Special Quasirandom Structures: a selection approach for stochastic homogenization
LE BRIS ; LEGOLL ; MINVIELLE
Type de document
ARTICLE A COMITE DE LECTURE REPERTORIE DANS BDI (ACL)
Langue
anglais
Auteur
LE BRIS ; LEGOLL ; MINVIELLE
Résumé / 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.
Source
Monte Carlo Methods and Applications, num. 1, pp. 25-54 p.
Editeur
Walter de Gruyter
