KAUST DepartmentApplied Mathematics and Computational Science Program
Earth Science and Engineering Program
Numerical Porous Media SRI Center (NumPor)
Physical Sciences and Engineering (PSE) Division
Environmental Science and Engineering Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractIn this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul. 8 (2010) 1461-1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high-and low-conductivity inclusions. © 2014 World Scientific Publishing Company.
SponsorsThis publication is based in part on work supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST).
PublisherWorld Scientific Pub Co Pte Lt