Comparative study of projection schemes for stochastic finite element analysis

We present a comparison of subspace projection schemes for stochastic finite element analysis in terms of accuracy and computational efficiency. More specifically, we compare the polynomial chaos projection scheme with reduced basis projection schemes based on the preconditioned stochastic Krylov subspace. Numerical studies are presented for two problems: (1) static analysis of a plate with random Young’s modulus and (2) settlement of a foundation supported on a randomly heterogeneous soil. Monte Carlo simulation results based on exact structural analysis are used to generate benchmark results against which the projection schemes are compared. We show that stochastic reduced basis methods require significantly less computer memory and execution time compared to the polynomial chaos approach, particularly for large-scale problems with many random variables. For the class of problems considered, we find that stochastic reduced basis methods can be up to orders of magnitude faster, while providing results of comparable or better accuracy.