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Detailed view Article in peer-reviewed journal
Electronic Transactions on Numerical Analysis 40 (2013) 148-169
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Toward an Optimized Global-in-Time Schwarz Algorithm for Diffusion Equations with Discontinuous and Spatially Variable Coefficients, Part 1: The Constant Coefficients Case
Florian Lemarié1, Laurent Debreu1, Eric Blayo1

In this paper we present a global-in-time non-overlapping Schwarz method applied to the one dimen- sional 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 condi- tions in a Robin-Neumann case and in a two-sided Robin-Robin case. The performance of the proposed schemes are illustrated by numerical experiments
1:  INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann - MOISE
optimized Schwarz methods – waveform relaxation – alternating and parallel Schwarz methods