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J4 ›› 2011, Vol. 46 ›› Issue (12): 1-5.

• 论文 •    下一篇

二维热传导方程的有限差分区域分解算法

李宛珊,王文洽*   

  1. 山东大学数学学院, 山东 济南 250100
  • 收稿日期:2011-01-07 出版日期:2011-12-20 发布日期:2011-12-24
  • 通讯作者: 王文洽(1950- ),男,教授,研究方向为偏微分方程数值解法. Email:wangwq@sdu.edu.cn
  • 作者简介:李宛珊(1988- ),女,硕士研究生,研究方向为偏微分方程数值解法. Email:liwanshan0320@gmail.com
  • 基金资助:

    国家自然科学基金资助项目(10671113)

Algorithms of finite difference domain decomposition for two-heat equation

LI Wan-shan, WANG Wen-qia*   

  1. School of Mathematics, Shandong University, Jinan  250100, Shandong, China
  • Received:2011-01-07 Online:2011-12-20 Published:2011-12-24

摘要:

对于应用区域分解方法求解二维热传导方程的问题,本文提出一种绝对稳定的显-隐差分格式。该算法在内边界点上采用显格式计算,在子区域内部采用全隐格式;之后给出了算法的稳定性和收敛性分析,并用数值结果验证了相关结论。

关键词:  二维热传导方程;区域分解算法;有限差分;并行计算

Abstract:

Considering algorithms of finite difference domain decomposition for twodimensional heat equation, a new kind of explicitimplicit difference schemes which is of unconditional stability is developed. The corresponding schemes consist of one explicit difference schemes at the interface point and fully implicit schemes in the subdomains. The stability and error estimates of the schemes are derived. Finally, the numerical experiment is presented which confirm the results and conclusions.

Key words:  two-dimensional heat equation; domain decomposition algorithm; finite difference; parallel computation

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