Commun. Comput. Phys., 6 (2009), pp. 1063-1094.


IMEX Evolution of Scalar Fields on Curved Backgrounds

S. R. Lau 1*, H. P. Pfeiffer 2, J. S. Hesthaven 3

1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA; and Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA.
2 Theoretical Astrophysics and Relativity Group 130-33, California Institute of Technology, Pasadena, CA 91125, USA.
3 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.

Received 19 August 2008; Accepted (in revised version) 16 April 2009
Available online 14 May 2009

Abstract

Inspiral of binary black holes occurs over a time-scale of many orbits, far longer than the dynamical time-scale of the individual black holes. Explicit evolutions of a binary system therefore require excessively many time-steps to capture interesting dynamics. We present a strategy to overcome the Courant-Friedrichs-Lewy condition in such evolutions, one relying on modern implicit-explicit ODE solvers and multidomain spectral methods for elliptic equations. Our analysis considers the model problem of a forced scalar field propagating on a generic curved background. Nevertheless, we encounter and address a number of issues pertinent to the binary black hole problem in full general relativity. Specializing to the Schwarzschild geometry in Kerr-Schild coordinates, we document the results of several numerical experiments testing our strategy.

AMS subject classifications: 65M70, 83-08, 83C57
PACS: 04.25.Dm, 02.70.Hm
Key words: Implicit-explicit schemes, spectral methods, numerical relativity, black holes.

*Corresponding author.
Email: lau@dam.brown.edu (S. R. Lau), harald@tapir.caltech.edu (H. P. Pfeiffer), Jan_Hesthaven@brown.edu (J. S. Hesthaven)
 

The Global Science Journal