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    Multilevel Monte Carlo Approaches for Numerical Homogenization

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    Type
    Article
    Authors
    Efendiev, Yalchin R. cc
    Kronsbein, Cornelia
    Legoll, Frédéric
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Numerical Porous Media SRI Center (NumPor)
    Date
    2015-10-01
    Online Publication Date
    2015-10-01
    Print Publication Date
    2015-01
    Permanent link to this record
    http://hdl.handle.net/10754/593668
    
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    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.
    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
    DOI
    10.1137/130905836
    arXiv
    1301.2798
    Additional Links
    http://epubs.siam.org/doi/10.1137/130905836
    ae974a485f413a2113503eed53cd6c53
    10.1137/130905836
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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