Adaptive Importance Sampling Algorithms for Transport Problems

Abstract

We describe how importance sampling methods may be applied adaptively to the solution of particle transport problems. While the methods apply quite generally, we have so far studied in detail only problems involving planar geometry.

The technique used is to represent the global solution of the transport equation as a linear combination of appropriately chosen basis functions and estimate a finite number of the resulting coefficients in stages. Each stage processes a fixed number of random walks making use of an importance function that has been determined from the previous stage. Special methods have been developed for importance sampling the resulting source and kernel, and some of these will be described. Numerical results exhibiting geometric convergence for the resulting algorithm will be presented.