A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations

Abstract : In this paper, we propose a multiscale coupling approach to perform Monte-Carlo simulations on systems described at the atomic scale and subjected to random phenomena. The method is based on the Arlequin framework, developed to date for deterministic models involving coupling a region of interest described at a particle scale with a coarser model (continuum model). The new method can result in a dramatic reduction in the number of degrees of freedom necessary to perform Monte-Carlo simulations on the fully atomistic structure. The focus here is on the construction of an equivalent stochastic continuum model and its coupling with a discrete particle model through a stochastic version of the Arlequin method. Concepts from the Stochastic Finite Element Method, such as the Karhünen–Loeve expansion and Polynomial Chaos, are extended to multiscale problems so that Monte-Carlo simulations are only performed locally in subregions of the domain occupied by particles. Preliminary results are given for a 1D structure with harmonic interatomic potentials.
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Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (43-44), pp.3530-3546. 〈10.1016/j.cma.2008.04.013〉
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https://hal.archives-ouvertes.fr/hal-01580941
Contributeur : Ludovic Chamoin <>
Soumis le : dimanche 3 septembre 2017 - 23:23:22
Dernière modification le : vendredi 23 novembre 2018 - 08:53:26

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Ludovic Chamoin, J. Tinsley Oden, Serge Prudhomme. A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2008, 197 (43-44), pp.3530-3546. 〈10.1016/j.cma.2008.04.013〉. 〈hal-01580941〉

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