CaltechAUTHORS
  A Caltech Library Service

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 . http://resolver.caltech.edu/CaltechAUTHORS:20100817-080404692

[img]
Preview
PDF - Published Version
See Usage Policy.

357Kb

Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechAUTHORS:20100817-080404692

Abstract

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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevD.82.024037 DOIUNSPECIFIED
http://prd.aps.org/abstract/PRD/v82/i2/e024037PublisherUNSPECIFIED
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.
Group:TAPIR
Funders:
Funding AgencyGrant Number
Sherman Fairchild Foundation UNSPECIFIED
Brinson Foundation UNSPECIFIED
NSFPHY-0601459
NSFPHY-0652995
NSFDMS-0553302
NSFPHY-0652952
NSFDMS-0553677
NSFPHY-0652929
NASANNX09AF96G
Classification Code:PACS: 04.25.D-, 02.60.Cb, 02.70.Hm, 02.70.Jn
Record Number:CaltechAUTHORS:20100817-080404692
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100817-080404692
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19458
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:17 Aug 2010 17:16
Last Modified:26 Dec 2012 12:19

Repository Staff Only: item control page