时变Stokes方程迭代方法的研究

doi:10.12068/j.issn.1005-3026.2014.07.031

东北大学学报:自然科学版 ›› 2014, Vol. 35 ›› Issue (7): 1051-1053.DOI: 10.12068/j.issn.1005-3026.2014.07.031

时变Stokes方程迭代方法的研究

沈海龙，李晓莎，邵新慧

(东北大学理学院，辽宁沈阳110819)

收稿日期:2013-08-28 修回日期:2013-08-28 出版日期:2014-07-15 发布日期:2014-04-11
通讯作者: 沈海龙
作者简介:沈海龙(1971-)，男，朝鲜族，吉林延吉人，东北大学讲师，博士.
基金资助:
国家自然科学基金资助项目(11371081);中央高校基本科研业务费专项资金资助项目(N090405013).

Study of Iterative Methods for TimeDependent Stokes Equations

SHEN Hailong， LI Xiaosha， SHAO Xinhui

School of Sciences， Northeastern University， Shenyang 110819， China.

Received:2013-08-28 Revised:2013-08-28 Online:2014-07-15 Published:2014-04-11
Contact: SHEN Hailong
About author:-
Supported by:
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摘要/Abstract

摘要： 时变Stokes方程的求解在物理学、离散动力学系统和科学计算等领域具有广泛的应用，但是时变Stokes方程是一个随时间变化的偏微分方程组，在实际中求解非常困难.针对时变Stokes方程在预处理基础上构造了一个新的双预优迭代方法，然后给出了迭代格式、收敛域以及一些相关的结论.通过改进迭代法中参数的选取和对方程组本身进行预处理等方式，提高了迭代方法的收敛速度.最后用数值算例验证了双预优迭代方法的可行性和有效性.

关键词: 微分代数方程, 时变Stokes方程, 双预优方法, 迭代方法, 收敛域

Abstract: The solution to the timedependent Stokes equations has broad application in physics， discrete dynamic system， scientific computing， and other fields.However， the equations are timedependent partial differential equations and very difficult to solve in practice. To solve this problem， a new dual preconditioned method was firstly constructed based on preconditioned technology. Then their iterative formats， convergence domains and the corresponding conclutions were given. The convergence rate of the iterative method was improved by modifying the parameters in the iterative method and preprocessing on the equations themselves. Finally， the feasibility and effectiveness of the dual preconditioned iterative method were verified with numerical examples.

Key words: differentialalgebra equation, timedependent Stokes equations, dual preconditioned method, iterative method, convergence domain

中图分类号:

TP274

沈海龙，李晓莎，邵新慧. 时变Stokes方程迭代方法的研究[J]. 东北大学学报:自然科学版, 2014, 35(7): 1051-1053.

SHEN Hailong， LI Xiaosha， SHAO Xinhui. Study of Iterative Methods for TimeDependent Stokes Equations[J]. Journal of Northeastern University Natural Science, 2014, 35(7): 1051-1053.

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时变Stokes方程迭代方法的研究

Study of Iterative Methods for TimeDependent Stokes Equations

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