Research on Potential Problem based on Singular Decomposition and Boundary FM-BEM Algorithm

In order to overcome the difficulties of low computational efficiency and high memory requirement in the conventional boundary element method for solving large-scale potential problems, a fast multipole boundary element method for the problems of Poisson equation is presented. First of all, through the multipole expansion and local expansion for the basic solution of the kernel function of the Poisson equation, the boundary integral equation of the fast multipole boundary element method for Poisson equation was obtained; secondly, the Laplasse transform is used for the Singularity processing treatment of Poisson equation; then, the realize the algorithm design of fast multipole boundary element method, the calculating flow of the algorithm is given; finally, a numerical example is given to verify the accuracy and the efficiency of the fast multipole boundary element method.