Simplex Elements Stochastic Collocation in Higher-Dimensional Probability Spaces

A Simplex Elements Stochastic Collocation (SESC) method is introduced for robust and efficient propagation of uncertainty through computational models. The presented non– intrusive Uncertainty Quantification (UQ) method is based on adaptive grid refinement of a simplex elements discretization in probability space. The approach is equally robust as Monte Carlo (MC) simulation in terms of the Extremum Diminishing (ED) robustness concept. The efficiency of SESC is based on high degree polynomial interpolation, randomized refinement sampling, and Essentially Extremum Diminishing (EED) extrapolation. This results in a superlinear convergence rate and a linear increase of the initial number of samples with dimensionality. The flexibility of simplex elements is further employed to discretize non–hypercube probability spaces with correlated random parameters.