Variance Reduction in Stochastic Homogenization Using Antithetic Variables
2012, v.18, Issue 1, 31-66
Some theoretical issues related to the problem of variance reduction in numerical approaches for stochastic homogenization are examined. On some simple, yet representative cases, it is demonstrated theoretically that a technique based on antithetic variables can indeed reduce the variance of the output of the computation, and decrease the overall computational cost of such a multiscale problem. The theoretical considerations presented here are companion to numerical experiments presented in [X. Blanc, R. Costaouec, C. Le Bris and F. Legoll, Variance reduction in stochastic homogenization: the technique of antithetic variables. Numerical Analysis and Multiscale Computations, B. Engquist, O. Runborg and Y.-H.R. Tsai (eds.), Lect. Notes Comput. Sci. Eng., 2012, v.82, Springer, 47--70] that corroborate the theoretical results enclosed.
Keywords: stochastic homogenization,variance reduction,antithetic variables