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IMEX evolution of scalar fields on curved backgrounds

Lau, Stephen R. and Pfeiffer, Harald P. and Hesthaven, Jan S. (2009) IMEX evolution of scalar fields on curved backgrounds. Communications in Computational Physics, 6 (5). pp. 1063-1094. ISSN 1815-2406. https://resolver.caltech.edu/CaltechAUTHORS:20090930-112727240

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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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/0808.2597v2arXivUNSPECIFIED
ORCID:
AuthorORCID
Pfeiffer, Harald P.0000-0001-9288-519X
Additional Information:Received 19 August 2008; accepted (in revised version) 16 April 2009; available online 14 May 2009. We would like to thank Thomas Hagstrom, Lawrence Kidder, Lee Lindblom, Geoffrey Lovelace, Michael Minion, Mark Scheel and Saul Teukolsky for useful discussions. Most of the numerical simulations presented here were performed using the Spectral Einstein Code (SpEC) developed at Caltech and Cornell primarily by Larry Kidder, H. P., and Mark Scheel. We also thank the referee for comments which led to the experiment considered in Subsection IVD. Revisions were carried out after S. L. had moved to UNM. This work was supported by grants from the Sherman Fairchild Foundation and from the Brinson Foundation to Caltech; by grants DMS 0554377 and DARPA/AFOSR FA9550-05-1-0108 to Brown University; and by NSF grants PHY-0601459, PHY-0652995 and NASA grant NNG05GG52G to Caltech.
Funders:
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
Brinson FoundationUNSPECIFIED
NSFDMS 0554377
DARPA/AFOSAFA9550-05-1-0108
NSFPHY-0601459
NSFPHY-0652995
NASANNG05GG52G
Subject Keywords:Implicit-explicit schemes; spectral methods; numerical relativity; black holes.
Issue or Number:5
Classification Code:AMS subject classifications: 65M70, 83-08, 83C57; PACS numbers 04.25.Dm, 02.70.Hm
Record Number:CaltechAUTHORS:20090930-112727240
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090930-112727240
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16128
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:06 Oct 2009 21:29
Last Modified:09 Mar 2020 13:19

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