A Multiscale Enrichment Procedure for Nonlinear Monotone Operators

Handle URI:
http://hdl.handle.net/10754/555795
Title:
A Multiscale Enrichment Procedure for Nonlinear Monotone Operators
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Galvis, J.; Presho, M.; Zhou, J.
Abstract:
In this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and Y. Efendiev, SIAM Multiscale Model. Simul. 8 (2010) 1461–1483.] is extended to treat a class of nonlinear elliptic operators. The proposed method requires the solutions of (small dimension and local) nonlinear eigenvalue problems in order to systematically enrich the coarse solution space. Convergence of the method is shown to relate to the dimension of the coarse space (due to the enrichment procedure) as well as the coarse mesh size. In addition, it is shown that the coarse mesh spaces can be effectively used in two-level domain decomposition preconditioners. A number of numerical results are presented to complement the analysis.
KAUST Department:
SRI-Center for Numerical Porous Media
Citation:
A Multiscale Enrichment Procedure for Nonlinear Monotone Operators 2014, 48 (2):475 ESAIM: Mathematical Modelling and Numerical Analysis
Publisher:
EDP Sciences
Journal:
ESAIM: Mathematical Modelling and Numerical Analysis
Issue Date:
11-Mar-2014
DOI:
10.1051/m2an/2013116
Type:
Article
ISSN:
0764-583X; 1290-3841
Additional Links:
http://www.esaim-m2an.org/10.1051/m2an/2013116
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorGalvis, J.en
dc.contributor.authorPresho, M.en
dc.contributor.authorZhou, J.en
dc.date.accessioned2015-05-26T08:02:16Zen
dc.date.available2015-05-26T08:02:16Zen
dc.date.issued2014-03-11en
dc.identifier.citationA Multiscale Enrichment Procedure for Nonlinear Monotone Operators 2014, 48 (2):475 ESAIM: Mathematical Modelling and Numerical Analysisen
dc.identifier.issn0764-583Xen
dc.identifier.issn1290-3841en
dc.identifier.doi10.1051/m2an/2013116en
dc.identifier.urihttp://hdl.handle.net/10754/555795en
dc.description.abstractIn this paper, multiscale finite element methods (MsFEMs) and domain decomposition techniques are developed for a class of nonlinear elliptic problems with high-contrast coefficients. In the process, existing work on linear problems [Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Submitted.; Y. Efendiev, J. Galvis and X. Wu, J. Comput. Phys. 230 (2011) 937–955; J. Galvis and Y. Efendiev, SIAM Multiscale Model. Simul. 8 (2010) 1461–1483.] is extended to treat a class of nonlinear elliptic operators. The proposed method requires the solutions of (small dimension and local) nonlinear eigenvalue problems in order to systematically enrich the coarse solution space. Convergence of the method is shown to relate to the dimension of the coarse space (due to the enrichment procedure) as well as the coarse mesh size. In addition, it is shown that the coarse mesh spaces can be effectively used in two-level domain decomposition preconditioners. A number of numerical results are presented to complement the analysis.en
dc.publisherEDP Sciencesen
dc.relation.urlhttp://www.esaim-m2an.org/10.1051/m2an/2013116en
dc.rightsArchived with thanks to ESAIM: Mathematical Modelling and Numerical Analysisen
dc.subjectGeneralized multiscale finite element methoden
dc.subjectnonlinear equationsen
dc.subjecthigh-contrasten
dc.titleA Multiscale Enrichment Procedure for Nonlinear Monotone Operatorsen
dc.typeArticleen
dc.contributor.departmentSRI-Center for Numerical Porous Mediaen
dc.identifier.journalESAIM: Mathematical Modelling and Numerical Analysisen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics and Institute for Scientific Computation, Texas A & M University, College Station, TX 77843, USAen
dc.contributor.institutionDepartmento de matematics, Universidad Nacional de Colombia, Bogota D.C., Colombiaen
kaust.authorEfendiev, Yalchin R.en
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