A GPU-accelerated mixed-precision WENO method for extremal black hole and gravitational wave physics computations

TL;DR

This paper introduces a GPU-accelerated mixed-precision WENO method for solving the Teukolsky equation, significantly improving computational speed and stability in black hole and gravitational wave physics simulations.

Contribution

The paper presents a novel mixed-precision WENO scheme combined with GPU acceleration, outperforming traditional methods in stability and speed for black hole perturbation computations.

Findings

WENO methods outperform higher-order finite-difference methods in stability.

Mixed-precision approach yields a 3.3x speedup in WENO computations.

GPU acceleration further enhances computational efficiency.

Abstract

We develop and use a novel mixed-precision weighted essentially non-oscillatory (WENO) method for solving the Teukolsky equation, which arises when modeling perturbations of Kerr black holes. We show that WENO methods outperform higher-order finite-difference methods, standard in the discretization of the Teukolsky equation, due to the need to add dissipation for stability purposes in the latter. In particular, as the WENO scheme uses no additional dissipation it is well-suited for scenarios requiring long-time evolution such as the study of Price tails and gravitational wave emission from extreme mass ratio binaries. In the mixed-precision approach, the expensive computation of the WENO weights is performed in reduced floating-point precision that results in a significant speedup factor of 3.3. In addition, we use state-of-the-art Nvidia general-purpose graphics processing units and cluster parallelism to further accelerate the WENO computations. Our optimized WENO solver can be used to quickly generate accurate results of significance in the field of black hole and gravitational wave physics. We apply our solver to study the behavior of the Aretakis charge -- a conserved quantity, that if detected by a gravitational wave observatory like LIGO/Virgo would prove the existence of extremal black holes.