Generalized multiscale finite element methods for problems in perforated heterogeneous domains

Handle URI:
http://hdl.handle.net/10754/566115
Title:
Generalized multiscale finite element methods for problems in perforated heterogeneous domains
Authors:
Chung, Eric T.; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Li, Guanglian; Vasilyeva, Maria; Vasilyeva, Maria
Abstract:
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. © 2015 Taylor & Francis
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Publisher:
Informa UK Limited
Journal:
Applicable Analysis
Issue Date:
8-Jun-2015
DOI:
10.1080/00036811.2015.1040988
ARXIV:
arXiv:1501.03536v1
Type:
Article
ISSN:
00036811
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorChung, Eric T.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorLi, Guanglianen
dc.contributor.authorVasilyeva, Mariaen
dc.contributor.authorVasilyeva, Mariaen
dc.date.accessioned2015-08-12T09:28:54Zen
dc.date.available2015-08-12T09:28:54Zen
dc.date.issued2015-06-08en
dc.identifier.issn00036811en
dc.identifier.doi10.1080/00036811.2015.1040988en
dc.identifier.urihttp://hdl.handle.net/10754/566115en
dc.description.abstractComplex 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. © 2015 Taylor & Francisen
dc.publisherInforma UK Limiteden
dc.subjectelasticity equationen
dc.subjectLaplace equationen
dc.subjectmodel reductionen
dc.subjectmultiscale finite element methoden
dc.subjectperforated domainen
dc.subjectStokes equationsen
dc.titleGeneralized multiscale finite element methods for problems in perforated heterogeneous domainsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalApplicable Analysisen
dc.contributor.institutionDepartment of Mathematics, The Chinese University of Hong Kong (CUHK), Hong Kong SAR, Chinaen
dc.contributor.institutionDepartment of Mathematics & Institute for Scientific Computation (ISC), Texas A&M University, College Station, TX, USAen
dc.contributor.institutionDepartment of Mathematics, Texas A&M University, College Station, TX, 77843-3368USAen
dc.contributor.institutionDepartment of Computational Technologies, Institute of Mathematics and Informatics, North-Eastern Federal University, Yakutsk, Republic of Sakha (Yakutia), 677980Russiaen
dc.contributor.institutionInstitute for Scientific Computation, Texas A&M University, College Station, TX, 77843-3368USAen
dc.identifier.arxividarXiv:1501.03536v1en
kaust.authorEfendiev, Yalchin R.en
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