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Article: Generalized multiscale finite element methods for problems in perforated heterogeneous domains

TitleGeneralized multiscale finite element methods for problems in perforated heterogeneous domains
Authors
KeywordsLaplace equation
elasticity equation
model reduction
multiscale finite element method
perforated domain
Stokes equations
Issue Date2016
Citation
Applicable Analysis, 2016, v. 95, n. 10, p. 2254-2279 How to Cite?
Abstract© 2015 Taylor & Francis. Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere.
Persistent Identifierhttp://hdl.handle.net/10722/286905
ISSN
2020 Impact Factor: 1.429
2020 SCImago Journal Rankings: 0.576
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorChung, Eric T.-
dc.contributor.authorEfendiev, Yalchin-
dc.contributor.authorLi, Guanglian-
dc.contributor.authorVasilyeva, Maria-
dc.date.accessioned2020-09-07T11:45:59Z-
dc.date.available2020-09-07T11:45:59Z-
dc.date.issued2016-
dc.identifier.citationApplicable Analysis, 2016, v. 95, n. 10, p. 2254-2279-
dc.identifier.issn0003-6811-
dc.identifier.urihttp://hdl.handle.net/10722/286905-
dc.description.abstract© 2015 Taylor & Francis. Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales. Moreover, these problems are intrinsically multiscale and their discretizations can yield very large linear or nonlinear systems. In this paper, we investigate multiscale approaches that attempt to solve such problems on a coarse grid by constructing multiscale basis functions in each coarse grid, where the coarse grid can contain many perforations. In particular, we are interested in cases when there is no scale separation and the perforations can have different sizes. In this regard, we mention some earlier pioneering works, where the authors develop multiscale finite element methods. In our paper, we follow Generalized Multiscale Finite Element Method (GMsFEM) and develop a multiscale procedure where we identify multiscale basis functions in each coarse block using snapshot space and local spectral problems. We show that with a few basis functions in each coarse block, one can approximate the solution, where each coarse block can contain many small inclusions. We apply our general concept to (1) Laplace equation in perforated domains; (2) elasticity equation in perforated domains; and (3) Stokes equations in perforated domains. Numerical results are presented for these problems using two types of heterogeneous perforated domains. The analysis of the proposed methods will be presented elsewhere.-
dc.languageeng-
dc.relation.ispartofApplicable Analysis-
dc.subjectLaplace equation-
dc.subjectelasticity equation-
dc.subjectmodel reduction-
dc.subjectmultiscale finite element method-
dc.subjectperforated domain-
dc.subjectStokes equations-
dc.titleGeneralized multiscale finite element methods for problems in perforated heterogeneous domains-
dc.typeArticle-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1080/00036811.2015.1040988-
dc.identifier.scopuseid_2-s2.0-84930739817-
dc.identifier.volume95-
dc.identifier.issue10-
dc.identifier.spage2254-
dc.identifier.epage2279-
dc.identifier.eissn1563-504X-
dc.identifier.isiWOS:000381313600008-
dc.identifier.issnl0003-6811-

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