Two-Level Domain Decomposition Methods for Highly Heterogeneous Darcy Equations. Connections with Multiscale Methods

Victorita Dolean (1) , Pierre Jolivet (2, 3) , Frédéric Nataf (4) , Nicole Spillane (5) , Hua Xiang

1 University of Strathclyde [Glasgow]
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CNRS - Centre National de la Recherche Scientifique
4 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
5 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

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.

Domaines: Physique [physics]

Victorita Dolean, Pierre Jolivet, Frédéric Nataf, Nicole Spillane, Hua Xiang. Two-Level Domain Decomposition Methods for Highly Heterogeneous Darcy Equations. Connections with Multiscale Methods. Oil & Gas Science and Technology - Revue d'IFP Energies nouvelles, 2014, 69 (4), pp.731-752. ⟨10.2516/ogst/2013206⟩. ⟨hal-01933398⟩