Communications in Applied Mathematics and Computational Science

Time-parallel gravitational collapse simulation

Andreas Kreienbuehl, Pietro Benedusi, Daniel Ruprecht, and Rolf Krause

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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 subcritical and black hole case; our experiments show that Parareal generates substantial speedup and, in the supercritical regime, can reproduce Choptuik’s black hole mass scaling law.

Article information

Commun. Appl. Math. Comput. Sci., Volume 12, Number 1 (2017), 109-128.

Received: 24 April 2016
Revised: 28 December 2016
Accepted: 18 April 2017
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Primary: 35Q76: Einstein equations 65M25: Method of characteristics 65Y05: Parallel computation 83C57: Black holes

Einstein–Klein–Gordon gravitational collapse Choptuik scaling Parareal spatial coarsening load balancing speedup


Kreienbuehl, Andreas; Benedusi, Pietro; Ruprecht, Daniel; Krause, Rolf. Time-parallel gravitational collapse simulation. Commun. Appl. Math. Comput. Sci. 12 (2017), no. 1, 109--128. doi:10.2140/camcos.2017.12.109.

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