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Mathematics > Numerical Analysis

arXiv:1008.3809 (math)
[Submitted on 23 Aug 2010 (v1), last revised 25 Dec 2010 (this version, v2)]

Title:Hyperboloidal layers for hyperbolic equations on unbounded domains

Authors:Anil Zenginoglu
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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.
Comments: 23 pages, 23 figures
Subjects: Numerical Analysis (math.NA); General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1008.3809 [math.NA]
  (or arXiv:1008.3809v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.1008.3809
Journal reference: J.Comput.Phys.230:2286-2302,2011
Related DOI: https://doi.org/10.1016/j.jcp.2010.12.016

Submission history

From: Anil Zenginoglu C [view email]
[v1] Mon, 23 Aug 2010 12:46:04 UTC (1,180 KB)
[v2] Sat, 25 Dec 2010 01:53:51 UTC (2,104 KB)
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