Asymptotic expansions for high-contrast elliptic equations

Handle URI:
http://hdl.handle.net/10754/563410
Title:
Asymptotic expansions for high-contrast elliptic equations
Authors:
Calo, Victor M. ( 0000-0002-1805-4045 ) ; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Galvis, Juan
Abstract:
In 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.
KAUST Department:
Applied 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
Publisher:
World Scientific Pub Co Pte Lt
Journal:
Mathematical Models and Methods in Applied Sciences
Issue Date:
Mar-2014
DOI:
10.1142/S0218202513500565
Type:
Article
ISSN:
02182025
Sponsors:
This 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).
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorCalo, Victor M.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, Juanen
dc.date.accessioned2015-08-03T11:47:52Zen
dc.date.available2015-08-03T11:47:52Zen
dc.date.issued2014-03en
dc.identifier.issn02182025en
dc.identifier.doi10.1142/S0218202513500565en
dc.identifier.urihttp://hdl.handle.net/10754/563410en
dc.description.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.en
dc.description.sponsorshipThis 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).en
dc.publisherWorld Scientific Pub Co Pte Lten
dc.subjectasymptotic expansionsen
dc.subjectdomain decomposition methodsen
dc.subjectHigh-contrast elliptic equationsen
dc.titleAsymptotic expansions for high-contrast elliptic equationsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentEarth Science and Engineering Programen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalMathematical Models and Methods in Applied Sciencesen
dc.contributor.institutionDepartment of Mathematics, Texas A and M University, College Station, TX 77843, United Statesen
dc.contributor.institutionDepartamento de Mateḿaticas, Universidad Nacional de Colombia, Bogot́a, Colombiaen
kaust.authorCalo, Victor M.en
kaust.authorEfendiev, Yalchin R.en
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