The Method of Fundamental Solutions and the Quasi-Monte Carlo Method for Poisson’s Equation

A multivariate integration method based on the quasi-Monte Carlo method which alleviates the problem of domain discretization has been implemented for computing particular solutions of Poisson’s equation. Coupled with the method of fundamental solutions, a simpler and versatile technique, we have demonstrated a simple computational method which provides means of shifting the effort from analyst to computer. For illustration, we give three numerical examples for a set of standard problems and compare results of different methods.