Multiscale Model Reduction for the Solution of Stochastic Partial Differential Equations With Localized Sources of Uncertainties

The presence of numerous localized sources of uncertainties in stochastic models leads to high dimensional and multiscale problems. A numerical strategy is here proposed to propagate the uncertainties through such models. It is based on a multiscale domain decomposition method that exploits the localized side of uncertainties. The separation of scales has the double benefit of improving the conditioning of the problem as well as the convergence of tensor based methods (namely Proper Generalized Decomposition methods) used within the strategy for the separated representation of high dimensional stochastic parametric solutions.