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Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations

Abstract : This paper is concerned with global-in-time, nonoverlapping domain decomposition methods for the mixed formulation of the diffusion problem. Two approaches are considered: one uses the time-dependent Steklov-Poincaré operator and the other uses Optimized Schwarz Waveform Relaxation (OSWR) based on Robin transmission conditions. For each method, a mixed formulation of an interface problem on the space-time interfaces between subdomains is derived, and different time grids are employed to adapt to different time scales in the subdomains. Demonstrations of the well-posedness of the subdomain problems involved in each method and a convergence proof of the OSWR algorithm are given for the mixed formulation. Numerical results for 2D problems with strong heterogeneities are presented to illustrate the performance of the two methods.
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Submitted on : Sunday, March 24, 2013 - 2:49:39 PM
Last modification on : Friday, January 21, 2022 - 3:19:39 AM
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Thi Thao Phuong Hoang, Jérôme Jaffré, Caroline Japhet, Michel Kern, Jean Roberts. Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations. SIAM Journal on Numerical Analysis, 2013, 51 (6), pp.3532-3559. ⟨10.1137/130914401⟩. ⟨hal-00803796⟩



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