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Couplage stochastique-déterministe dans le cadre Arlequin et estimations d'erreurs en quantités d'intérêt

Abstract : In design process, uncertainties have to be taken into account. Stochastic methods have therefore been proposed. Furthermore, in many cases, local defects affect strongly the behavior of a structure in a localized region while the rest of the structure is only slightly affected. In these cases, it is not reasonable to model the structure entirely at a fine scale, and multiscale methods are thus appealing. In this framework, we focused on the evaluation of a local specific quantity of interest when the Arlequin method is used to couple a deterministic model with a stochastic one. First, we give ingredients needed for the use of the method in this particular context. Second, to control the quality of the approximate solution obtained with such an approach, a goal-oriented method is introduced. Using residual-types estimates and adjoint-based techniques, a strategy for goal-oriented error estimation is presented for this coupling. Contributions of various error sources (modeling, space discretization, and discretization along the random dimension) are assessed. From information on error sources, an adaptive procedure is proposed to guaranty a given error tolerance. Finally, the described method is applied to study the infiltration of resin inside collagen network in the dentine.
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https://tel.archives-ouvertes.fr/tel-00865192
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Submitted on : Tuesday, September 24, 2013 - 10:12:43 AM
Last modification on : Wednesday, July 8, 2020 - 11:10:20 AM
Long-term archiving on: : Wednesday, December 25, 2013 - 4:32:30 AM

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Cédric Zaccardi. Couplage stochastique-déterministe dans le cadre Arlequin et estimations d'erreurs en quantités d'intérêt. Autre. Ecole Centrale Paris, 2013. Français. ⟨NNT : 2013ECAP0008⟩. ⟨tel-00865192⟩

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