An Iterative Monte Carlo Scheme with Relaxation

A Monte Carlo Scheme for the solution of Poisson's equation is presented. The solution technique applies a unique iterative, boundary propagation scheme that uses successive-under-relaxation (SUR). The relaxation scheme adheres to the traditional SOR iteration matrix splitting; however, it is confined to SUR to achieve convergence. Analogously, it is demonstrated that the convergence of the SUR approach is accelerated by incrementally reducing the scale of the under-relaxation parameter w once per iteration sweep. It is believed that this is the first such example of a relaxation scheme applied to this particular Monte Carlo solution approach. In this presentation, the notion of an iterative scheme will be examined and its use in the design of the method given.