A Stochastic-deterministic Coupling Method for Multiscale Problems. Application to Numerical Homogenization of Random Materials

摘要

In this paper, we describe a multiscale strategy that allows to couple stochastic and deterministic models. The transition condition enforced between the two models is weak, in the sense that it is based on volume coupling in space (rather than more classical boundary coupling) and on a volume/sample average in the random dimension. The paper then concentrates on the application of this weak coupling technique for the development of a new iterative method for the homogenization of random media. The technique is based on the coupling of the stochastic microstructure to a tentative homogenized medium, the parameters of which are initially chosen at will. Based on the results of the coupled simulation, for which Dirichlet or Neumann boundary conditions are posed at the boundary of the tentative homogenized medium, the parameters of the homogenized medium are then iteratively updated. An example shows the efficiency of the proposed approach compared to the classical KUBC and SUBC approaches in stochastic homogenization.