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Schwarz waveform relaxation methods: optimized interface conditions and short time behavior

Defense Thèse de doctorat : Univ. Genève, 2011 - Sc. 4357 - 2011/09/29
Abstract Schwarz waveform relaxation algorithms (SWR) are naturally parallel solvers for evolution partial differential equations. They are based on a decomposition of the spatial domain into subdomains, and a partition of the time interval of interest into time windows. On each time window, an iteration, during which subproblems are solved in space-time subdomains, is then used to obtain better and better approximations of the overall solution. The information exchange between subdomains in space-time is performed through classical or optimized transmission conditions (TCs). We analyze in this Thesis the SWR algorithm in three different contexts. First, we apply for the first time the SWR method to the evolution Maxwell's equation and deploy an advanced analysis of the convergence of the algorithm. A further analysis of the TCs is leading to optimized TCs and optimized parameters used in the optimal TCs. A second chapter is devoted to the heat equation. Proof of convergences in very general contexts and the behavior of the SWR method for short time windows is analyzed. Finally, a first approach of the SWR algorithm applied to systems of reaction-diffusion equations is proposed, and an optimized version of TCs is analyzed leading to optimal parameters involved in the optimized TCs.
Keywords Schwarz waveform relaxationOptimized robin transmission conditionsHeatMaxwellReaction-diffusionNumerical analysisPartial differential equationDomain decomposition
URN: urn:nbn:ch:unige-178675
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COURVOISIER, Yves. Schwarz waveform relaxation methods: optimized interface conditions and short time behavior. Université de Genève. Thèse, 2011. https://archive-ouverte.unige.ch/unige:17867

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Deposited on : 2011-12-21

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