Abstract:The fast multipole method (FMM) and generalized minimal residual (GMRES) algorithm are applied to virtual boundary element least square method to solve three dimensional potential problems, so that the amount of the computational elapsed time and the memory volume of the storage problems with the calculation of demand are linearly proportional to the number of degrees of freedom of the problem to be solved. Then the numerical simulation large scale degrees of freedom question might be achieved by the method. Based on the numerical form of virtual boundary element least square method for potential problems, the fundamental solutions of three dimensional potential problems are derived as the numerical scheme to be more suitable for FMM, through the introduction of concepts of diagonalization and exponential expansion moments, in order to further improve the efficiency of the problem with almost the same high precison. The GMRES algorithm is adopted to find the solution of matrix equation. The numerical examples relating to simulation of large scale problems achieved by the method verify the feasibility, efficiency and calculation precision of the method.
