Volume 40, pp. 170-186, 2013.

Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. Part 2: the variable coefficients case

Florian Lemarié, Laurent Debreu, and Eric Blayo

Abstract

This paper is the second part of a study dealing with the application of a global-in-time Schwarz method to a one-dimensional diffusion problem defined on two non-overlapping subdomains. In the first part, we considered the case that the diffusion coefficients were constant and possibly discontinuous. In the present study, we address the problem for spatially variable coefficients with a discontinuity at the interface between subdomains. For this particular case, we derive a new approach to analytically determine the convergence factor of the associated algorithm. The theoretical results are illustrated by numerical experiments with Dirichlet-Neumann and Robin-Robin interface conditions. In the Robin-Robin case, thanks to the convergence factor found at the analytical level, we can optimize the convergence speed of the Schwarz algorithm.

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Key words

optimized Schwarz methods, waveform relaxation, alternating and parallel Schwarz methods

AMS subject classifications

65M55, 65F10, 65N22, 35K15, 76F40

Links to the cited ETNA articles

[9]Vol. 40 (2013), pp. 148-169 Florian Lemarié, Laurent Debreu, and Eric Blayo: Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. Part 1: the constant coefficients case

ETNA articles which cite this article

Vol. 40 (2013), pp. 148-169 Florian Lemarié, Laurent Debreu, and Eric Blayo: Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. Part 1: the constant coefficients case

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