Nous proposons dans la présente Note une méthode pour calculer au premier ordre le comportement homogénéisé d'un milieu consistant en un matériau périodique de référence perturbé de manière stochastique. L'approche, très efficace en termes de coût calcul, admet une justification rigoureuse dans certains cas, et a été testée numériquement avec succès pour des cas plus généraux.
We present in this Note an approach aiming at computing the first-order homogenized behaviour of a medium consisting of a randomly perturbed periodic reference material. The approach, which proves to be very efficient from a computational point of view, is rigorously founded in a certain class of settings and has been successfully numerically tested for more general settings.
Accepté le :
Publié le :
Arnaud Anantharaman 1 ; Claude Le Bris 1
@article{CRMATH_2010__348_9-10_529_0,
author = {Arnaud Anantharaman and Claude Le Bris},
title = {Homog\'en\'eisation d'un mat\'eriau p\'eriodique faiblement perturb\'e al\'eatoirement},
journal = {Comptes Rendus. Math\'ematique},
pages = {529--534},
publisher = {Elsevier},
volume = {348},
number = {9-10},
year = {2010},
doi = {10.1016/j.crma.2010.03.001},
language = {fr},
}
TY - JOUR AU - Arnaud Anantharaman AU - Claude Le Bris TI - Homogénéisation d'un matériau périodique faiblement perturbé aléatoirement JO - Comptes Rendus. Mathématique PY - 2010 SP - 529 EP - 534 VL - 348 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2010.03.001 LA - fr ID - CRMATH_2010__348_9-10_529_0 ER -
Arnaud Anantharaman; Claude Le Bris. Homogénéisation d'un matériau périodique faiblement perturbé aléatoirement. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 529-534. doi : 10.1016/j.crma.2010.03.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.03.001/
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[2] A. Anantharaman, C. Le Bris, A numerical approach based on defect-type theories for some weakly random problems in homogenization, en préparation
[3] A. Anantharaman, C. Le Bris, Mathematical foundations and genericity of a numerical approach for some weakly random problems in homogenization, en préparation
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