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Article: Generalized multiscale finite element methods: Oversampling strategies

TitleGeneralized multiscale finite element methods: Oversampling strategies
Authors
KeywordsHigh contrast
Oversampling
Generalized multiscale finite element method
Issue Date2014
Citation
International Journal for Multiscale Computational Engineering, 2014, v. 12, n. 6, p. 465-484 How to Cite?
Abstract© 2014 by Begell House, Inc. In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local spectral problems. We present numerical results and compare various oversampling techniques in order to complement the proposed technique and analysis.
Persistent Identifierhttp://hdl.handle.net/10722/286894
ISSN
2020 Impact Factor: 1.508
2020 SCImago Journal Rankings: 0.430
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorGalvis, Juan-
dc.contributor.authorLi, Guanglian-
dc.contributor.authorPresho, Michael-
dc.date.accessioned2020-09-07T11:45:57Z-
dc.date.available2020-09-07T11:45:57Z-
dc.date.issued2014-
dc.identifier.citationInternational Journal for Multiscale Computational Engineering, 2014, v. 12, n. 6, p. 465-484-
dc.identifier.issn1543-1649-
dc.identifier.urihttp://hdl.handle.net/10722/286894-
dc.description.abstract© 2014 by Begell House, Inc. In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local spectral problems. We present numerical results and compare various oversampling techniques in order to complement the proposed technique and analysis.-
dc.languageeng-
dc.relation.ispartofInternational Journal for Multiscale Computational Engineering-
dc.subjectHigh contrast-
dc.subjectOversampling-
dc.subjectGeneralized multiscale finite element method-
dc.titleGeneralized multiscale finite element methods: Oversampling strategies-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1615/IntJMultCompEng.2014007646-
dc.identifier.scopuseid_2-s2.0-84906995780-
dc.identifier.volume12-
dc.identifier.issue6-
dc.identifier.spage465-
dc.identifier.epage484-
dc.identifier.isiWOS:000342967300001-
dc.identifier.issnl1543-1649-

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