KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Porous Media SRI Center (NumPor)
MetadataShow full item record
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.
CitationMultilevel Monte Carlo Approaches for Numerical Homogenization 2015, 13 (4):1107 Multiscale Modeling & Simulation
JournalMultiscale Modeling & Simulation