Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation

Laurence Halpern (1) , Jérémie Szeftel (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 MAB - Laboratoire de Mathématiques Appliquées de Bordeaux

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.

Mots clés: Domain decomposition; Schwarz Waveform relaxation; Nonlinear Problems

Domaines: Analyse numérique [math.NA]

Laurence Halpern, Jérémie Szeftel. Nonlinear Nonoverlapping Schwarz Waveform Relaxation for Semilinear Wave Propagation. 2007. ⟨hal-00128219⟩