A triangular mesh random walk for Dirichlet problems

This paper presents a new Monte Carlo technique called the equilateral triangular mesh random walk. A major advantage of the method over the classical Monte Carlo techniques, such as the fixed random walk and the floating random walk, is that it is capable of handling Neumann problems which the classical Monte Carlo methods cannot handle. However, the presentation in this paper is limited to the application of the triangular mesh random walk to Dirichlet problems of Laplace's and Poisson's equations. Numerical experiments involving two-dimensional problems confirm the accuracy of the triangular mesh random walk.