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Hyperboloidal layers for hyperbolic equations on unbounded domains

Zenginoğlu, Anıl (2011) Hyperboloidal layers for hyperbolic equations on unbounded domains. Journal of Computational Physics, 230 (6). pp. 2286-2302. ISSN 0021-9991. https://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.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2010.12.016DOIUNSPECIFIED
http://www.sciencedirect.com/science/article/B6WHY-51S25PB-5/2/a1bb43d5400cfcb37b646d0d4698dd09PublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSF07-07949
Marie Curie Transfer of KnowledgeMTKD-CT-2006-042360
Agence Nationale de la Recherche (ANR) 06-2-134423
NSFPHY-0601459
Sherman Fairchild Foundation UNSPECIFIED
Subject Keywords:Transparent (non reflecting, absorbing) boundary conditions; Perfectly matched layers; Hyperboloidal layers; Hyperboloidal compactification; Wave equations; Maxwell equations
Issue or Number:6
Record Number:CaltechAUTHORS:20110317-103847658
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110317-103847658
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:03 Oct 2019 02:41

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