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Controlling the growth of constraints in hyperbolic evolution systems

Lindblom, Lee and Scheel, Mark A. and Kidder, Lawrence E. and Pfeiffer, Harald P. and Shoemaker, Deirdre and Teukolsky, Saul A. (2004) Controlling the growth of constraints in hyperbolic evolution systems. Physical Review D, 69 (12). Art. No. 124025. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:LINprd04

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Abstract

Motivated by the need to control the exponential growth of constraint violations in numerical solutions of the Einstein evolution equations, two methods are studied here for controlling this growth in general hyperbolic evolution systems. The first method adjusts the evolution equations dynamically, by adding multiples of the constraints, in a way designed to minimize this growth. The second method imposes special constraint preserving boundary conditions on the incoming components of the dynamical fields. The efficacy of these methods is tested by using them to control the growth of constraints in fully dynamical 3D numerical solutions of a particular representation of the Maxwell equations that is subject to constraint violations. The constraint preserving boundary conditions are found to be much more effective than active constraint control in the case of this Maxwell system.


Item Type:Article
Additional Information:©2004 The American Physical Society. Received 4 February 2004; published 28 June 2004. We thank Michael Holst, Oscar Reula, Olivier Sarbach, and Manuel Tiglio for helpful discussions concerning this work. This work was supported in part by NSF grants PHY-0099568 and PHY-0244906 and NASA grants NAG5-10707 and NAG5-12834 at Caltech, and NSF grants PHY-9900672 and PHY-0312072 at Cornell.
Group:TAPIR
Subject Keywords:Einstein field equations; Maxwell equations; hyperbolic equations
Record Number:CaltechAUTHORS:LINprd04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:LINprd04
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.69.124025
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1980
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Feb 2006
Last Modified:26 Dec 2012 08:46

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