Spectral Representations of Uncertainty: Algorithms and Applications

The objectives of this project were: (1) Develop a general algorithmic framework for stochastic ordinary and partial differential equations. (2) Set polynomial chaos method and its generalization on firm theoretical ground. (3) Quantify uncertainty in large-scale simulations involving CFD, MHD and microflows. The overall goal of this project was to provide DOE with an algorithmic capability that is more accurate and three to five orders of magnitude more efficient than the Monte Carlo simulation