Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation

Details Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation

2007-01-31

arxiv.org/abs/math/0701915v1

Mathematics

Numerical Analysis

20 pages

Scientific paper

We introduce a non-overlapping 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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