The failure is test_1063_constrained_freeslip_parallel[ti] (37.7525 against a recorded 37.0780); it fails identically on Viscoelastic stress past the conformation limit: a positive-definite convected step and a log-conformation history #795's 05d5248, so it predates this PR. The serial transport/NS/VE set: 393 passed.

Underworld development team with AI support from Claude Code