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arXiv · 1605.05941

Space-time domain decomposition for advection-diffusion problems in mixed formulations

Thi-Thao-Phuong Hoang·Caroline Japhet·Michel Kern·Jean E. Roberts
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Abstract

This paper is concerned with the numerical solution of porous-media flow and transport problems , i. e. heterogeneous, advection-diffusion problems. Its aim is to investigate numerical schemes for these problems in which different time steps can be used in different parts of the domain. Global-in-time, non-overlapping domain-decomposition methods are coupled with operator splitting making possible the different treatment of the advection and diffusion terms. Two domain-decomposition methods 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 interface is derived, and different time grids are employed to adapt to different time scales in the subdomains. A generalized Neumann-Neumann preconditioner is proposed for the first method. To illustrate the two methods numerical results for two-dimensional problems with strong heterogeneities are presented. These include both academic problems and more realistic prototypes for simulations for the underground storage of nuclear waste.

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Thi-Thao-Phuong Hoang, Caroline Japhet, Michel Kern, Jean E. Roberts. 2016-05-19. Space-time domain decomposition for advection-diffusion problems in mixed formulations. https://arxiv.org/abs/1605.05941

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