并行求解抛物型方程的AGE算法在边值处的改进
The Improvements of AGE Algorithm for Parallel Solving Parabolic Equations at the Boundary

作者: 王栋 :山西师范大学,临汾; 杨鹏 :吉林大学,长春;

关键词: 抛物型方程差分格式并行算法Parabolic Equation Difference Scheme Parallel Algorithm

摘要:
AGE方法是一种求解偏微分方程的并行算法,通过重新构造有限差分格式,把所要求解的差分方程组分裂成若干个可以独立并行求解的规模较小的方程组。但此种算法在靠近边值处误差较高,本文在靠近左右边界处对格式进行改进,得到一种在边值处改进的AGE方法。该方法在边界附近尽可能的保持较小的截断误差,从而提高了计算精度。

Abstract:
AGE method is a parallel algorithm for solving partial differential equations, by re-construct a finite difference scheme, so the required solution of difference equations can be split into several smaller inde-pendent parallel solution of equations. However, this algorithm gets higher truncation errors near the boun-dary. In this paper, I get an improvement AGE method, by improving the format close to the left and right boundaries. The method stays as smaller truncation errors in border, so can improve the calculation ac-curacy.

文章引用: 王栋 , 杨鹏 (2011) 并行求解抛物型方程的AGE算法在边值处的改进。 理论数学, 1, 85-91. doi: 10.12677/pm.2011.12018

参考文献

[1] 康立山, 全惠云. 数值解高维偏微分方程的分裂法[M]. 第一版. 上海: 上海科学技术出版社, 1990: 1-127.

[2] 李荣华, 刘播. 偏微分方程数值解法[M]. 第三版. 北京: 高等教育出版社, 2009: 107-149.

[3] D. J. Evans, A. R. B. Aboullah. Group explicit methods for parabolic equations. International Journal of Computer Mathematics, 1983, 14(1): 73-105.

[4] D. J. Evans, A. R. B. Abdullah. A new method for the solution of . International Journal of Computer Mathematics, 1991(38): 241-255.

[5] 李德元. 关于解一维抛物型方程组的差分格式[J]. 计算数学, 1982, 4(1): 80-92.

[6] 陈光男. 解一维抛物型方程组的交替计算格式[J]. 计算数学, 1985, 7(2): 164-174.

[7] J. Dauglas Jr. A survey of numerical methods for parabolic differential equation. Advances in Computer, Academic Press, 1961, 2: 1-52.

[8] 张宝琳, 苏秀敏. 求解隐式差分方程的并行算法[J]. 计算物理, 1992, 9(2): 250-256.

[9] 侯淑轩. 抛物型方程的一类交替分组迭代法[D]. 山东大学:山东大学数学学院, 2005.

[10] 张宝琳, 谷同祥, 莫则尧. 数值并行计算原理与方法[M]. 第一版. 国防工业出版社, 1999: 183-275.

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