The method of fundamental solutions for solving Poisson problems

Traditionally the method of fundamental solutions (MFS) is used to approximate solution of linear homogeneous equations. For nonhomogeneous problems, one needs to couple other numerical schemes, such as domain integration, polynomial or radial basis functions interpolation, to evaluate particular solutions. In this paper we propose to unify the MFS as a numerical method for directly approximating homogeneous solution and particular solution in a similar manner. The major advantage of such approach is that the particular solution can be easily obtained and evaluated. The numerical results show that such approach can be highly accurate.