Three Dimensional Fast Multipole Bem For Potential Problems

In this paper, Boundary Element Method (BEM) is developed for 3-D potential problems. Sub-element method is used to solve the singular integrals. Based on traditional three-dimensional Boundary Element Method, combining with Multipole Expansion Method and Generalized Minimal Residual Method, 3-D fast Multipole BEM is given out in this paper. Then 3-D surface fast Multipole BEM is developed. The above method is highly efficient and the demanding of its computing memory is very low, which makes the large-scale computing possible. The paper includes five chapters. Chapter 1 is introduction, which presents the significance of the task and the major work of the paper. Briefly it introduces three widely used numerical methods and discusses their advantages and disadvantages. And the development history, present state and perspectives of BEM are introduced. In chapter 2, the boundary integral equation of the potential problem is illustrated. It also illustrates how to deal with domain integral and the third boundary condition. At the same time,the boundary integral equation formulae for potential field are presented in this paper to calculate the potential field and gradient. The corresponding computer program was designed. By comparison with ANSYS,it was clear that BEM could solve the problem not only effectively but also precisely. In chapter 3, the theory of Multipole Expansion Method is introduced. In chapter 4, Generalized Minimal Residual Method is illustrated. Through the appropriate decomposition of traditional basic solution and combing with Multipole Expansion Method and Generalized Minimal Residual Method; taking the boundary elements as the units, 3-D fast Multipole-BEM for potential problems is developed from traditional BEM. The numerical experiments show that with the same precision, Multipole-BEM is with higher computing speed and lower memory demanding for large-scale problems. When the DOF is less than 1300, the computing efficiency is lower than tradition BEM but the memory demanding is very low. The temperature distribution of bearing chock in 2200mm aluminium foil four-high mill is simulated. In chapter 5, based on fast Multipole-BEM, the surface fast Multipole-BEM is deduced.