Publications

Scaling of intrusive stochastic collocation and stochastic galerkin methods for uncertainty quantification in Monte Carlo particle transport

Olson, Aaron J.; Franke, Brian C.; Prinja, Anil K.

A Monte Carlo solution method for the system of deterministic equations arising in the application of stochastic collocation (SCM) and stochastic Galerkin (SGM) methods in radiation transport computations with uncertainty is presented for an arbitrary number of materials each containing two uncertain random cross sections. Moments of the resulting random flux are calculated using an intrusive and a non-intrusive Monte Carlo based SCM and two different SGM implementations each with two different truncation methods and compared to the brute force Monte Carlo sampling approach. For the intrusive SCM and SGM, a single set of particle histories is solved and weight adjustments are used to produce flux moments for the stochastic problem. Memory and runtime scaling of each method is compared for increased complexity in stochastic dimensionality and moment truncation. Results are also compared for efficiency in terms of a statistical figure-of-merit. The memory savings for the total-order truncation method prove significant over the full-tensor-product truncation. Scaling shows relatively constant cost per moment calculated of SCM and tensor-product SGM. Total-order truncation may be worthwhile despite poorer runtime scaling by achieving better accuracy at lower cost. The figure-of-merit results show that all of the intrusive methods can improve efficiency for calculating low-order moments, but the intrusive SCM approach is the most efficient for calculating high-order moments.