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Article Dans Une Revue Monte Carlo Methods and Applications Année : 2016

Special Quasirandom Structures: a selection approach for stochastic homogenization

Résumé

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.

Dates et versions

hal-01194480 , version 1 (07-09-2015)

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Claude Le Bris, Frédéric Legoll, William Minvielle. Special Quasirandom Structures: a selection approach for stochastic homogenization. Monte Carlo Methods and Applications, 2016, 22 (1), pp.25-54. ⟨hal-01194480⟩
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