Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionNumerical Porous Media SRI Center (NumPor)
Date
2015-10-01Online Publication Date
2015-10-01Print Publication Date
2015-01Permanent link to this record
http://hdl.handle.net/10754/593668
Metadata
Show full item recordAbstract
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 & SimulationJournal
Multiscale Modeling & SimulationarXiv
1301.2798Additional Links
http://epubs.siam.org/doi/10.1137/130905836ae974a485f413a2113503eed53cd6c53
10.1137/130905836