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Testing outer boundary treatments for the Einstein equations

Rinne, Oliver and Lindblom, Lee and Scheel, Mark A. (2007) Testing outer boundary treatments for the Einstein equations. Classical and Quantum Gravity, 24 (16). pp. 4053-4078. ISSN 0264-9381. http://resolver.caltech.edu/CaltechAUTHORS:RINcqg07

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Abstract

Various methods of treating outer boundaries in numerical relativity are compared using a simple test problem: a Schwarzschild black hole with an outgoing gravitational wave perturbation. Numerical solutions computed using different boundary treatments are compared to a 'reference' numerical solution obtained by placing the outer boundary at a very large radius. For each boundary treatment, the full solutions including constraint violations and extracted gravitational waves are compared to those of the reference solution, thereby assessing the reflections caused by the artificial boundary. These tests are based on a first-order generalized harmonic formulation of the Einstein equations and are implemented using a pseudo-spectral collocation method. Constraint-preserving boundary conditions for this system are reviewed, and an improved boundary condition on the gauge degrees of freedom is presented. Alternate boundary conditions evaluated here include freezing the incoming characteristic fields, Sommerfeld boundary conditions, and the constraint-preserving boundary conditions of Kreiss and Winicour. Rather different approaches to boundary treatments, such as sponge layers and spatial compactification, are also tested. Overall the best treatment found here combines boundary conditions that preserve the constraints, freeze the Newman–Penrose scalar Ψ0, and control gauge reflections.


Item Type:Article
Additional Information:Copyright © Institute of Physics and IOP Publishing Limited 2007. Received 4 April 2007, in final form 6 July 2007; Published 31 July 2007; Print publication: Issue 16 (21 August 2007) We thank Luisa Buchman, Jan Hesthaven, Larry Kidder, Harald Pfeiffer, Olivier Sarbach and Jeff Winicour for helpful discussions concerning this work. The numerical simulations presented here were performed using the Spectral Einstein Code (SpEC) developed at Caltech and Cornell primarily by Larry Kidder, Mark Scheel and Harald Pfeiffer. This work was supported in part by grants from the Sherman Fairchild Foundation, and from the Brinson Foundation; by NSF grants PHY-0099568, PHY-0244906, PHY-0601459, DMS-0553302 and NASA grants NAG5-12834, NNG05GG52G.
Group:TAPIR
Record Number:CaltechAUTHORS:RINcqg07
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:RINcqg07
Alternative URL:http://dx.doi.org/10.1088/0264-9381/24/16/006
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8284
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:01 Aug 2007
Last Modified:25 Feb 2014 23:12

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