Sequential Correlated Sampling Methods for Some Transport Problems
In this paper, we will describe how to extend to the solution of certain simple particle transport problems a sequential correlated sampling method introduced by Halton in 1962 for the efficient solution of certain matrix problems. Although the methods apply quite generally, we have so far studied in detail only problems involving planar geometry.
We will describe important features of the resulting algorithm in which random walks are processed in stages, each stage producing a small “correction” to the solution obtained from the previous stage. Issues encountered in the course of implementing such an algorithm for practical transport problems will be discussed and numerical evidence of the geometric convergence achieved will be presented for several model problems.
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