A coupling method for stochastic continuum models at diff erent scales

Yves Le Guennec (1) , Régis Cottereau (1) , Didier Clouteau (1) , Christian Soize (2)

1 MSSMat - Laboratoire de mécanique des sols, structures et matériaux
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

In this paper, we present a novel approach that allows to couple two stochastic continuum models describing the same random medium at different observation scales. The coupling strategy is performed in the Arlequin framework, which is based on a volume coupling and a partition of the energy. Suitable functional space and coupling operator are chosen for the weak enforcement of the continuity between the two models. This choice ensures that the resulting mixed problem is well posed. The Monte-Carlo based numerical strategy for the solution of the mixed problem is briefly outlined. An application is presented, emphasizing on the interest of the chosen coupling operator. Finally, some remarks are provided concerning a stochastic multi-model coupling.

Mots clés: Uncertainty quantification; Arlequin method; Stochastic mechanics; Coupling numerical method; Multiscale modeling; Uncertainties

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Yves Le Guennec, Régis Cottereau, Didier Clouteau, Christian Soize. A coupling method for stochastic continuum models at diff erent scales. Probabilistic Engineering Mechanics, 2014, 37 (-), pp.138-147. ⟨10.1016/j.probengmech.2013.10.005⟩. ⟨hal-00940047⟩