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Spectral methods for the wave equation in second-order form

Taylor, Nicholas W. and Kidder, Lawrence E. and Teukolsky, Saul A. (2010) Spectral methods for the wave equation in second-order form. Physical Review D, 82 (2). Art. No. 024037 . ISSN 1550-7998 .

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Current spectral simulations of Einstein’s equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudospectral evolutions of second order in space wave equations. The penalties are constructed as functions of Legendre polynomials and are added to the equations of motion everywhere, not only on the boundaries. Using energy methods, we prove semidiscrete stability of the new method for the scalar wave equation in flat space and show how it can be applied to the scalar wave on a curved background. Numerical results demonstrating stability and convergence for multidomain second-order scalar wave evolutions are also presented. This work provides a foundation for treating Einstein’s equations directly in second-order form by spectral methods.

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Additional Information:© 2010 The American Physical Society. Received 17 May 2010; published 28 July 2010. We would like to thank Carsten Gundlach, Jan Hesthaven, and Manuel Tiglio for valuable comments. Most of the numerical tests were performed within the framework of the Spectral Einstein Code (SpEC) developed at Cornell and Caltech primarily by L. K., Harald Pfeiffer, and Mark Scheel [23]. This work is supported in part by grants from the Sherman Fairchild Foundation to Caltech and Cornell, and from the Brinson Foundation to Caltech, by NSF Grants No. PHY-0601459, No. PHY- 0652995, and No. DMS-0553302 at Caltech, by NSF Grants No. PHY-0652952, No. DMS-0553677, No. PHY- 0652929, and NASA Grant No. NNX09AF96G at Cornell.
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Sherman Fairchild Foundation UNSPECIFIED
Brinson Foundation UNSPECIFIED
Classification Code:PACS: 04.25.D-, 02.60.Cb, 02.70.Hm, 02.70.Jn
Record Number:CaltechAUTHORS:20100817-080404692
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19458
Deposited By: Tony Diaz
Deposited On:17 Aug 2010 17:16
Last Modified:26 Dec 2012 12:19

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