A New Fast Multipole Boundary Element Method For Plane Elasticity

Boundary element method(BEM) is a numerical scheme along with the development of the finite element method(FEM).Compared with FEM,BEM has its own advantage.However,the coefficient matrix arising from BEM is always dense and asymmetric.Solving such equation system by traditional techniques needs lots of memory and operation. As the scale of computation increases, the computational efficiency decreases drastically.Fast multipole BEM is a new algorithm developed for BEM these years.The computational cost and memory requirement of fast multipole BEM is more than an order of magnitude lower than that of traditional BEM without changing accuracy, making it possible to solve large scale problems on a common desktop.Because the fundamental solutions of elasticity is complex, the expansion coefficients and translation relationships in fast multipole BEM are fussy, which make the computational efficiency become low.Basing on the plane elasticity in complex analytic form,the boundary integral concluding fundamental solution is changed to a new format which connect to Green's function for potential problems,a new expansion and translation format is derived by fast multipole algorithm,simplifying the expansion coefficients and translation relationships in fast multipole BEM.The numerical results show that,computational cost and memory requirement of the new fast multipole BEM is more than an order of magnitude lower than that of traditional BEM without losing accuracy; Compared with the fast multipole BEM using another expansion and translation formats,the convergence speed of the new fast multipole is more quick than before, which is propitious to improve the computational efficiency for large scale numerical computation.A large scale numerical computation about square plate with many randomly distributed holes is finished on a desktop finally in this paper.The numerical example indicates that the new fast multipole BEM has advantages at large scale numerical computation, and it has an extensive applied prospect.