Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

Handle URI:
http://hdl.handle.net/10754/597557
Title:
Analysis of global multiscale finite element methods for wave equations with continuum spatial scales
Authors:
Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor
Abstract:
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Citation:
Jiang L, Efendiev Y, Ginting V (2010) Analysis of global multiscale finite element methods for wave equations with continuum spatial scales. Applied Numerical Mathematics 60: 862–876. Available: http://dx.doi.org/10.1016/j.apnum.2010.04.011.
Publisher:
Elsevier BV
Journal:
Applied Numerical Mathematics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
Aug-2010
DOI:
10.1016/j.apnum.2010.04.011
Type:
Article
ISSN:
0168-9274
Sponsors:
We are grateful to reviewers who provided many insightful comments and suggestions to improve presentation of the paper. L. Jiang would like to acknowledge partial support from Chinese NSF 10901050. Y. Efendiev would like to acknowledge a partial support from NSF and DOE. Efendiev's work was also partially supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). V. Ginting's work was supported in part by the Department of Energy (DE-NT00047-30).
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Full metadata record

DC FieldValue Language
dc.contributor.authorJiang, Lijianen
dc.contributor.authorEfendiev, Yalchinen
dc.contributor.authorGinting, Victoren
dc.date.accessioned2016-02-25T12:42:00Zen
dc.date.available2016-02-25T12:42:00Zen
dc.date.issued2010-08en
dc.identifier.citationJiang L, Efendiev Y, Ginting V (2010) Analysis of global multiscale finite element methods for wave equations with continuum spatial scales. Applied Numerical Mathematics 60: 862–876. Available: http://dx.doi.org/10.1016/j.apnum.2010.04.011.en
dc.identifier.issn0168-9274en
dc.identifier.doi10.1016/j.apnum.2010.04.011en
dc.identifier.urihttp://hdl.handle.net/10754/597557en
dc.description.abstractIn this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.en
dc.description.sponsorshipWe are grateful to reviewers who provided many insightful comments and suggestions to improve presentation of the paper. L. Jiang would like to acknowledge partial support from Chinese NSF 10901050. Y. Efendiev would like to acknowledge a partial support from NSF and DOE. Efendiev's work was also partially supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). V. Ginting's work was supported in part by the Department of Energy (DE-NT00047-30).en
dc.publisherElsevier BVen
dc.subjectContinuum scalesen
dc.subjectGalerkin multiscale finite elementen
dc.subjectWave equationsen
dc.titleAnalysis of global multiscale finite element methods for wave equations with continuum spatial scalesen
dc.typeArticleen
dc.identifier.journalApplied Numerical Mathematicsen
dc.contributor.institutionHunan Normal University, Changsha, Chinaen
dc.contributor.institutionUniversity of Minnesota Twin Cities, Minneapolis, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionUniversity of Wyoming, Laramie, United Statesen
kaust.grant.numberKUS-CI-016-04en
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