Non—intrusive polynomial chaos expansion (PCE) and stochastic collocation (SC) methods are attractive techniques for uncertainty quantification due to their abilities to produce functional representations of stochastic variability and to achieve exponential convergence rates in statistics of interest. Whereas PCE estimates coefficients for known orthogonal polynomial basis functions, SC forms Lagrange interpolants for known coefficients. The latest results in comparing PCE and SC and embedding these methods within design under uncertainty will be presented.
Time permitting, a short overview of DAKOTA will also be provided. DAKOTA is the software delivery vehicle for much of the uncertainty quantification research at the DOE defense laboratories.
Center for Computational and Applied Mathematics (CCAM)
Birck Nanotechnology Center, Room 1001, Purdue University, West Lafayette, IN