VALIDATION & PROOF · SOLVER V&V REPORT V3

Verification and validation of the FEA Preview solver.

Verification and validation of the FEA Preview solver.

One solver route under one stated scope: regular, axis-aligned HEXA8 discretisations of small-displacement, linear, isotropic static elasticity, with homogeneous displacement supports and consistently integrated loads, exercised through the shipping entry points on the packaged Metal route. Every number in the report was read from machine-generated evidence, and every acceptance decision is a named gate with an observed value, a comparator and a limit frozen before the runs.

Verdict: PASS for the defined release scope

Generated 2026-09-04 · 146 pages

Host: Apple M5 Pro · macOS 26.5 · release build

Nothing here is a certification by ASME, NAFEMS or any other standards body, and no equivalence to ANSYS, NASTRAN, Abaqus or any other commercial code is claimed or implied. The thresholds are Lattiform release criteria chosen by Lattiform; the words verification and validation are used in the ASME V&V 10/20 sense, which is a vocabulary, not an accreditation.

VERDICT

131 PASS · 0 FAIL · 1 PARTIAL · 10 NOT SUPPORTED.

Row outcomes from summary.json. A PASS row passed every applicable frozen gate on the packaged production route. Failing rows would have been retained and published as failures. PARTIAL means evidence exists but a coverage or provenance requirement is incomplete. NOT SUPPORTED is stated explicitly rather than left unmentioned.

131

rows PASS

0

rows FAIL

1

row PARTIAL

10

rows NOT SUPPORTED

1,886

individually named gates declared, frozen before the runs

1,885

gates evaluated, none failed

1

gate NOT RUN, never counted as a pass; its row is PARTIAL

WHAT IS CHECKED

Verification first, then validation, then the boundaries.

The report is organised so that a formulation error, an implementation error and a modelling limit are caught by different groups of gates and cannot be mistaken for one another.

§6–8

Code verification

Rigid-body and null modes, six manufactured constant-stress patch states on both backends, and the closed-form axial response.

§9–10

Invariance and mesh convergence

Invariance sweeps and refinement ladders with an observed order of accuracy, reported only where the ladder is resolution limited.

§11–12

External correlation

NASA SP-224(03) problem 1-8-1 against its published table, the MacNeal–Harder cantilever against the published theoretical column, and the benchmarks recorded NOT SUPPORTED.

§13–14

Parity and determinism

CPU/Metal parity in L2 and L∞ on displacement, reactions, stress and energy; five repeats per problem with one distinct displacement hash.

§15–16

Boundary sweeps and fail-closed

Poisson’s ratio toward 0.5, element aspect ratio from 200 to 0.125, and a 22-row fail-closed matrix of invalid, degenerate or over-budget studies, each refused before any result is published.

§17–19

Performance, limits, reproduction

Fresh-process and warm timings with no speedup claim, the limitations stated in full, and the evidence index that regenerates the report from one command.

EXTERNAL CORRELATION

Published tables, not re-derived formulas.

V1 compared against a beam formula re-derived inside the test. V3 compares against the published tables themselves, station by station, at every refinement level.

NASA SP-224(03) problem 1-8-1 · structured-grid adaptation · five refinement levels

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Grid

Elements

DOF

Max station error

Published σ error

Iterations

10 × 4 × 1

40

330

0.072 %

0.103 %

52

20 × 8 × 2

320

1,701

0.0181 %

0.0323 %

104

30 × 12 × 3

1,080

4,836

0.00803 %

0.0164 %

173

40 × 16 × 4

2,560

10,455

0.00452 %

0.0106 %

224

50 × 20 × 5

5,000

19,278

0.00289 %

0.00769 %

276

SAME TABLE, DRAWN · MAX STATION ERROR AND PUBLISHED σ ERROR BY GRID, LOG SCALE

Validation & Proof — Lattiform FEA Preview0.001 %0.01 %0.1 %1 %Error10 × 4 × 120 × 8 × 230 × 12 × 340 × 16 × 450 × 20 × 5
Max station errorPublished σ error

The station error falls from 0.072 % to 0.00289 % across the five levels, and the report tests where the remaining disagreement comes from rather than asserting it: on the 40 × 16 × 4 grid, tightening only the solver tolerance from 2 × 10⁻⁵ to 1 × 10⁻⁸ leaves the published-value error at 0.00452 %, so at this level it is not solver truncation. Agreement with the table is correlation evidence about this solver, not a reproduction of NASTRAN’s answer, because the element topology differs.

MSC Nastran Verification Guide 1.1 straight cantilever · load-distribution adaptation · displacement error against the published theoretical column

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Level · grid

Extension

In-plane shear

Out-of-plane shear

1 · 6 × 1 × 1

1.44 %

12.3 %

13.2 %

2 · 12 × 2 × 1

0.720 %

4.84 %

10.7 %

3 · 24 × 4 × 2

0.366 %

1.82 %

3.84 %

4 · 48 × 8 × 4

0.195 %

0.754 %

1.36 %

5 · 96 × 16 × 8

0.120 %

0.364 %

0.578 %

SAME TABLE, DRAWN · TIP DISPLACEMENT ERROR BY REFINEMENT LEVEL, LOG SCALE

Validation & Proof — Lattiform FEA Preview0.1 %1 %10 %100 %Error1 · 6 × 1 × 12 · 12 × 2 × 13 · 24 × 4 × 24 · 48 × 8 × 45 · 96 × 16 × 8
ExtensionIn-plane shearOut-of-plane shear

The unit tip force is applied as a consistently integrated uniform traction because the source does not state how it is distributed, which is why this is an adaptation rather than an exact representation. These are validation ladders: the residual gap at the finest mesh includes beam-theory model error and the clamped-end effect the published problem specifies. The twist case is not compared, and both distorted-mesh variants are NOT SUPPORTED, because this route discretises a regular axis-aligned grid only; the report states that this is the most important limitation of its external correlation.

SCALE

One million elements on the packaged Metal route.

Four frozen targets, each solved with one discarded warm-up and ten timed repeats, with the independent double-precision residual recomputed at scale and peak resident memory read from the kernel. Measured on an Apple M5 Pro, macOS 26.5, release build. A measurement on one host on one day, with no baseline and no comparative claim.

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Target

Grid

Elements

DOF

Median total

Peak resident

100k

120 × 30 × 30

108,000

348,843

1.610 s

266 MiB

250k

160 × 40 × 40

256,000

811,923

4.791 s

548 MiB

500k

200 × 50 × 50

500,000

1,568,403

11.675 s

972 MiB

1M

252 × 63 × 63

1,000,188

3,108,864

27.898 s

1.28 GiB

STATED, NOT OMITTED

Ten rows recorded NOT SUPPORTED.

Each carries the reason it cannot be posed through this route, so that a reader near that boundary knows what they are looking at.

Benchmarks the route cannot represent

  • NAFEMS P18 LE10 thick elliptical plate: curved geometry the regular grid cannot represent without a stair-stepped approximation that would change the benchmark

  • NAFEMS P18 LE11: curved geometry plus a thermal load path the study model does not expose

  • MacNeal–Harder solid patch test: defined by prescribed non-zero displacements, which the per-node component mask cannot express

  • MacNeal–Harder membrane patch test: a plane-stress problem, outside a 3D solid route

  • MSC cantilever trapezoidal and parallelogram meshes: distorted elements on a regular axis-aligned grid

Capabilities outside the boundary

  • NASA SP-224(03) 1-9-1 subcase 2: a uniform temperature field, not exposed through the FEA Preview study model

  • MSC cantilever twist: the published quantity is a tip rotation the source does not define for a solid element, so it is recorded as not compared rather than measured against an invented rotation

  • The three-level resident multilevel Metal route as a general release backend: it refuses grids it cannot certify, and is never used as a silent substitute

  • Nonlinear, contact, plastic, dynamic, modal, buckling, fatigue, anisotropic, distorted or unstructured analysis: outside the implemented physics and formulation boundary

LIMITATIONS

What the report does not prove.

Stated because a V&V document that lists only what it proves is not a V&V document.

  • Geometry is restricted to axis-aligned regular grids; curved and inclined boundaries are stair-stepped approximations

  • The independent residual shares the 24 × 24 element stiffness generator with the product; everything downstream of it is independent

  • The CPU/double reference is the same codebase, not a third-party solver, so parity bounds implementation divergence and says nothing about a shared formulation error

  • Timoshenko beam theory at span-to-depth 4 carries several percent of its own model error, which is why validation is reported separately from self-convergence

  • SP-224 1-8-1 is a structured-grid adaptation: agreement is correlation, not reproduction

  • Stress is compared away from singularities by construction; no statement is made about peak stress at a re-entrant corner or a support edge

  • Determinism is established within one host and one build; cross-device determinism is not claimed

  • Performance figures describe one machine on one day and support no comparative claim

  • The host-memory budget is enforced at the preflight layer only

  • Thermal loading exists in the element core but is not exposed through the study model

REPRODUCTION

Everything regenerates from one command.

The runner refuses to publish if any applicable gate fails, if runtime Metal source compilation occurs, if a fallback is recorded, if a required artifact is missing or empty, or if the acceptance hash carried in the provenance, verification and summary artifacts disagree. The solve itself is bitwise deterministic, so re-running on the same commit and host is expected to reproduce every number except the timings.

Lattiform FEA Preview

Finite element analysis, built for the Mac. Linear static stress studies on a structured HEXA8 grid, solved locally on Apple Silicon with Metal. Coming soon.

Built and validated by Lattiform. Write to beta@lattiform.com with a question or a study file.

© 2026 Lattiform. Lattiform FEA Preview is coming soon. Nothing on this site is a certification by ASME, NAFEMS or any other body, and no equivalence to ANSYS, NASTRAN or any other commercial code is claimed.