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AbstractWe describe multiscale mortar mixed finite element discretizations for second-order elliptic and nonlinear parabolic equations modeling Darcy flow in porous media. The continuity of flux is imposed via a mortar finite element space on a coarse grid scale, while the equations in the coarse elements (or subdomains) are discretized on a fine grid scale. We discuss the construction of multiscale mortar basis and extend this concept to nonlinear interface operators. We present a multiscale preconditioning strategy to minimize the computational cost associated with construction of the multiscale mortar basis. We also discuss the use of appropriate quadrature rules and approximation spaces to reduce the saddle point system to a cell-centered pressure scheme. In particular, we focus on multiscale mortar multipoint flux approximation method for general hexahedral grids and full tensor permeabilities. Numerical results are presented to verify the accuracy and efficiency of these approaches. © 2010 John Wiley & Sons, Ltd.
CitationWheeler MF, Wildey T, Xue G (2010) Efficient algorithms for multiscale modeling in porous media. Numerical Linear Algebra with Applications 17: 771–785. Available: http://dx.doi.org/10.1002/nla.742.
SponsorsContract/grant sponsor: Publishing Arts Research Council; contract grant/number: 98-1846389Contract/grant sponsor: DOE Energy Frontier Research Center; contract/grant number: DE-SC0001114Contract/grant sponsor: NSF-CDI; contract/grant number: DMS 0835745Contract/grant sponsor: King Abdullah University of Science and Technology; contract/grant number: (KAUST)-AEA-UTA08-687Contract/grant sponsor: KAUST; contract/grant number: KUS-F1-032-04