BHaHAHA: A Fast, Robust Apparent Horizon Finder Library for Numerical Relativity

TL;DR

BHaHAHA is an open-source, infrastructure-agnostic library for apparent horizon finding in numerical relativity, utilizing a novel hyperbolic flow approach with significant speed improvements.

Contribution

It introduces the first hyperbolic flow-based method for AH finding, achieving high speed and robustness across different NR codes.

Findings

64x speedup over naive hyperbolic relaxation on single slices

Achieves within 10% of AHFinderDirect runtimes on a single core

Approximately 2.1 times faster than AHFinderDirect on HPC clusters

Abstract

Apparent horizon (AH) finders are essential for characterizing black holes and excising their interiors in numerical relativity (NR) simulations. However, open-source AH finders to date are tightly coupled to individual NR codes. We introduce BHaHAHA, the BlackHoles@Home Apparent Horizon Algorithm, the first open-source, infrastructure-agnostic library for AH finding in NR. BHaHAHA implements the first-ever hyperbolic flow-based approach, recasting the elliptic partial differential equation for a marginally outer trapped surface as a damped nonlinear wave equation. To enhance performance, BHaHAHA incorporates a multigrid-inspired refinement strategy, an over-relaxation technique, and OpenMP parallelization. When compared to a na\"ive hyperbolic relaxation implementation, these enhancements result in 64x speedups for difficult common-horizon finds on a single spacetime slice, enabling BHaHAHA to achieve runtimes within 10% of the widely used (single-core) AHFinderDirect and outperform it on multiple cores. For dynamic horizon tracking with typical core counts on a high-performance-computing cluster, BHaHAHA is approximately 2.1 times faster than AHFinderDirect at accuracies limited by interpolation of metric data from the host NR code. Implemented and tested in both the Einstein Toolkit and BlackHoles@Home, BHaHAHA demonstrates that hyperbolic relaxation can be a robust, versatile, and performant approach for AH finding.