A new parallel algorithm for solving parabolic equations

被引：0
作者：
Guanyu Xue
Hui Feng
机构：
[1] Wuhan University,School of Mathematics and Statistics
来源：
Advances in Difference Equations | / 2018卷
关键词：
Parabolic equations; Finite difference; Unconditional stability; Parallelism;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, a new parallel algorithm for solving parabolic equations is proposed. The new algorithm includes two domain decomposition methods, each method is applied to compute the values at (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n+1)$\end{document}st time level by use of known numerical solutions at nth time level, respectively. Then the average of two above values is chosen to be the numerical solutions at (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n+1)$\end{document}st time level. The new algorithm obtains satisfactory accuracy while maintaining parallelism and unconditional stability. This algorithm can be extended to solve two-dimensional parabolic equations by alternating direction implicit (ADI) technique. Both error analysis and numerical experiments illustrate the accuracy and efficiency of the new algorithm.
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