臺灣博碩士論文加值系統

本論文, 我們探討無網格有限圓球法, 並且把這個方法應用到解對流主導之邊界值問題

In this paper, we study the basic ideas of the meshless finite spheres method proposed by De and Bathe and the mathematical foundation of the partition of unity. Although the theory are valid in n dimension. we focus on the plication of the method to some one-dimensional convection dominated two point boundary value problems. By a proper selection of the local basis functions, we find out that the meshless finite spheres method provides an efficient alternative for the underlying problems.

1.Introduction
2.Mathematical Foundation of the Partition of Unity
3.The Method of Finite Spheres

4.Two Point Boundary Value Problems
5.Numerical Examples and Concluding Remarks

1. I. Babuska and J.M. Melenk, The partition of unity method. Int. J.Num.Meth. Eng., 40:727--758, 1997.
2. S. De and K.J. Bathe, The method of finite spheres. Comput. Mech., 25: 329--345, 2000.
3. C.A. Duarte and J.T. Oden, H-p clouds an h-p meshless method. Num. Meth. Partial Differential Equations, 12:673--705, 1996.
4. J.M. Melenk and I. Babuska, The partition of unity finite element method: basic theory and applications. Comp. Meth. Appl. Mech. Eng., 139:289--314, 1996.
5. D. Shepard, A two-dimensional interpolation function for irregularly spaced data. Proc. 23rd Nat. Conf. ACM, 517--524, 1968.