ABSTRACT
Handling Neumann problems requires the introduction of a Monte Carlo technique called the equilateral triangular random walk. This chapter focuses on this technique for solving potential problems in general, especially those with Neumann boundary conditions. It presents two examples that illustrate the application of the equilateral triangular random walk method. The first example involves a Laplace's equation with Neumann boundary condition, and the second one deals with Poisson's equation with Neumann condition. The first example has an analytic solution so that the accuracy and validity of the triangular mesh random walk method can be checked. In the second example, the solution is compared with that of the finite difference method. The two examples were calculated on an IBM PC. The two examples considered in the chapter show that the triangular random walk method provides solutions that always converge to the exact solution.
