Fast iterative methods for discrete-ordinates particle transport calculations

In discrete-ordinates (S-N) simulations of large problems involving linear interactions between radiation and matter, the underlying linear Boltzmann problem is discretized and the resulting system of algebraic equations is solved iteratively. If the physical system contains subregions that are optically thick with small absorption, the simplest iterative process, Source Iteration, is inefficient and costly. During the past 40 years, significant progress has been achieved in the development of acceleration methods that speed up the iterative convergence of these problems. This progress consists of (i) a theory to derive the acceleration strategies, (ii) a theory to predict the convergence properties of the new strategies, and (iii) the implementation of these concepts in production computer codes. In this Review we discuss the theoretical foundations of this work, the important results that have been accomplished, and remaining open questions. (C) 2002 Published by Elsevier Science Ltd.