Spectral stochastic homogenization of divergence-type PDEs Original Research Article

This paper presents a formulation and numerical analysis of the homogenization of stochastic PDEs. The framework of homogenization is adopted to describe an effective medium that is equivalent in some sense to a heterogeneous medium of interest. The parameters of the resulting homogeneous medium are described as stochastic processes characterized by their polynomial chaos decomposition. The formulation yields a chaos decomposition for the predicted behavior of the homogeneous medium that captures, in addition to the effect of heterogeneity, the effect of variability. Once this description has been computed, various statistics of the solution can be efficiently evaluated.