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Efficient algorithms for multiscale modeling in porous media
Author(s) -
Wheeler Mary F.,
Wildey Tim,
Xue Guangri
Publication year - 2010
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.742
Subject(s) - discretization , finite element method , nonlinear system , mathematics , grid , curvilinear coordinates , mathematical optimization , basis function , mortar , computer science , algorithm , mathematical analysis , geometry , history , physics , archaeology , quantum mechanics , thermodynamics
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. Copyright © 2010 John Wiley & Sons, Ltd.