• 论文 • 上一篇    下一篇

椭圆外区域上Helmholtz问题的自然边界元法

张敏,杜其奎,   

  1. 南京师范大学数学与计算机科学学院,南京师范大学数学与计算机科学学院 南京 210097,南京 210097
  • 出版日期:2008-01-14 发布日期:2008-01-14

张敏,杜其奎,. 椭圆外区域上Helmholtz问题的自然边界元法[J]. 计算数学, 2008, 30(1): 75-88.

NATURAL BOUNDARY ELEMENT METHOD FOR THE HELMHOLTZ PROBLEM IN AN EXTERIOR ELLIPTIC DOMAIN

  1. Zhang Min Du Qikui (School of Mathematics and Computer Science,Nanjing Normal University,Nanjing 210097,China)
  • Online:2008-01-14 Published:2008-01-14
本文研究椭圆外区域上Helmholtz方程边值问题的自然边界元法.利用自然边界归化原理,获得该问题的Poisson积分公式及自然积分方程,给出了自然积分方程的数值方法.由于计算的需要,我们详细地讨论了Mathieu函数的计算方法(当0
In this paper,we investigate the natural boundary element method for the boundary value problem of Helmholtz equation in an exterior elliptic domain.By the principle of the natural boundary reduction,we obtain the Poisson integral formula and the natural integral equation of this problem,develop a numerical method to solve the natural integral equation.For computation,we discuss the numerical methods of the Mathieu functions when 0
()

[1]冯康.论微分与积分方程及有限元与无限元.计算数学
[J],1980,2(1):100-105.
[2]Feng Kang.Canonical boundary reduction and finite element method
[C].Proceedings of Inter- national Symposium on the Finite Element Methods(1981,Hefei),Beijing:Science Press,1982, 330-352.
[3]Feng Kang,Yu Dehao.Canonical integral equations of elliptic boundary value problems and their numerical solutions
[C].Proceedings of China-France Symposium on the Finite Eleraent Meth- ods(1982,Beijing),Beijing:Science Press,1983,211-252.
[4]Feng Kang.Finite element Method and natural boundary reducation
[C].Proceedings of the In- ternational Congress Mathematicians,Warszawa:Polish Academy Press,1983,1439-1453.
[5]余德浩.自然边界元方法的数学理论
[M].北京:科学出版社,1993.
[6]邬吉明,余德浩.椭圆外区域上的自然边界元法
[J].计算数学,2000,22(3):355-368.
[7]李霞,李瑞遐.Helmholtz方程外Dirichlet问题的边界积分法
[J].华东理工大学学报(自),2005,31(4):517-520.
[8]Ben-Porat G,Givoli D.Solution of unbounded domain problems using elliptic artificial bound- ary
[J].Communication in Numerical Methods in Engineering,1995,11:735-741.
[9]王竹溪,郭敦仁.特殊函数概论
[M].北京:科学出版社,1979.
[10]李瑞遐.Helmholtz方程外边值问题的自然边界元法
[J].高校应用数学学报,1997,12A(3):369-374.
[11]李瑞遐.一个扩散问题的自然边界元法与有限元法组合
[J].高校应用数学学报,1998,13A(3):333-341.
[12]张善杰,沈耀春.马丢函数的数值计算
[J].电子学报,1995,23(9):41-46.
[13]隋国芳,丁芝莱.马丢函数的一种计算方法
[J].数值计算与计算机应用,1987,3:165-170.
[14]中国科学院沈阳计算技术研究所等.电子计算机常用算法
[M].北京:科学出版社,1976.
[15]Huang Hongying,Yu Dehao.Natural boundary element method for three dimensional exterior harmonic problem with an inner prolate spheroid boundary
[J].Journal of Computational Mathe- matics,2006,24(2):193-208.
[16]余德浩,贾祖朋.椭圆边界上的自然积分算子及各向异性外问题的耦合算法
[J].计算数学,2002,24(3):375-384;
[17]Yu Dehao.Natural Boundary Integral Method and Its Applications
[M].Science Press/Kluwer Academic Publishers,2002.
[18]Daisuke Koyama.Error estimates of the DtN finite element method for the exterior Helmholtz problem
[J].Journal of Computational and Applied Mathematics,2007,200(1):21-31.
No related articles found!
阅读次数
全文


摘要