Zenginoğlu, Anıl (2011) Hyperboloidal layers for hyperbolic equations on unbounded domains. Journal of Computational Physics, 230 (6). pp. 2286-2302. ISSN 0021-9991 http://resolver.caltech.edu/CaltechAUTHORS:20110317-103847658
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Abstract
We show how to solve hyperbolic equations numerically on unbounded domains by compactification, thereby avoiding the introduction of an artificial outer boundary. The essential ingredient is a suitable transformation of the time coordinate in combination with spatial compactification. We construct a new layer method based on this idea, called the hyperboloidal layer. The method is demonstrated on numerical tests including the one dimensional Maxwell equations using finite differences and the three dimensional wave equation with and without nonlinear source terms using spectral techniques.
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| Additional Information: | © 2010 Elsevier Inc. Received 24 August 2010; revised 11 December 2010; accepted 13 December 2010. Available online 21 December 2010. I thank Daniel Appelö, Eliane Bécache, and Frédéric Nataf for discussions, Larry Kidder for his help with SpEC, and Piotr Bizoń, Philippe LeFloch, and Eitan Tadmor for support. This research was supported by the National Science Foundation (NSF) grant 07-07949 in Maryland, by the Marie Curie Transfer of Knowledge contract MTKD-CT-2006-042360 in Kraków, by the Agence Nationale de la Recherche (ANR) grant 06-2-134423 entitled "Mathematical Methods in General Relativity" in Paris, by the NSF grant PHY-0601459 and by a Sherman Fairchild Foundation grant to Caltech in Pasadena. | ||||||||||||
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| Subject Keywords: | Transparent (non reflecting, absorbing) boundary conditions; Perfectly matched layers; Hyperboloidal layers; Hyperboloidal compactification; Wave equations; Maxwell equations | ||||||||||||
| Record Number: | CaltechAUTHORS:20110317-103847658 | ||||||||||||
| Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20110317-103847658 | ||||||||||||
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| Official Citation: | Anil Zenginoglu, Hyperboloidal layers for hyperbolic equations on unbounded domains, Journal of Computational Physics, Volume 230, Issue 6, 20 March 2011, Pages 2286-2302, ISSN 0021-9991, DOI: 10.1016/j.jcp.2010.12.016. (http://www.sciencedirect.com/science/article/B6WHY-51S25PB-5/2/a1bb43d5400cfcb37b646d0d4698dd09) | ||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
| ID Code: | 22953 | ||||||||||||
| Collection: | CaltechAUTHORS | ||||||||||||
| Deposited By: | Tony Diaz | ||||||||||||
| Deposited On: | 17 Mar 2011 19:20 | ||||||||||||
| Last Modified: | 17 Mar 2011 19:20 |
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