Abstract
We adapt and study a variance reduction approach for the homogenization of elliptic equations in divergence form. The approach, borrowed from atomistic simulations and solid-state science [23], [24], [25], consists in selecting random realizations that best satisfy some statistical properties (such as the volume fraction of each phase in a composite material) usually only obtained asymptotically. We study the approach theoretically in some simplified settings (one-dimensional setting, perturbative setting in higher dimensions), and numerically demonstrate its efficiency in more general cases.
Funding source: ONR
Award Identifier / Grant number: N00014-12-1-0383
Funding source: EOARD
Award Identifier / Grant number: FA8655-13-1-3061
Funding source: ANR
Award Identifier / Grant number: Investments for the Future ANR-11-LABX-022-01
The first two authors would like to thank E. Cancès for introducing them to the SQS approach in the context of solid state physics, pointing out to them [23], [24], [25], as well as for several stimulating discussions in the early stages of this work. The authors also thank J.-D. Deuschel for his helpful comments and for pointing out [10], and X. Blanc for his remarks on a draft version of this article.
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