A numerical approach related to defect-type theories for some weakly random problems in homogenization

Details A numerical approach related to defect-type theories for some weakly random problems in homogenization A numerical approach related to defect-type theories for some weakly random problems in homogenization

2010-05-21

arxiv.org/abs/1005.3910v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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