Analysis of a Monte Carlo boundary propagation method

A modified Monte Carlo technique, first developed in estimating a solution to Poissonʹs equation, is described and estimates of its computational complexities are derived. The method yields better estimates than the standard Monte Carlo approach by incorporating boundary information more efficiently and by the implicit reuse of random walk information gathered throughout the course of the computation. The new approach reduces the computational complexity of the length of a random walk by one order of magnitude as compared to a standard method described in many text books. Also, the number of walks necessary to achieve a desired accuracy is reduced.