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Constraint damping in first-order evolution systems for numerical relativity

Owen, Robert (2007) Constraint damping in first-order evolution systems for numerical relativity. Physical Review D, 76 (4). Art. No. 044019. ISSN 2470-0010. doi:10.1103/PhysRevD.76.044019.

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A new constraint suppressing formulation of the Einstein evolution equations is presented, generalizing the five-parameter first-order system due to Kidder, Scheel, and Teukolsky (KST). The auxiliary fields, introduced to make the KST system first order, are given modified evolution equations designed to drive constraint violations toward zero. The algebraic structure of the new system is investigated, showing that the modifications preserve the hyperbolicity of the fundamental and constraint evolution equations. The evolution of the constraints for perturbations of flat spacetime is completely analyzed, and all finite-wavelength constraint modes are shown to decay exponentially when certain adjustable parameters satisfy appropriate inequalities. Numerical simulations of a single Schwarzschild black hole are presented, demonstrating the effectiveness of the new constraint-damping modifications.

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Additional Information:©2007 The American Physical Society (Received 29 March 2007; published 23 August 2007) I thank Lee Lindblom for extensive discussions and advice, and also Harald Pfeiffer and Mark Scheel, for help on the manuscript and for assistance on the use of their code. Michael Boyle provided access to some input files and numerical results of Ref. [37], which were of great help in debugging and understanding the numerical issues. The numerical calculations presented in this paper were performed with the Caltech/Cornell Spectral Einstein Code (SpEC) written primarily by Lawrence E. Kidder, Harald P. Pfeiffer, and Mark A. Scheel. This work was supported in part by NSF grants No. PHY-0099568, No. PHY-0244906, No. PHY-0601459, and No. DMS-0553302, NASA grants No. NAG5-12834 and No. NNG05GG52G, and a grant from the Sherman Fairchild Foundation. Some of the numerical calculations leading to this paper were performed with the Tungsten cluster at NCSA.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8640
Deposited By: Archive Administrator
Deposited On:02 Sep 2007
Last Modified:08 Nov 2021 20:52

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