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Article: Randomized oversampling for generalized multiscale finite element methods

TitleRandomized oversampling for generalized multiscale finite element methods
Authors
KeywordsHigh contrast
Generalized multiscale finite element method
Oversampling
Snapshot spaces construction
Ran-domized approximation
Issue Date2016
Citation
Multiscale Modeling and Simulation, 2016, v. 14, n. 1, p. 482-501 How to Cite?
Abstract© 2016 Society for Industrial and Applied Mathematics. In this paper, we develop efficient multiscale methods for ows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approxi- mates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the random- ized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Persistent Identifierhttp://hdl.handle.net/10722/286927
ISSN
2020 Impact Factor: 1.93
2020 SCImago Journal Rankings: 1.037
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorCalo, Victor M.-
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorGalvis, Juan-
dc.contributor.authorLi, Guanglian-
dc.date.accessioned2020-09-07T11:46:02Z-
dc.date.available2020-09-07T11:46:02Z-
dc.date.issued2016-
dc.identifier.citationMultiscale Modeling and Simulation, 2016, v. 14, n. 1, p. 482-501-
dc.identifier.issn1540-3459-
dc.identifier.urihttp://hdl.handle.net/10722/286927-
dc.description.abstract© 2016 Society for Industrial and Applied Mathematics. In this paper, we develop efficient multiscale methods for ows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approxi- mates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the random- ized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.-
dc.languageeng-
dc.relation.ispartofMultiscale Modeling and Simulation-
dc.subjectHigh contrast-
dc.subjectGeneralized multiscale finite element method-
dc.subjectOversampling-
dc.subjectSnapshot spaces construction-
dc.subjectRan-domized approximation-
dc.titleRandomized oversampling for generalized multiscale finite element methods-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1137/140988826-
dc.identifier.scopuseid_2-s2.0-84963677657-
dc.identifier.volume14-
dc.identifier.issue1-
dc.identifier.spage482-
dc.identifier.epage501-
dc.identifier.eissn1540-3467-
dc.identifier.isiWOS:000373366500017-
dc.identifier.issnl1540-3459-

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