Verification gallery

PRISM's regression suite (src/tests/prism/regression/, PRISM regression) pins every case to a golden digest; this page shows the cases that also carry an oracle: a check.sh that asserts a physical or structural property of the run (an invariant, a symmetry, an agreement between two discretisations of the same problem) rather than a stored number. The figures are drawn from the runs by src/tests/prism/regression/make_doc_figures.py (each check run with --keep); the runs use the CPU backend unless stated, PRISM_EXE=exe/adam_prism_fnl runs a check on the GPU (FNL) backend.

Analytic oracles for the physics (plane wave and Gaussian pulse convergence, PEC image, cavity mode, PML reflection against angle, infinite wire against Biot–Savart, Larmor orbit, plasma frequency) are tracked in #106; the Fresnel slab against its exact spectral solution in #105.

cd src/tests/prism/regression/rmf-amr-fd-pulse && ./check.sh       # CPU backend
PRISM_EXE=$PWD/../../../../../exe/adam_prism_fnl ./check.sh        # FNL backend (GPU)

AMR

Quadtree 2:1 seams: the source-free pulse

A quadtree ([amr] ratio = 4) refines x and y only: its blocks span the domain along z at every level, so a 2:1 seam is 2:1 in x and y and 1:1 in z. Until #46 the seam machinery (ghost restriction, coarse-fine interpolation, reflux) assumed an octree, and the coarse cells beside a quadtree seam picked up a spurious z dependence; quadtree AMR was refused at initialisation.

Case. rmf-amr-fd-pulse: the source-free Gaussian EM pulse (B0 = 10, σ = 0.01) travelling along +y across a 2:1 seam at x = 0 (the x < 0 half refined one level), fd_centered order 6, SSP-54, 5 steps, 1 rank. The pulse is uniform in x and z, so the seam is the only thing that can perturb it: it generates By, and the seam div(B) source of #29 (a truncation-order quantity the check pins to a baseline).

Oracle (the quadtree leg of check.sh, default-on). The same case runs on the octree of the regression case and on a quadtree with nk = 16 (z cells of 7.5·10⁻³ against the octree's finest 1.875·10⁻³). PRISM's time step is CFL · min(dx, dy, dz) / c, set on both trees by the finest x and y cells, so the two runs take the same steps; the pulse is uniform in z, so both stay z-invariant. quadtree_oracle.py (shared with FLUME's MV-15) keys the cells by their (x, y) centre and asserts, per field:

• the z spread of every (x, y) column of each run at most 1e-13;
• the quadtree against the octree at the same (x, y) at most 1e-13.

Each field is measured against the largest magnitude of its vector (D, B, J): the pulse carries Dz and Bx, and the seam adds By; the other components are round-off on the octree (Dx, Dy ~ 3·10⁻¹⁸, Bz ~ 5·10⁻¹⁶ against |Bx| = 10) and exactly zero on the quadtree, and scaled by their own magnitude they would compare round-off with round-off. The leg also holds the quadtree's div(D) to the structural round-off invariant of the case.

Results (CPU; FNL in parentheses where it differs):

Quantity	Octree	Quadtree
z spread of a column, max over D and B	2.6·10⁻¹⁶ (FNL 3.6·10⁻¹⁶)	0
against the octree, per (x, y) column, max over D and B	—	1.8·10⁻¹⁶ (FNL 3.6·10⁻¹⁶)
seam max|div(B)| at step 5	12.65004	12.65004
max|div(D)|	3.1·10⁻¹⁵	0

The quadtree reproduces the octree to round-off, including the seam's div(B) source to every printed digit: on a z-invariant field the per-axis seam formulas (restriction over 2×2 fine cells, coincident interpolation rows along z) give the same values as the octree's 2×2×2 ones on two identical z layers. The octree's own z spread and its non-zero div(D) are round-off of its z interpolation (its tricubic weights depend on the z sub-position); the quadtree has neither.

Top row: Bx on z = 0 (quadtree, blocks outlined: the refined half x < 0 and the seam at x = 0), and Bx on y = 0 for both trees: the octree refines its x < 0 blocks in z as well, the quadtree keeps one z layer of blocks. Bottom row: the quadtree against the octree per (x, y) column (relative to each vector's magnitude); By, the field the seam generates; and the divergence histories of the two runs, superposed.