Volume 40, pp. 148-169, 2013.

Toward an optimized global-in-time Schwarz algorithm for diffusion equations with discontinuous and spatially variable coefficients. Part 1: the constant coefficients case

Florian Lemarié, Laurent Debreu, and Eric Blayo

Abstract

In this paper we present a global-in-time non-overlapping Schwarz method applied to the one-dimensional unsteady diffusion equation. We address specifically the problem with discontinuous diffusion coefficients, our approach is therefore especially designed for subdomains with heterogeneous properties. We derive efficient interface conditions by solving analytically the minmax problem associated with the search for optimized conditions in a Robin-Neumann case and in a two-sided Robin-Robin case. The performance of the proposed schemes are illustrated by numerical experiments.

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Key words

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

AMS subject classifications

65M55, 65F10, 65N22, 35K15

Links to the cited ETNA articles

[7]	Vol. 31 (2008), pp. 228-255 Martin J. Gander: Schwarz methods over the course of time
[18]	Vol. 40 (2013), pp. 170-186 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 2: the variable coefficients case

ETNA articles which cite this article

Vol. 40 (2013), pp. 170-186 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 2: the variable coefficients case

Vol. 49 (2018), pp. 151-181 Sarah Ali Hassan, Caroline Japhet, and Martin Vohralík: A posteriori stopping criteria for space-time domain decomposition for the heat equation in mixed formulations

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