Time parallel gravitational collapse simulation

TL;DR

This paper explores the use of the Parareal parallel-in-time method to efficiently simulate gravitational collapse in Einstein's equations, demonstrating significant speedups and accurate reproduction of black hole mass scaling.

Contribution

It introduces a tailored load balancing scheme for Parareal in gravitational collapse simulations and evaluates its performance in different regimes.

Findings

Parareal achieves substantial speedup in simulations.

The method accurately reproduces black hole mass scaling law.

Performance varies between sub-critical and super-critical regimes.

Abstract

This article demonstrates the applicability of the parallel-in-time method Parareal to the numerical solution of the Einstein gravity equations for the spherical collapse of a massless scalar field. To account for the shrinking of the spatial domain in time, a tailored load balancing scheme is proposed and compared to load balancing based on number of time steps alone. The performance of Parareal is studied for both the sub-critical and black hole case; our experiments show that Parareal generates substantial speedup and, in the super-critical regime, can reproduce Choptuik's black hole mass scaling law.