首页 | 官方网站   微博 | 高级检索  
     

无界区域抛物方程自然边界元方法
引用本文:朱昌杰,杜其奎.无界区域抛物方程自然边界元方法[J].数学研究与评论,2002,22(2):177-188.
作者姓名:朱昌杰  杜其奎
作者单位:1. 淮北煤炭师范学院,安徽,淮北,235000
2. 南京师范大学数学与计算机科学学院,江苏,南京,210097
基金项目:National Natural Science Foundation of China(19701001)
摘    要:本文应用自然边界元方法求解无界区域抛物型初边值问题。首先将控制方程对时间进行离散化,得到关于时间步长离散化的椭圆型问题。通过Fourier展开,导出相应问题的自然积分方程和Poisson积分公式。研究了自然积分算子的性质,并讨论了自然积分方程的数值解法,最后给出数值例子。从而解决了抛物型问题的自然边界归化和自然边界元方法。

关 键 词:无界区域  抛物方程  自然边界元方法  初边值问题  自然积分方程  积分算子  数值解法
收稿时间:1999/5/26 0:00:00

Natural Boundary Element Method for ParabolicEquations in an Unbounded Domain
ZHU Chang-jie and DU Qi-kui.Natural Boundary Element Method for ParabolicEquations in an Unbounded Domain[J].Journal of Mathematical Research and Exposition,2002,22(2):177-188.
Authors:ZHU Chang-jie and DU Qi-kui
Affiliation:Huaibei Coal Industry Normal College; Anhui; China;School of Math. & Comp. Sci.; Nanjing Normal Uuiversity; Jiangsu; China
Abstract:In this paper we introduce an implementation for the efficient numericalsolution of exterior initial boundary value problem for parabolic equation. The problemis reformulated as an equivalent one on a boundary T using natural boundary reduction.The governing equation is first discretized in time, leading to a time-stepping scheme,where an exterior elliptic problem has to be solved in each time step. By Fourier ex-pansion, we derive a natural integral equation of the elliptic problem related to timestep and Poisson integral integral formula over exterior circular domain. Finite elementdiscretization of the natural integral equation is employed to solve this problem. Thecomputational aspects of this method are discussed. Numerical results are presented toillustrate feasibility and efficiency of our method.
Keywords:parabolic problem  natural boundary reduction  exterior problem  numer-ical implementation  finite element  
本文献已被 CNKI 维普 万方数据 等数据库收录!
点击此处可从《数学研究与评论》浏览原始摘要信息
点击此处可从《数学研究与评论》下载全文
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司    京ICP备09084417号-23

京公网安备 11010802026262号