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Optimal constraint projection for hyperbolic evolution systems

Holst, Michael and Lindblom, Lee and Owen, Robert and Pfeiffer, Harald P. and Scheel, Mark A. and Kidder, Lawrence E. (2004) Optimal constraint projection for hyperbolic evolution systems. Physical Review D, 70 (8). Art. No. 084017. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:HOLprd04

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Abstract

Techniques are developed for projecting the solutions of symmetric-hyperbolic evolution systems onto the constraint submanifold (the constraint-satisfying subset of the dynamical field space). These optimal projections map a field configuration to the nearest configuration in the constraint submanifold, where distances between configurations are measured with the natural metric on the space of dynamical fields. The construction and use of these projections are illustrated for a new representation of the scalar field equation that exhibits both bulk and boundary generated constraint violations. Numerical simulations on a black hole background show that bulk constraint violations cannot be controlled by constraint-preserving boundary conditions alone, but are effectively controlled by constraint projection. Simulations also show that constraint violations entering through boundaries cannot be controlled by constraint projection alone, but are controlled by constraint-preserving boundary conditions. Numerical solutions to the pathological scalar field system are shown to converge to solutions of a standard representation of the scalar field equation when constraint projection and constraint-preserving boundary conditions are used together.


Item Type:Article
Additional Information:©2004 The American Physical Society. Received 2 July 2004; published 13 October 2004. We thank Saul Teukolsky and Manuel Tiglio for helpful comments. Some of the computations for this project were performed with the Tungsten cluster at NCSA. This work was supported in part by NSF Grants Nos. PHY-0099568, PHY-0244906 and NASA Grant Nos. NAG5-10707, NAG5-12834 at Caltech, NSF Grant Nos. DMS-9875856, DMS-0208449, DMS-0112413 at UCSD, and NSF Grant Nos. PHY-9900672, PHY-0312072 at Cornell.
Group:TAPIR
Subject Keywords:hyperbolic equations; space-time configurations; Einstein field equations; black holes; Schwarzschild metric
Record Number:CaltechAUTHORS:HOLprd04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:HOLprd04
Alternative URL:http://dx.doi.org/10.1103/PhysRevD.70.084017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5018
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Sep 2006
Last Modified:26 Dec 2012 09:03

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