Overlapping Schwarz waveform relaxation for the heat equation in \(n\) dimensions. (English) Zbl 1022.65112

Gander, Martin J.; Zhao, Hongkai

BIT 42, No. 4, 779-795 (2002).

The authors analyze overlapping Schwarz waveform relaxation for the heat equations in general dimensions. The linear convergence of the algorithm on unbounded time intervals and superlinear convergence on bounded time intervals are proved. In both cases the convergence rates depend on the size of the overlap. The linear convergence result depends also on the number of subdomains. On the other hand the superlinear convergence result is independent of the number of subdomains. The presented numerical experiments confirm the analysis.

Reviewer: Vit Dolejsi (Praha)

MSC:

65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K05	Heat equation

Keywords:

domain decomposition; heat equations; overlapping Schwarz waveform relaxation; superlinear convergence; algorithm; numerical experiments