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Absorbing boundary conditions for the wave equation and parallel computing


Authors: Martin J. Gander and Laurence Halpern
Journal: Math. Comp. 74 (2005), 153-176
MSC (2000): Primary 65M55, 35L20
DOI: https://doi.org/10.1090/S0025-5718-04-01635-7
Published electronically: March 18, 2004
MathSciNet review: 2085406
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Abstract: Absorbing boundary conditions have been developed for various types of problems to truncate infinite domains in order to perform computations. But absorbing boundary conditions have a second, recent and important application: parallel computing. We show that absorbing boundary conditions are essential for a good performance of the Schwarz waveform relaxation algorithm applied to the wave equation. In turn this application gives the idea of introducing a layer close to the truncation boundary which leads to a new way of optimizing absorbing boundary conditions for truncating domains. We optimize the conditions in the case of straight boundaries and illustrate our analysis with numerical experiments both for truncating domains and the Schwarz waveform relaxation algorithm.


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Additional Information

Martin J. Gander
Affiliation: Department of Mathematics and Statistics, McGill University, Montreal, Canada

Laurence Halpern
Affiliation: Département de Mathématiques, Université Paris XIII, 93430 Villetaneuse, France
Email: halpern@math.univ-paris13.fr

DOI: https://doi.org/10.1090/S0025-5718-04-01635-7
Received by editor(s): September 10, 2002
Received by editor(s) in revised form: May 12, 2003
Published electronically: March 18, 2004
Article copyright: © Copyright 2004 American Mathematical Society

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