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dc.contributor.authorAlOtaibi, Manal
dc.contributor.authorCalo, Victor M.
dc.contributor.authorEfendiev, Yalchin R.
dc.contributor.authorGalvis, Juan
dc.contributor.authorGhommem, Mehdi
dc.date.accessioned2015-08-12T08:57:58Z
dc.date.available2015-08-12T08:57:58Z
dc.date.issued2014-11-24
dc.identifier.issn00457825
dc.identifier.doi10.1016/j.cma.2014.10.034
dc.identifier.urihttp://hdl.handle.net/10754/565981
dc.description.abstractIn this paper, we combine discrete empirical interpolation techniques, global mode decomposition methods, and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM), to reduce the computational complexity associated with nonlinear flows in highly-heterogeneous porous media. To solve the nonlinear governing equations, we employ the GMsFEM to represent the solution on a coarse grid with multiscale basis functions and apply proper orthogonal decomposition on a coarse grid. Computing the GMsFEM solution involves calculating the residual and the Jacobian on a fine grid. As such, we use local and global empirical interpolation concepts to circumvent performing these computations on the fine grid. The resulting reduced-order approach significantly reduces the flow problem size while accurately capturing the behavior of fully-resolved solutions. We consider several numerical examples of nonlinear multiscale partial differential equations that are numerically integrated using fully-implicit time marching schemes to demonstrate the capability of the proposed model reduction approach to speed up simulations of nonlinear flows in high-contrast porous media.
dc.description.sponsorshipYE's work is partially supported by the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project, and the grant FA9550-11-1-0341 from the Air Force Office of Scientific Research.
dc.publisherElsevier BV
dc.relation.urlhttp://arxiv.org/pdf/1407.0782
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in [JournalTitle]. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in [JournalTitle], [[Volume], [Issue], (2014-11-24)] DOI: 10.1016/j.cma.2014.10.034 . © 2014. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsThis file is an open access version redistributed from: http://arxiv.org/pdf/1407.0782
dc.subjectDiscrete empirical interpolation
dc.subjectGeneralized multiscale finite element method
dc.subjectHeterogeneous porous media
dc.subjectNonlinear PDEs
dc.subjectProper orthogonal decomposition
dc.titleGlobal-local nonlinear model reduction for flows in heterogeneous porous media
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentBusiness Development
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentEarth Science and Engineering Program
dc.contributor.departmentMarketing
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)
dc.contributor.departmentPhysical Science and Engineering (PSE) Division
dc.identifier.journalComputer Methods in Applied Mechanics and Engineering
dc.rights.embargodate2016-03-15
dc.eprint.versionPost-print
dc.contributor.institutionDepartment of Mathematics and Institute for Scientific Computation (ISC), Texas A and M University, College Station, TX, USA
dc.contributor.institutionDepartamento de Matemáticas, Universidad Nacional de Colombia, Carrera 45 No 26-85 - Edificio Uriel Gutierréz, Bogotá D.C., Colombia
dc.identifier.arxividarXiv:1407.0782
kaust.personCalo, Victor M.
kaust.personEfendiev, Yalchin R.
kaust.personGhommem, Mehdi
kaust.personAlOtaibi, Manal
refterms.dateFOA2020-04-22T13:02:52Z


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