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Article: Cluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients

TitleCluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients
Authors
KeywordsClustering algorithm
Generalized multiscale finite element method (GMsFEM)
Karhunen–Loève expansion
Multiscale basis functions
Stochastic partial differential equations (SPDEs)
Issue Date2018
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jcp
Citation
Journal of Computational Physics, 2018, v. 371, p. 606-617 How to Cite?
AbstractWe propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage, we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite element basis functions. In addition, we coarsen the corresponding random space through a clustering algorithm. In the online stage, we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis. The new GMsFEM can be applied to multiscale SPDE starting with a relatively coarse grid, without requiring the coarsest grid to resolve the smallest-scale of the solution. The new method offers considerable savings in solving multiscale SPDEs. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.
Persistent Identifierhttp://hdl.handle.net/10722/261128
ISSN
2023 Impact Factor: 3.8
2023 SCImago Journal Rankings: 1.679
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChung, E-
dc.contributor.authorEfendiev, Y-
dc.contributor.authorLeung, W-
dc.contributor.authorZhang, Z-
dc.date.accessioned2018-09-14T08:52:57Z-
dc.date.available2018-09-14T08:52:57Z-
dc.date.issued2018-
dc.identifier.citationJournal of Computational Physics, 2018, v. 371, p. 606-617-
dc.identifier.issn0021-9991-
dc.identifier.urihttp://hdl.handle.net/10722/261128-
dc.description.abstractWe propose a generalized multiscale finite element method (GMsFEM) based on clustering algorithm to study the elliptic PDEs with random coefficients in the multi-query setting. Our method consists of offline and online stages. In the offline stage, we construct a small number of reduced basis functions within each coarse grid block, which can then be used to approximate the multiscale finite element basis functions. In addition, we coarsen the corresponding random space through a clustering algorithm. In the online stage, we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis. The new GMsFEM can be applied to multiscale SPDE starting with a relatively coarse grid, without requiring the coarsest grid to resolve the smallest-scale of the solution. The new method offers considerable savings in solving multiscale SPDEs. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.-
dc.languageeng-
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jcp-
dc.relation.ispartofJournal of Computational Physics-
dc.subjectClustering algorithm-
dc.subjectGeneralized multiscale finite element method (GMsFEM)-
dc.subjectKarhunen–Loève expansion-
dc.subjectMultiscale basis functions-
dc.subjectStochastic partial differential equations (SPDEs)-
dc.titleCluster-based generalized multiscale finite element method for elliptic PDEs with random coefficients-
dc.typeArticle-
dc.identifier.emailZhang, Z: zhangzw@hku.hk-
dc.identifier.authorityZhang, Z=rp02087-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jcp.2018.05.041-
dc.identifier.scopuseid_2-s2.0-85048450874-
dc.identifier.hkuros291362-
dc.identifier.volume371-
dc.identifier.spage606-
dc.identifier.epage617-
dc.identifier.isiWOS:000438393900029-
dc.publisher.placeUnited States-
dc.identifier.issnl0021-9991-

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