[1]鞠 银,刘三明,王美珍.椭圆外区域上双曲问题的自然边界元法[J].南京师范大学学报(自然科学版),2013,36(01):29-36.
 Ju Yin,Liu Sanming,Wang Meizhen.Natural Boundary Element Method for the Hyperbolic Problems in an Exterior Elliptic Domain[J].Journal of Nanjing Normal University(Natural Science Edition),2013,36(01):29-36.
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椭圆外区域上双曲问题的自然边界元法()
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《南京师范大学学报》(自然科学版)[ISSN:1001-4616/CN:32-1239/N]

卷:
第36卷
期数:
2013年01期
页码:
29-36
栏目:
数学
出版日期:
2013-03-31

文章信息/Info

Title:
Natural Boundary Element Method for the Hyperbolic Problems in an Exterior Elliptic Domain
作者:
鞠 银刘三明王美珍
上海电机学院数理教学部,上海200240
Author(s):
Ju YinLiu SanmingWang Meizhen
Department of Mathematics and Physics,Shanghai Dianji University,Shanghai 200240,China
关键词:
椭圆外区域双曲方程外问题自然边界归化数值解
Keywords:
exterior elliptic domainhyperbolic equationexterior problemnatural boundary reductionnumerical solution
分类号:
O241.82
摘要:
研究了椭圆外区域上双曲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,最后给出数值例子以示文中所得的人工边界条件的有效性.
Abstract:
In this paper,we investigate the natural boundary element method for the hyperbolic problems in an exterior elliptic domain.By the principle of the natural boundary reduction,we obtain the Poisson integral formula and the natural integral equation,and give the numberical method of the natural integral equation.Finally,we presented some numerical examples to demonstrate the performance of our method.

参考文献/References:

[1] 冯康.论微分与积分方程及有限元与无限元[J].计算数学,1980,2(1):100-105.
[2]Feng Kang.Canonical boundary reduction and finite element method[C]//Proceedings of International 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 Element Methods(1982,Beijing).Beijing:Science Press,1983:211-252.
[4]余德浩.自然边界元方法的数学理论[M].北京:科学出版社,1993.
[5]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.
[6]张敏,杜其奎.椭圆外区域上Helmholtz方程的自然边界元法[J].计算数学,2008,30(1):75-88.
[7]Huang Hongying,Yu Dehao.Natural boundary element method for three dimensional exterior harmonic problem with an inner prolate spheroid boundary[J].Journal of Computational Mathematics,2006,24(2):193-208.
[8]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.
[9]Han Houde,Zheng Chunxiong.Exact nonreflecting boundary conditions for exterior problems of the hyperbolic equation[J].Chinese Journal of Computational Physics,2005,22(1):95-107.
[10]Han Houde,Huang Zhongyi.A class of artificial boundary conditions for heat equation in unbounded domains[J].Computers and Mathematics with Applications,2002,43:889-900.
[11]Du Qikui,Tang Minxia.Exact and approximate artificial boundary conditions for the hyperbolic problems in unbounded domains[J].Applied Mathematics and Computation,2005,169(1):585-594.
[12]郝萍,杜其奎.各向异性抛物外问题的自然边界元法[J].高校应用数学学报,2009,24(3):368-378.
[13]王竹溪,郭敦仁.特殊函数概论[M].北京:科学出版社,1979.

备注/Memo

备注/Memo:
收稿日期:2012-02-23.
基金项目:上海市自然科学基金(12ZR1411600).
通讯联系人:鞠银,讲师,研究方向:微分方程数值解.E-mail:juyinxue@tom.com
更新日期/Last Update: 2013-03-31