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arXiv · 1303.5985

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

Thi Thao Phuong Hoang·Jérôme Jaffré·Caroline Japhet·Michel Kern·Jean Roberts
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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-Poincar\'e 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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Thi Thao Phuong Hoang, Jérôme Jaffré, Caroline Japhet, Michel Kern, Jean Roberts. 2013-03-24. Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations. https://arxiv.org/abs/1303.5985

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