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Mathematics of Computation

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Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation

Authors: Laurence Halpern and Jérémie Szeftel
Journal: Math. Comp. 78 (2009), 865-889
MSC (2000): Primary 65F10, 65N22
Published electronically: July 1, 2008
MathSciNet review: 2476563
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Abstract: We introduce a nonoverlapping variant of the Schwarz waveform relaxation algorithm for semilinear wave propagation in one dimension. Using the theory of absorbing boundary conditions, we derive a new nonlinear algorithm. We show that the algorithm is well-posed and we prove its convergence by energy estimates and a Galerkin method. We then introduce an explicit scheme. We prove the convergence of the discrete algorithm with suitable assumptions on the nonlinearity. We finally illustrate our analysis with numerical experiments.

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Additional Information

Laurence Halpern
Affiliation: LAGA, Institut Galilée, Université Paris XIII, 93430 Villetaneuse, France

Jérémie Szeftel
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, and C.N.R.S., Mathématiques Appliquées de Bordeaux, Université Bordeaux 1, 351 cours de la Libération, 3 3405 Talence cedex France

Keywords: Domain decomposition, waveform relaxation, Schwarz methods, semilinear wave equation
Received by editor(s): January 31, 2007
Received by editor(s) in revised form: March 27, 2008
Published electronically: July 1, 2008
Additional Notes: The second author was partially supported by NSF Grant DMS-0504720
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.