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H 1 Variance reduction approaches for stochastic homogenization

Auteurs : Legoll, Frédéric (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : The simulation of random heterogeneous materials is often very expensive. For instance, in a homogenization setting, the homogenized coefficient is defined from the so-called corrector function, that solves a partial differential equation set on the entire space. This is in contrast with the periodic case, where he corrector function solves an equation set on a single periodic cell. As a consequence, in the stochastic setting, the numerical approximation of the corrector function (and therefore of the homogenized coefficient) is a challenging computational task.
    In practice, the corrector problem is solved on a truncated domain, and the exact homogenized coefficient is recovered only in the limit of infinitely large domains. As a consequence of this truncation, the approximated homogenized coefficient turns out to be stochastic, even though the exact homogenized coefficient is deterministic. One then has to resort to Monte-Carlo methods, in order to compute the expectation of the (approximated, apparent) homogenized coefficient within a good accuracy. Variance reduction questions thus naturally come into play, in order to increase the accuracy (e.g. reduce the size of the confidence interval) for a fixed computational cost. In this talk, we will present some variance reduction approaches to address this question.

    Codes MSC :
    35B27 - Homogenization; equations in media with periodic structure [See also 74Qxx, 76M50]
    35R60 - PDEs with randomness, stochastic PDE
    60Hxx - Stochastic analysis, See also {58G32}

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 28/05/14
      Date de captation : 07/08/13
      Collection : Research talks ; Partial Differential Equations ; Probability and Statistics
      Format : quicktime ; audio/x-aac
      Durée : 00:44:00
      Domaine : Probability & Statistics ; PDE
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2013-08-07_Legoll.mp4

    Informations sur la rencontre

    Nom de la rencontre : CEMRACS : Modelling and simulation of complex systems : stochastic and deterministic approaches / CEMRACS : Modéliser et simuler la complexité : approches stochastiques et déterministes
    Organisateurs de la rencontre : Champagnat, Nicolas ; Lelièvre, Tony ; Nouy, Anthony
    Dates : 22/07/13 - 30/08/13
    Année de la rencontre : 2013
    URL Congrès : http://smai.emath.fr/cemracs/cemracs13/i...

    Citation Data

    DOI : 10.24350/CIRM.V.18586803
    Cite this video as: Legoll, Frédéric (2013). Variance reduction approaches for stochastic homogenization. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18586803
    URI : http://dx.doi.org/10.24350/CIRM.V.18586803