Special Quasirandom Structures: a selection approach for stochastic homogenization
Numerical Analysis
2015-09-07 v1 Probability
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 [von Pezold et al, Physical Review B 2010; Wei et al, Physical Review B 1990; Zunger et al, Physical Review Letters 1990], 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.
Cite
@article{arxiv.1509.01258,
title = {Special Quasirandom Structures: a selection approach for stochastic homogenization},
author = {Claude Le Bris and Frederic Legoll and William Minvielle},
journal= {arXiv preprint arXiv:1509.01258},
year = {2015}
}