Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations

Stephane Descombes (1) , Victorita Dolean (1, 2) , Martin Gander (3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 NACHOS - Numerical modeling and high performance computing for evolution problems in complex domains and heterogeneous media
3 Section de mathématiques [Genève]

Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the computational domain and the subdomain iteration uses an overlapping decomposition in space. There are only few convergence studies for non-linear PDEs. We analyze in this paper the convergence of Schwarz waveform relaxation applied to systems of semi-linear reaction-diffusion equations. We show that the algorithm converges linearly under certain conditions over long time intervals. We illustrate our results, and further possible convergence behavior, with numerical experiments.

Domaines: Analyse numérique [math.NA]

Stephane Descombes, Victorita Dolean, Martin Gander. Schwarz Waveform Relaxation Methods for Systems of Semi-Linear Reaction-Diffusion Equations. 2010. ⟨hal-00491292⟩