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Two-level domain decomposition methods for highly heterogeneous Darcy equations. Connections with multiscale methods

Dolean, Victorita and Jolivet, Pierre and Nataf, Frederic and Spillane, Nicole and Xiang, Hua (2014) Two-level domain decomposition methods for highly heterogeneous Darcy equations. Connections with multiscale methods. Oil & Gas Science and Technology, 69 (4). pp. 731-752. ISSN 1294-4475

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    Abstract

    Multiphase, compositional porous media flow models lead to the solution of highly heterogeneous systems of Partial Differential Equations (PDE). We focus on overlapping Schwarz type methods on parallel computers and on multiscale methods. We present a coarse space [Nataf F., Xiang H., Dolean V., Spillane N. (2011) SIAM J. Sci. Comput. 33, 4, 1623-1642] that is robust even when there are such heterogeneities. The two-level domain decomposition approach is compared to multiscale methods.