Generalized multiscale finite element method for elasticity equations

Handle URI:
http://hdl.handle.net/10754/563788
Title:
Generalized multiscale finite element method for elasticity equations
Authors:
Chung, Eric T.; Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Fu, Shubin
Abstract:
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Nature
Journal:
GEM - International Journal on Geomathematics
Issue Date:
5-Oct-2014
DOI:
10.1007/s13137-014-0066-0
Type:
Article
ISSN:
18692672
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorChung, Eric T.en
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorFu, Shubinen
dc.date.accessioned2015-08-03T12:10:07Zen
dc.date.available2015-08-03T12:10:07Zen
dc.date.issued2014-10-05en
dc.identifier.issn18692672en
dc.identifier.doi10.1007/s13137-014-0066-0en
dc.identifier.urihttp://hdl.handle.net/10754/563788en
dc.description.abstractIn this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.en
dc.publisherSpringer Natureen
dc.subjectElasticityen
dc.subjectModel reductionen
dc.subjectMultiscaleen
dc.subjectMultiscale finite element methoden
dc.titleGeneralized multiscale finite element method for elasticity equationsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalGEM - International Journal on Geomathematicsen
dc.contributor.institutionDepartment of Mathematics, The Chinese University of Hong KongHong Kong, Hong Kongen
dc.contributor.institutionDepartment of Mathematics, Texas A&M UniversityCollege Station, TX, United Statesen
kaust.authorEfendiev, Yalchin R.en
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