A Multiscale Direct Solver for the Approximation of Flows in High Contrast Porous Media

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dc.contributor.authorAkbari, H.
dc.contributor.authorEngsig-Karup, A. P.
dc.contributor.authorGinting, V.
dc.contributor.authorPereira, L. Felipe
dc.contributor.utdAuthorPereira, L. Felipe
dc.date.accessioned2019-10-31T15:24:17Z
dc.date.available2019-10-31T15:24:17Z
dc.date.created2019-03-22
dc.descriptionFull text access from Treasures at UT Dallas is restricted to current UTD affiliates (use the provided Link to Article).
dc.description.abstractWe consider a non-overlapping domain decomposition approach to approximate the solution of elliptic boundary value problems with high contrast in their coefficients. We propose a method such that initially local solutions subject to Robin boundary conditions in each primal subdomain are constructed with (locally conservative) finite element or finite volume methods. Then, a novel approach is introduced to obtain a (discontinuous) global solution in terms of linear combination of the local subdomain solutions. In the proposed algorithm the computation of local solutions for unions of subdomains are localized at nearest-neighbor subdomain boundaries, thus avoiding the solution of global interface problems. We remove discontinuities in a smoothing step that is defined on a staggered grid or dual subdomains. The resulting algorithm is naturally parallelizable and can be employed as a parallel direct solver, offering great potential for the numerical solution of large problems. In fact, subdomains can be considered small enough to fit well in GPUs and the proposed procedure can handle adaptive (in space) simulations effectively. Numerical simulations are presented and discussed. We demonstrate the effectiveness of the proposed approach with two and three dimensional high contrast and channelized coefficients, that lead to challenging approximation problems. The new procedure, although designed for parallel processing, is also of value for serial calculations. ©2019 Elsevier B.V.
dc.description.departmentSchool of Natural Sciences and Mathematics
dc.description.sponsorshipHA and APEK have been financially supported by The Danish Advanced Technology Foundation in the OPTION Project (J. nr 6320133). FP was funded in part by NSF-DMS 1514808.
dc.identifier.bibliographicCitationAkbari, H., A. P. Engsig-Karup, V. Ginting, and F. Pereira. 2019. "A multiscale direct solver for the approximation of flows in high contrast porous media." Journal of Computational and Applied Mathematics 359: 88-101, doi: 10.1016/j.cam.2019.03.028
dc.identifier.issn0377-0427
dc.identifier.urihttps://hdl.handle.net/10735.1/7068
dc.identifier.volume359
dc.language.isoen
dc.publisherElsevier B.V.
dc.relation.urihttps://dx.doi.org/10.1016/j.cam.2019.03.028
dc.rights©2019 Elsevier B.V. All Rights Reserved.
dc.source.journalJournal of Computational and Applied Mathematics
dc.subjectAlgorithms
dc.subjectEquations, Elliptic
dc.subjectParallel computing
dc.subjectBoundary value problems
dc.subjectComputational fluid dynamics
dc.subjectDecomposition method
dc.subjectFinite volume method
dc.subjectPorous materials
dc.titleA Multiscale Direct Solver for the Approximation of Flows in High Contrast Porous Media
dc.type.genrearticle

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