Vol. 12, No. 1, 2017

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ISSN: 2157-5452 (e-only)
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Time-parallel gravitational collapse simulation

Andreas Kreienbuehl, Pietro Benedusi, Daniel Ruprecht and Rolf Krause

Vol. 12 (2017), No. 1, 109–128
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 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.

Keywords
Einstein–Klein–Gordon gravitational collapse, Choptuik scaling, Parareal, spatial coarsening, load balancing, speedup
Mathematical Subject Classification 2010
Primary: 35Q76, 65M25, 65Y05, 83C57
Milestones
Received: 24 April 2016
Revised: 28 December 2016
Accepted: 18 April 2017
Published: 8 May 2017
Authors
Andreas Kreienbuehl
Center for Computational Sciences and Engineering
Lawrence Berkeley National Laboratory
1 Cyclotron Road
Berkeley, CA 94720
United States
Pietro Benedusi
Institute of Computational Science
Faculty of Informatics
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH-6904 Lugano
Switzerland
Daniel Ruprecht
School of Mechanical Engineering
University of Leeds
Woodhouse Lane
Leeds
LS2 9JT
United Kingdom
Rolf Krause
Institute of Computational Science
Faculty of Informatics
Università della Svizzera italiana
Via Giuseppe Buffi 13
CH-6904 Lugano
Switzerland