Dear all,

Please accept a correction to my previous email, which I sent out before checking it carefully. My apologies for the noise. Three clarifications:

1. The numbers 256, 128 and 2048 that I called "resolution" are in fact run lengths (cctk_itlast, the number of evolution iterations) of the same GW150914 3-level Carpet AMR run -- not grid resolutions. The corrected statement is: the 100-particle geodesic run with cctk_itlast=256 (metric_interp=aei, time_interp=linear) is bit-for-bit identical to the reference run over their common time range -- all compared output blocks, covering t = 0 .. 0.3356, show zero numerical difference, with 0 dropped particles and 0 NaNs. This is a statement about the reproducibility of the numerical integration (same code, same input), not about exactness against an analytic solution, which of course does not exist for this non-stationary spacetime. The full-length production run uses cctk_itlast=2048.

2. "40 particle blocks of 100" was unclear: the run contains 100 particles, and the comparison covers 40 output blocks in the common time range.

3. For reproduction: the exact code used for these runs is now in the Geodesic thorn repository (branch main, commit 60c900e "robust metric sampling + GW150914 aei (2048)"), together with the production parameter file par/aei_2048.par, so the reported results can be reproduced directly.

The main conclusion is unchanged: the aei sampler on the GW150914 BBH AMR evolution is verified and reproducible. The other samplers (local27 and its time-linear variant l27lin, plus carpet) are still under test, and I will report on them once they pass verification.

Best regards, Yuhua Li

At 2026-10-01 23:10:41, "Yuhua Li via Users" users@einsteintoolkit.org wrote:

Dear all,

Following my previous updates, I would like to report progress on applying the samplers to the GW150914 binary-black-hole (BBH) spacetime on a 3- level Carpet AMR mesh -- the first fully realistic (non-stationary) test case for the geodesic probe.

Completed this week: the aei sampler (metric_interp=aei, time_interp= linear). The 100-particle geodesic run at 256 resolution reproduces the reference run exactly: all compared steps (t = 0 .. 0.3356, 40 particle blocks of 100) agree to full double precision, with 0 dropped particles and 0 NaNs. At 128 resolution the t=0 block likewise matches a 2048 reference to full precision, and the residual difference at t=0.2753 (position ~5e-4) is consistent with the expected convergence of the sampler. In short, aei on the GW150914 AMR evolution is now verified and reproducible.

Still under test (no result this week): the remaining samplers (local27 and its time-linear variant l27lin, plus carpet) on the BBH AMR mesh. In particular l27lin shows particle loss in the strong-curvature region near the horizons; I am debugging the metric/Christoffel sampling path there. I have no conclusion to report on them yet.

So this week's deliverable is a single, clean result: aei on GW150914 is verified reproducible. The other samplers on the BBH AMR remain under verification, and I will report a concrete result once they pass.

As before, I am most comfortable continuing in writing. Any questions or suggestions on the strong-curvature path are welcome.

Best regards, Yuhua Li