We consider Uncertainty Quanti¿cation (UQ) by expanding the solution in so-called generalized Polynomial Chaos expansions. In these expansions the solution is decomposed into a series with orthogonal polynomials in which the parameter dependency becomes an argument of the orthogonal polynomial basis functions. The time and space dependency remains in the coef¿cients. In UQ two main approaches are in use: Stochastic Collocation (SC) and Stochastic Galerkin (SG).
Practice shows that in many cases SC is more ef¿cient for similar accuracy as obtained by SG. In SC the coef¿cients in the expansion are approximated by quadrature and thus lead to a large series of deterministic simulations for several parameters. We consider strategies to ef¿ciently perform this series of deterministic simulations within SC.