hal-00487759, version 1
A numerical approach related to defect-type theories for some weakly random problems in homogenization
Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal: A SIAM Interdisciplinary Journal 9, 2 (2011) 513-544
Résumé : 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.
- 1 :
- Ecole des Ponts ParisTech – INRIA
- 2 :
- Ecole des Ponts ParisTech
- Domaine : Mathématiques/Equations aux dérivées partielles
- Mots-clés : Homogenization – Random Media – Defects
- Commentaire : 35 pages
- hal-00487759, version 1
- http://hal.archives-ouvertes.fr/hal-00487759
- oai:hal.archives-ouvertes.fr:hal-00487759
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- Soumis le : Lundi 31 Mai 2010, 09:26:03
- Dernière modification le : Jeudi 22 Décembre 2011, 11:46:02
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