Fast Multipole Virtual Boundary Element Collocation Method for Solving Threedimensional Problems

Abstract:

In the research background of the three dimensional elasticity problem,the idea of the threedimensional fast multipole virtual boundary element collocation method is proposed,in other words,the generalized minimal residual (GMRES) algorithm and the basic idea of fast multipole method (FMM) are jointly employed to solve the equations related to virtual boundary element collocation method (VBEM).The fundamental solutions of threedimensional problem of elasticity are derived as the numerical scheme to be suitable for the FMM of virtual boundary element method.After the evolution of numerical format,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.The numerical examples have proved the feasibility,efficiency and calculating precision of the method.Moreover,the idea of the proposed method has the generality and the extension in the engineering applications.