A triangular mesh random walk for Dirichlet problems (Q1921951)

A new Monte Carlo technique for the solution of Dirichlet problems for Laplace and Poisson equations is considered. The presented new technique is called the equilateral triangular mesh random walk. It is shown that the main advantage of the method over the classical Monte Carlo technique, such as fixed random walk and floating random walk, is that it is capable for handling Neumann problems which are difficult to be solved by the classical Monte Carlo methods. However, this work is limited to the application of the triangular mesh random walk to Dirichlet problems for Laplace and Poisson equations. Some illustrative numerical examples are given. They include two-dimensional problems and confirm the accuracy of the triangular mesh random walk.