A method of fundamental solution without fictitious boundary

摘要

This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program, and truly meshless. Like the method of fundamental solution (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation points of the SBM coincide on the physical boundary without the requirement of fictitious boundary. In order to avoid the singularity at origin, this method proposes an inverse interpolation technique to evaluate the singular diagonal elements of the interpolation matrix. This study tests the SBM successfully to three benchmark problems, which shows that the method has rapid convergent rate and is numerically stable.