Special Quasirandom Structures: a selection approach for stochastic homogenization

2015/09/03 by Bris, Claude Le, Frédéric Legoll, Legoll, Frederic +2 · 1 citation
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Block Copolymer Self-Assembly #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.1509.01258

openalex publication_date 2015/09/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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