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 1, * Laurent Debreu 1 Eric Blayo 1
* Corresponding author
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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 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 determine analytically 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.
Keywords : Optimized Schwarz Methods Waveform Relaxation Alternating and Parallel Schwarz Methods
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Journal articles
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Florian Lemarié, Laurent Debreu, 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. Electronic Transactions on Numerical Analysis, Kent State University Library, 2013, 40, pp.170-186. ⟨hal-00661978⟩

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