Hybrid Stochastic Finite Elements and Generalized Monte Carlo Simulation

A procedure is developed to integrate analytical solutions to problems featuring random media with Monte Carlo simulations in order to improve the efficiency of the simulations. This is achieved by developing a common theoretical framework that encompasses Monte Carlo procedures as well as various expansion solution techniques. This framework can be perceived as a natural extension of hybrid deterministic finite element procedures whereby refinement is achieved by simultaneously increasing the number of elements as well as the degree of interpolation within each element.