0.2.7 Large-Scale Readiness Evidence

Status and scope

WP12 records bounded readiness evidence for the existing structured TET4 linear-static route. It does not add a new element or a new physical model, and it does not claim universal one-million-DOF support. The measured source snapshot is 4971ac4f6c1e5cff2ca48e40ca6db5e8147d0d0a; the evidence was collected on that snapshot before the governance commit containing this report.

The model is a connected structured block with six TET4 per hexahedral cell, homogeneous isotropic linear elasticity, a uniform nodal UX dead load of 1000 N on the x=length face, and linear-static boundary conditions from the existing large-model generator. WEDGE6, nonlinear routes and post-buckling are out of scope.

Reproduction contract

python scripts/run_wp12_scaling.py --output qualification/0_2_7/wp12_scaling_evidence.json --targets 100000 300000 500000 750000 1000000 --replay-target 100000 --timeout-seconds 600 --max-rss-gb 4

The campaign runs isolated child processes with a 600 second timeout and a 4 GiB RSS ceiling. It records topology, timing, memory, sparse non-zeros when an assembled matrix exists, residuals, solution digests and environment metadata. High-DOF SciPy cases are rejected by the existing 200000-DOF guard before model allocation. The separate assembly-only 300k probe is recorded in qualification/0_2_7/wp12_assembly_probe_300k.json.

Environment: Windows 10 build 10.0.19045, Python 3.13.1, NumPy 2.2.6, SciPy 1.15.2, psutil 7.2.2, 12 logical CPUs and approximately 103 GB RAM. mpi4py was available; petsc4py and slepc4py were not available, so no PETSc/SLEPc verdict is issued.

Size ladder

Target	Actual DOF	Elements	Matrix-free CG	SciPy CG	SciPy direct
100k	107,811	196,608	PASS_ITERATIVE	PASS_FULL_SOLVE	RESOURCE_LIMITED_MEMORY
300k	311,469	584,016	PASS_ITERATIVE	SOLVER_LIMITED	SOLVER_LIMITED
500k	526,848	998,250	PASS_ITERATIVE	SOLVER_LIMITED	SOLVER_LIMITED
750k	750,141	1,429,968	PASS_ITERATIVE	SOLVER_LIMITED	SOLVER_LIMITED
1M	1,029,000	1,971,054	RESOURCE_LIMITED_TIME	SOLVER_LIMITED	SOLVER_LIMITED

PASS_ITERATIVE is a completed matrix-free solve with finite observables and relative residual between 9.732e-09 and 9.898e-09. The maximum completed matrix-free solve is 750,141 DOF. The 1M probe reached the declared 600 second limit at a peak sampled RSS of 557,006,848 bytes; it produced no numerical failure and is not a successful 1M solve.

The 100k SciPy CG full solve completed in 6.611 s with 3,813,789 assembled non-zeros, peak RSS 192,356,352 bytes and relative residual 1.169e-12. SciPy direct at the same size reached the 4 GiB RSS limit before completion. The higher SciPy sizes are SOLVER_LIMITED by the explicit 200000-DOF guard; no unbounded allocation was attempted.

300k assembly probe

The current-source assembly-only probe completed for 311,469 DOF and 584,016 TET4 elements. It measured 11,168,199 global non-zeros, 135,264,268 bytes of CSR storage, 217.882 s wall time and peak RSS 1,466,396,672 bytes. Phase timings were 158.609 s mesh validation, 10.554 s assembly planning, 45.662 s assembly, 34.220 s element kernels, 4.036 s sparse conversion and 0.069 s sparse finalization. The linear solve was deliberately NOT_RUN; this row is assembly evidence, not a full-solve result.

Numerical safety and replay

The 100k matrix-free replay produced the same input digest and result digest in two isolated runs and was classified deterministic. Existing targeted tests for matrix-free/SciPy equivalence and the no-dense-conversion guard pass. All completed campaign rows had finite metrics; the report contains zero numerical failures. The matrix-free residuals are consistent with its declared rtol=1e-8 contract, while the assembled SciPy CG residual is substantially smaller.

No FEM formulation, material law, load convention or existing element kernel was changed. The retained optimization WP12-OPT-001 caches the already grouped TET4 connectivity and flattened DOF indices in the matrix-free operator. Targeted equivalence remained passing, and a separate 30k engineering probe showed approximately 1.9x lower elapsed time after the cache change with the same iteration count and residual. This is a local engineering measurement, not a universal speedup claim.

Profile and bottlenecks

The 10k matrix-free profile identifies element matvec and scatter accumulation as the dominant solve work. The 300k assembly probe identifies generated-model validation/materialization as the dominant wall-time component, followed by element kernels and sparse conversion. The bounded ranking is:

1. matrix-free element matvec and scatter accumulation;
2. iteration count and preconditioner quality;
3. large-model validation and generated-model materialization;
4. assembled sparse storage and factorization for the SciPy direct route.

The recommended measured path is matrix-free CG for the high-DOF structured TET4 route, with assembled SciPy CG limited to its explicit configured domain. PETSc remains a future option only after its dependencies and reproducible execution environment are available.

Bounded conclusion

The campaign supports PASS_WITH_LIMITATIONS evidence for the declared structured TET4 linear-static route and is ready for Owner review. It supports completed iterative solves through 750,141 DOF, a characterized 311,469-DOF assembly-only result, and a bounded 1M readiness attempt. It does not support a public full-solve claim at 1M DOF, a multi-million-DOF claim, general topology scaling, or a claim that direct SciPy is viable at the measured high sizes.

Machine-readable records:

• wp12_state.json
• wp12_scaling_evidence.json
• wp12_assembly_probe_300k.json

The campaign report and this document are CONTROLLED_PROOF records. The Owner decision remains PROPOSED_OWNER_REVIEW; resource-limited and solver-limited rows are preserved rather than converted to PASS.