A numerical approach related to defect-type theories for some weakly random problems in homogenization
Analysis of PDEs
2010-05-24 v1
Abstract
We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a rare event at the microscopic level. It however affects the macroscopic properties of the material, and we indeed provide a method to compute the first and second-order corrections. To this end, we formally establish an asymptotic expansion of the macroscopic properties. Our perturbative approach shares common features with a defect-type theory of solid state physics. The computational efficiency of the approach is demonstrated.
Cite
@article{arxiv.1005.3910,
title = {A numerical approach related to defect-type theories for some weakly random problems in homogenization},
author = {Arnaud Anantharaman and Claude Le Bris},
journal= {arXiv preprint arXiv:1005.3910},
year = {2010}
}