Quality assurance: how do we compare?

Four independent ways to be wrong — and we check all of them before any number on this site is published.

Analytical solutions

The first line of defence is closed forms: Mie-series scattering, shoebox modal frequencies, piston directivity, Poiseuille and Taylor–Green flows, waveguide and cavity modes, Euler–Bernoulli beams, Kirchhoff plates, Lamé fields — plus manufactured-solution convergence ladders in every physics group and 46 self-contained reference-identity cases.

Wolfram oracles

79 integration tests check Sonium against 80 independent Wolfram Language oracles (.wls) with checked-in goldens — eigenfrequencies, eigenmodes, and transient fields for rooms, horns, membranes, mufflers, cloaks, solids, heat, and flow — plus 12 audio-DSP cases in a dedicated manifest. Open the Wolfram contracts ↓

Open-source engines

20 manifest cases replay independently harvested OpenCourant/OpenRadioss histories: material-point plasticity (LAW76, crushable foam), thick-cylinder and plate pressure holds. Around them: runnable FreeFEM (room) and FastBEM (BEM) cross-check binaries, CalculiX/Code_Aster/FEniCS spot checks on structural decks, and MFEM/Basix Piola identities for electromagnetics. Timed head-to-heads live on the perf page ↓.

Cross-validation

Backends prove each other: CPU-vs-CUDA-vs-Metal parity, dense-vs-compressed BEM parity (H-matrix/FMM against dense TBEM), FEM/BEM coupling traces, and same-mesh state identity — with FFTW and platform libm as the wave/fastmath anchors.

Groups

1. scattering

   Acoustic scattering — BEM · 151 binaries · 153 cases

   Rigid and penetrable spheres and cylinders, transmission, Galerkin formulations, and compressed operators (H-matrix, FMM, MLFMM) with mesh-convergence ladders and adjoint certification.

   Compared with: analytic Mie-series solutions via sonium-wave; dense-vs-compressed parity against dense TBEM; runnable FastBEM/EAA cross-checks.

2. room

   Room acoustics · 27 binaries · 27 cases

   Shoebox FEM benchmarks, mesh convergence, backend parity, energy balance, and gallery-manifest integrity for the room simulators and their RoomEQ data exports.

   Compared with: analytic shoebox modal frequencies; FEM-vs-fast-hybrid parity; a FreeFEM cross-check binary.

3. speaker

   Loudspeakers · 11 binaries · 11 cases

   Piston directivity benchmarks, port nonlinearity gates (Poiseuille, lumped-limit, THD), and rank-preservation checks behind the CEA-2034 simulation pipeline.

   Compared with: analytic piston directivity; lumped Helmholtz resonance; full-order FEM/BEM reference solves.

4. fan/prop

   Fans & propellers · 49 binaries · 49 cases

   PC-fan CFD/adjoint contracts and propeller aeroacoustic studies: actuator loading, retarded-time identities, gallery replay, and release evidence for shrouded and toroidal designs.

   Compared with: analytic identities (Farassat 1A, monopole/dipole, convected travel-time); actuator-disk bounds; converged CFD states.

5. structure

   Structures & elasticity · 45 binaries · 49 cases

   Cantilevers, plates with holes, thick cylinders, contact and dynamics: first bending frequencies, mass orthogonality, and Newton/Uzawa convergence with deterministic galleries.

   Compared with: Euler-Bernoulli closed forms; Wolfram solid-eigenmode tests; independently checked deck provenance.

6. em

   Electromagnetics · 29 binaries · 29 cases

   PEC cavities, TE10/TE11 waveguides, eddy currents, and magnetostatics on affine and curved meshes with Piola-mapped elements and orientation torture tests.

   Compared with: analytic waveguide and cavity modes; MFEM/Basix Piola reference identities; manufactured solutions.

7. fluids

   Fluids & thermal · 18 binaries · 29 cases

   Poiseuille and lid-driven-cavity flows, cylinder wakes, Boussinesq convection, and axisymmetric heat conduction with manufactured-solution convergence ladders.

   Compared with: Poiseuille and manufactured solutions; mass/momentum conservation identities; Wolfram heat/flow tests.

8. fem-core

   FEM methods & multiphysics · 96 binaries · 108 cases

   The shared FEM machinery every physics module stands on: assembly, solvers, transfers, and coupled FEM/BEM traces, exercised independently of any single application.

   Compared with: manufactured sine-product solutions; independent dense solves; same-mesh state identity.

9. solvers

   Solvers & preconditioners · 159 binaries · 159 cases

   Iterative, direct, eigen, optimization, and time-integration solvers with AMG/ILU preconditioners: determinism goldens, failure taxonomies, and cross-family result contracts.

   Compared with: exact residuals and known-solution vectors; cross-solver agreement; Wolfram scalar eigenproblems.

10. wave

    Wave, FFT & fastmath · 22 binaries · 22 cases

    Ducts, interfaces, and radiating cavities plus the FFT and vectorized-transcendental foundations: the analytic references other groups validate against.

    Compared with: manufactured wave solutions; an FFTW reference test; platform libm for fastmath accuracy.

11. mesh

    Meshes, MeshLang & interchange · 89 binaries · 89 cases

    Mesh validity and refinement, the MeshLang geometry compiler (parser, provenance, registries), and XEM schema envelopes with cross-language reader interop.

    Compared with: geometric invariants (volume conservation, manifoldness); schema round-trips; deterministic fixtures.

12. compute

    Compute backends · 33 binaries · 34 cases

    BLAS, BEM kernels, and block-Krylov workspaces across CPU, CUDA, and Metal: capability tables, residency accounting, and fault-injection contracts per lane.

    Compared with: CPU-vs-CUDA-vs-Metal backend parity; sonium-wave Green-function references.

13. reference

    Reference solutions · 46 binaries · 46 cases

    Self-contained closed-form identities and limiting/scaling checks, one per binary, across FEM physics — the quick reference-only companion to the gated suites.

    Compared with: closed-form identities evaluated inside each binary.

14. wolfram

    Wolfram contracts · 79 integration tests + 80 scripts

    Independent Wolfram Language solutions (.wls) for acoustic, structural, heat, and flow eigen- and time-domain problems, checked by dedicated integration tests — not binaries.

    Compared with: Wolfram-computed eigenfrequencies, eigenmodes, and transient fields (rooms, horns, membranes, mufflers, cloaks).