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FETI-DP for Stokes-Mortar-Darcy systems. (English) Zbl 1430.76440

Huang, Yunqing (ed.) et al., Domain decomposition methods in science and engineering XIX. Selected papers based on the presentations at the 19th international conference on domain decoposition (DD19), Zhanjiajie, China, August 17–22, 2009. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 78, 221-228 (2011).
Summary: We consider the coupling across an interface of a fluid flow and a porous media flow. The differential equations involve Stokes equations in the fluid region,Darcy equations in the porous region, plus a coupling through an interface with Beaver-Joseph-Saffman transmission conditions, see [T. Arbogast and D. S. Brunson, Comput. Geosci. 11, No. 3, 207–218 (2007; Zbl 1186.76660); M. Discacciati et al., SIAM J. Numer. Anal. 45, No. 3, 1246–1268 (2007; Zbl 1139.76030); the authors, ETNA, Electron. Trans. Numer. Anal. 26, 350–384 (2007; Zbl 1170.76024); W. J. Layton et al., SIAM J. Numer. Anal. 40, No. 6, 2195–2218 (2003; Zbl 1037.76014)]. The discretization consists of P2-P0 finite elements in the fluid region, the lowest order triangular Raviart-Thomas finite elements in the porous region, and the mortar piecewise constant Lagrange multipliers on the interface. Due to the small values of the permeability parameter \(\kappa\) of the porous medium, the resulting discrete symmetric saddle point system is very ill conditioned. Preconditioning is needed in order to efficiently solve the resulting discrete system. The purpose of this work is to present some preliminary results on the extension ofthe modular FETI type preconditioner proposed in [the authors, “Balancing domain decomposition methods for Mortar coupling Stokes-Darcy systems”, Lecture Notes in Computational Science and Engineering 55, 373–380 (2007; doi:10.1007/978-3-540-34469-8_46); Commun. Appl. Math. Comput. Sci. 5, No. 1, 1–30 (2010; Zbl 1189.35226)] to the multidomain FETI-DP case.
For the entire collection see [Zbl 1204.65002].

MSC:

76S05 Flows in porous media; filtration; seepage
76M10 Finite element methods applied to problems in fluid mechanics
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
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