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

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–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 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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Submitted on : Thursday, May 19, 2016 - 12:21:54 PM
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Thi-Thao-Phuong Hoang, Caroline Japhet, Michel Kern, Jean E. Roberts. Space-time domain decomposition for advection-diffusion problems in mixed formulations. Mathematics and Computers in Simulation, Elsevier, 2016, MAMERN VI-2015: 6th International Conference on Approximation Methods and Numerical Modeling in Environment and Natural Resources, 137, pp.24. ⟨https://mamern15.sciencesconf.org/⟩. ⟨10.1016/j.matcom.2016.11.002⟩. ⟨hal-01296348v2⟩

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