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Some Numerical Approaches for Weakly Random Homogenization

In: Numerical Mathematics and Advanced Applications 2009

Author

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  • Claude Le Bris

    (École Nationale des Ponts et Chaussées, CERMICS
    INRIA Rocquencourt, MICMAC project, Domaine de Voluceau)

Abstract

We overview a series of recent works addressing homogenization problems for some materials seen as small random perturbations of periodic materials (in a sense made precise in the body of the text). These recent works are joint works with several collaborators: Blanc (Paris 6), Lions (Collège de France), Legoll, Anantharaman, Costaouec (Ecole Nationale des Ponts et Chaussées and INRIA). The theory, developed in [C. R. Acad. Sci. Série I, 343, 717–724 (2006), Journal de Mathématiques Pures et Appliquées, 88, 34–63 (2007)], is only outlined. Next a collection of numerical appropriate approaches introduced in [Note aux Comptes Rendus de l’Académie des Sciences (2009), Thèse de l’ Université Paris Est, C. R. Acad. Sci. Série I, 348, 99–103 (2010)] is presented. The theoretical considerations and the numerical tests provided here show that for the materials with only a small amount of randomness that are considered, a dedicated approach is far more efficient than a direct, stochastic approach.

Suggested Citation

  • Claude Le Bris, 2010. "Some Numerical Approaches for Weakly Random Homogenization," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 29-45, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_3
    DOI: 10.1007/978-3-642-11795-4_3
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