MULTILEVEL MONTE CARLO APPROACHES FOR NUMERICAL HOMOGENIZATION Academic Article

abstract

• 2015 Society for Industrial and Applied Mathematics. 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.

authors

• Efendiev, Yalchin

published proceedings

• MULTISCALE MODELING & SIMULATION

author list (cited authors)

• Efendiev, Y., Kronsbein, C., & Legoll, F.

citation count

• 11

complete list of authors

• Efendiev, Yalchin||Kronsbein, Cornelia||Legoll, Frédéric

publication date

• January 2015

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM: Multiscale Modeling and Simulation  Journal

keywords

• Multi Level Monte Carlo Methods
• Numerical Homogenization
• Stochastic Homogenization

Digital Object Identifier (DOI)

• 10.1137/130905836

URI

• https://hdl.handle.net/1969.1/179920

start page

• 1107

end page

• 1135

volume

• 13

issue

• 4

URL

• http://dx.doi.org/10.1137/130905836