Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation

Halpern, Laurence; Szeftel, Jérémie

doi:10.1090/S0025-5718-08-02164-9

Nonlinear nonoverlapping Schwarz waveform relaxation for semilinear wave propagation
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by Laurence Halpern and Jérémie Szeftel;

Math. Comp. 78 (2009), 865-889

DOI: https://doi.org/10.1090/S0025-5718-08-02164-9

Published electronically: 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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