An Improved Formulation of Singular Boundary Method (Advances in Applied Mathematics and Mechanics, 2012)
This study proposes a new formulation of singular boundary method (SBM)to solve the 2D potential problems, while retaining its original meritsbeing free of integration and mesh, easy-to-program, accurate andmathematically simple without the requirement of a fictitious boundaryas in the method of fundamental solutions (MFS). The key idea of the SBMis to introduce the concept of the origin intensity factor to isolate thesingularity of fundamental solution so that the source points can be placeddirectly on the physical boundary. This paper presents a new approach toderive the analytical solution of the origin intensity factor based on theproposed subtracting and adding-back techniques. And the troublesome samplenodes in the ordinary SBM are avoided and the sample solution is also notnecessary for the Neumann boundary condition. Three benchmark problems aretested to demonstrate the feasibility and accuracy of the new formulationthrough detailed comparisons with the boundary element method (BEM), MFS,regularized meshless method (RMM) and boundary distributed source (BDS)method.