Efficient algorithms for multiscale modeling in porous media

Mary F. Wheeler, Tim Wildey, Guangri Xue

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We 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.
Original languageEnglish (US)
Pages (from-to)771-785
Number of pages15
JournalNumerical Linear Algebra with Applications
Issue number5
StatePublished - Sep 26 2010
Externally publishedYes


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