A FETI-DP based parallel hybrid stochastic finite element method for large stochastic systems

The computational cost of uncertainty propagation in a mechanics problem can become prohibitively large as the degrees of freedom (DOF) and the number of basic random variables - also referred to as stochastic dimensionality - increase. While a number of methods have been reported in the literature to address either large DOF or high stochastic dimensionality, there is no work addressing both. This work is aimed at filling this gap. Naturally, parallel computing becomes the only feasible option for these large problems. Accordingly, a parallel domain decomposition-based hybrid method combining stochastic Galerkin and Monte Carlo simulation is developed here. To achieve scalability, which is necessary for solving very large scale problems, first the dual-primal variant of the finite element tearing and interconnecting (FETI-DP) is chosen as the domain decomposition method. Then, three distinct approaches of parallel implementation are followed. Through a set of detailed numerical experiments, scalability and relative costs of computation and communication in these three approaches are studied. Finally, based on the observations in these experiments, the best approach is selected and used to solve a large three dimensional elasticity problem with high dimensional parametric uncertainty.