Multilevel Monte Carlo Approaches for Numerical Homogenization

Handle URI:
http://hdl.handle.net/10754/593668
Title:
Multilevel Monte Carlo Approaches for Numerical Homogenization
Authors:
Efendiev, Yalchin R. ( 0000-0001-9626-303X ) ; Kronsbein, Cornelia; Legoll, Frédéric
Abstract:
In this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizes of representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined with fewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions, different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional and two-dimensional test-cases that illustrate the efficiency of the approach.
KAUST Department:
Center for Numerical Porous Media (NumPor)
Citation:
Multilevel Monte Carlo Approaches for Numerical Homogenization 2015, 13 (4):1107 Multiscale Modeling & Simulation
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
Multiscale Modeling & Simulation
Issue Date:
1-Oct-2015
DOI:
10.1137/130905836
Type:
Article
ISSN:
1540-3459; 1540-3467
Additional Links:
http://epubs.siam.org/doi/10.1137/130905836
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorEfendiev, Yalchin R.en
dc.contributor.authorKronsbein, Corneliaen
dc.contributor.authorLegoll, Frédéricen
dc.date.accessioned2016-01-18T08:18:59Zen
dc.date.available2016-01-18T08:18:59Zen
dc.date.issued2015-10-01en
dc.identifier.citationMultilevel Monte Carlo Approaches for Numerical Homogenization 2015, 13 (4):1107 Multiscale Modeling & Simulationen
dc.identifier.issn1540-3459en
dc.identifier.issn1540-3467en
dc.identifier.doi10.1137/130905836en
dc.identifier.urihttp://hdl.handle.net/10754/593668en
dc.description.abstractIn this article, we study the application of multilevel Monte Carlo (MLMC) approaches to numerical random homogenization. Our objective is to compute the expectation of some functionals of the homogenized coefficients, or of the homogenized solutions. This is accomplished within MLMC by considering different sizes of representative volumes (RVEs). Many inexpensive computations with the smallest RVE size are combined with fewer expensive computations performed on larger RVEs. Likewise, when it comes to homogenized solutions, different levels of coarse-grid meshes are used to solve the homogenized equation. We show that, by carefully selecting the number of realizations at each level, we can achieve a speed-up in the computations in comparison to a standard Monte Carlo method. Numerical results are presented for both one-dimensional and two-dimensional test-cases that illustrate the efficiency of the approach.en
dc.language.isoenen
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/130905836en
dc.rightsArchived with thanks to Multiscale Modeling & Simulationen
dc.subjectnumerical homogenizationen
dc.subjectmulti level Monte Carlo methodsen
dc.subjectstochastic homogenizationen
dc.titleMultilevel Monte Carlo Approaches for Numerical Homogenizationen
dc.typeArticleen
dc.contributor.departmentCenter for Numerical Porous Media (NumPor)en
dc.identifier.journalMultiscale Modeling & Simulationen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, Texas A & M University, College Station, TX 77845en
dc.contributor.institutionFraunhofer ITWM & University of Kaiserslautern, 67663 Kaiserslautern, Germanyen
dc.contributor.institutionLaboratoire Navier, Ecole des Ponts ParisTech, Universite Paris-Est, 77455 Marne-La-Vallee Cedex 2, Franceen
dc.contributor.institutionNRIA Rocquencourt, MATHERIALS project-team, Domaine de Voluceau, B.P. 105, 78153 Le Chesnay Cedex, Franceen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorEfendiev, Yalchin R.en
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