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| HAL : hal-00487759, version 1 |
| arXiv : 1005.3910 |
| DOI : 10.1137/10079639X |
| Fiche détaillée |  Récupérer au format |
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| Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal: A SIAM Interdisciplinary Journal 9, 2 (2011) 513-544 |
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| A numerical approach related to defect-type theories for some weakly random problems in homogenization |
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Arnaud Anantharaman 1, 2Claude Le Bris 1, 2 |
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| (2011) |
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| 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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| 1 : | MICMAC (INRIA Paris - Rocquencourt) |
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Ecole des Ponts ParisTech – INRIA |
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| 2 : | Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS) |
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Ecole des Ponts ParisTech |
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| Domaine | : | Mathématiques/Equations aux dérivées partielles |
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| Homogenization – Random Media – Defects |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/1005.3910 |
| hal-00487759, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00487759 | |
| oai:hal.archives-ouvertes.fr:hal-00487759 | |
| Contributeur : Arnaud Anantharaman | |
| Soumis le : Lundi 31 Mai 2010, 09:26:03 | |
| Dernière modification le : Jeudi 22 Décembre 2011, 11:46:02 | |
