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Optimized Schwarz waveform relaxation algorithms with nonconforming time discretization for coupling convection-diffusion problems with discontinuous coefficients

Eric Blayo 1 Laurence Halpern 2 Caroline Japhet 2
1 MOISE - Modelling, Observations, Identification for Environmental Sciences
Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019], LJK [2007-2015] - Laboratoire Jean Kuntzmann [2007-2015], Inria Grenoble - Rhône-Alpes
Abstract : We present and study an optimized Schwarz Waveform Relaxation algorithm for convection-diffusion problems with discontinuous coefficients. Such analysis is a first step towards the coupling of heterogeneous climatic models. The SWR algorithms are global in time, and thus allow for the use of non conforming space-time discretizations. They are therefore well adapted to coupling models with very different spatial and time scales, as in ocean-atmosphere coupling. As the cost per iteration can be very high, we introduce new transmission conditions in the algorithm which optimize the convergence speed. In order to get higher order schemes in time, we use in each subdomain a discontinuous Galerkin method for the time-discretization. We present numerical results to illustrate this approach, and we analyse numerically the time-discretization error.
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Submitted on : Wednesday, November 14, 2007 - 5:14:06 PM
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Eric Blayo, Laurence Halpern, Caroline Japhet. Optimized Schwarz waveform relaxation algorithms with nonconforming time discretization for coupling convection-diffusion problems with discontinuous coefficients. Olof B. Widlund and Walter Zulehner. Domain Decomposition Methods in Science and Engineering XVI, 55, Springer Verlag, pp.267-274, 2007, Lecture Notes in Computational Science and Engineering, 978-3-540-34468-1. ⟨10.1007/978-3-540-34469-8_31⟩. ⟨inria-00187555⟩

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