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Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation
Author(s):
Laurence
Halpern;
Jérémie
Szeftel.
Journal:
Math. Comp.
MSC (2000):
Primary 65F10, 65N22
Posted:
July 1, 2008
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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
Email:
halpern@math.univ-paris13.fr
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
Email:
jszeftel@math.princeton.edu
DOI:
10.1090/S0025-5718-08-02164-9
PII:
S 0025-5718(08)02164-9
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
Posted:
July 1, 2008
Additional Notes:
The second author was partially supported by NSF Grant DMS-0504720
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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