Dear all,

At today's weekly users call I would like to briefly present Geodesic, a new thorn that integrates test-particle geodesics in Kerr--Schild Cartesian coordinates, and ask for feedback before submitting it to the Einstein Toolkit.

Features - Two metric modes: an exact analytic Kerr--Schild metric (grid-independent, symbolically verified to be a vacuum solution at machine precision), and a grid mode that samples the ADMBase fields with three interchangeable samplers selected by one parameter: local27 (default, 27-point local Lagrange fit), aei (fourth-order pointwise, via AEILocalInterp), and carpet (second-order pointwise quadratic Lagrange). - Adaptive RKF45 integration with per-step renormalization of the four-velocity; d_t g recovered from the three most recent ADMBase time levels (stationary metrics are auto-detected). - AMR-ready: each sampler reads the refinement level that contains the particle, so geodesics can be integrated inside a Carpet AMR evolution (with 4:1 subcycling) without any change to the integrator. - OpenMP-parallel particle loop: scales to 10^4 particles (9.2x speedup, 10.4% efficiency on 88 threads); embedded in a full GRHydro evolution, tracking 10^4 particles costs only ~3.1% of the wall time.

Verification - E, L_z and the norm conserved to ~1e-9 over T = 1000 M on three distinct bound orbits (circular, tilted, eccentric). - Grid convergence of the default sampler with a measured local order of 3.7 (formal order three) against an independent reference. - Five-way comparison of the exact metric and the three samplers on a precessing orbit of 200 particles close to the plunge boundary. - New: on a 3-level Carpet AMR mesh (50^3 base, dx=1; refinement boxes of half-width 16/8, factor 2), all three samplers reproduce the unigrid reference orbit of conv100 over ~1.05 orbital periods (t = 0..150.1): radial deviations 0.4% (local27), 0.5% (aei), 2.3% (carpet, consistent with its second formal order), with no lost particles and no NaNs.

Code and configurations - Repository (GPLv2+): https://github.com/wylyhzh/Geodesic - Includes a 7-test testsuite, ThornGuide documentation, and the parameter files used for the results above (including the three AMR-vs-unigrid comparison setups). - A paper describing the implementation and the verification suite is in preparation.

Known limitation - The multi-process (MPI) particle layout is implemented (DISTRIB=CONSTANT, rank-0 integration with state synchronization) but has not yet been exercised with the current rework; single-process OpenMP runs are the tested configuration. The aei sampler in addition needs single-process runs or AEILocalInterp's N_boundary_points_omit when its fourth-order stencil would cross a processor boundary.

Any feedback is very welcome - in particular on whether the thorn should be proposed as EinsteinAnalysis/Geodesic.

Best regards, Yuhua Li