计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  在线办公 | 
计算数学  2018, Vol. 40 Issue (3): 271-286    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
求解时谐涡流模型鞍点问题的分块交替分裂隐式迭代算法的改进
刘忠祥, 王翠薇, 王增琦
上海交通大学数学科学学院, 上海 200240
THE IMPROVEMENT OF BLOCK ALTERNATING IMPLICIT ITERATION METHODS FOR SADDLE-POINT PROBLEMS FROM TIME-HARMONIC EDDY CURRENT MODELS
Liu Zhongxiang, Wang Cuiwei, Wang Zengqi
Shanghai Jiao Tong University, School of Mathematical Sciences, Shanghai 200240, China
 全文: PDF (486 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 分块交替分裂隐式迭代方法是求解具有鞍点结构的复线性代数方程组的一类高效迭代法.本文通过预处理技巧得到原方法的一种加速改进方法,称之为预处理分块交替分裂隐式迭代方法.理论分析给出了新方法的收敛性结果.对于一类时谐涡旋电流模型问题,我们给出了若干满足收敛条件的迭代格式.数值实验验证了新型算法是对原方法的有效改进.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词时谐涡流模型   复线性鞍点问题   交替分裂隐式迭代法   预处理技术     
Abstract: Block alternating splitting implicit iteration method is the effective iteration methods for solving the complex saddle point linear systems. In the present paper, we accelerate the method with the preconditioning technique and obtain a new iteration methods, called preconditioned block alternating splitting implicit iteration method. By suitable splitting of the coefficient matrix, we obtain several iteration schemes for the complex linear systems arising from a class of time-harmonic eddy current problems. The comparison with the original methods illustrates that the accelerating technique improve the numerical performance significantly.
Key wordstime-harmonic eddy current problem   complex saddle-point problem   alternating splitting implicit iteration methods   preconditioned technique   
收稿日期: 2017-05-24;
基金资助:

国家自然科学基金(11371022)资助项目.

通讯作者: 王增琦,Email:wangzengqi@sjtu.edu.cn.     E-mail: wangzengqi@sjtu.edu.cn
引用本文:   
. 求解时谐涡流模型鞍点问题的分块交替分裂隐式迭代算法的改进[J]. 计算数学, 2018, 40(3): 271-286.
. THE IMPROVEMENT OF BLOCK ALTERNATING IMPLICIT ITERATION METHODS FOR SADDLE-POINT PROBLEMS FROM TIME-HARMONIC EDDY CURRENT MODELS[J]. Mathematica Numerica Sinica, 2018, 40(3): 271-286.
 
[1] Alonso R A,Alberto V.Hybrid formulation of eddy current problems[J].Numerical Methods for Partial Differential Equations,2005,21(4):742-763.
[2] Rodríguez A A,Hernández R V.Iterative methods for the saddle-point problem arising from the HC/EI formulation of the eddy current problem[J].SIAM Journal on Scientific Computing,2009,31(4):3155-3178.
[3] Alonso Rodríguez A,Valli A.Eddy current approximation of Maxwell equations[M].Springer Milan,2010.
[4] Brezzi F,Fortin M.Mixed and hybrid finite element methods[M].Springer-Verlag,1991.
[5] Bai Z Z.Block alternating splitting implicit iteration methods for saddle point problems from time-harmonic eddy current models[J].Numerical Linear Algebra with Applications,2012,19(6):914-936.
[6] Bai Z Z,Benzi M,Chen F.Modified HSS iteration methods for a class of complex symmetric linear systems[J].Computing,2010,87(3):93-111.
[7] Bai Z Z,Benzi M,Chen F.On preconditioned MHSS iteration methods for complex symmetric linear systems[J].Numerical Algorithms,2011,56(2):297-317.
[8] Bai Z Z,Golub G,Pan J-Y.Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems.Numerische Mathematik 2004,98:1-32.
[9] Benzi M,Golub G H.A Preconditioner for generalized saddle point problems[J].SIAM Journal on Matrix Analysis Applications,2004,26(1):20-41.
[10] Bai Z Z.Splitting iteration methods for non-Hermitian positive definite systems of linear equations.Hokkaido Math J 36:801-814[J].Hokkaido Mathematical Journal,2007,36(4):801-814.
[11] Bai Z Z,Golub G H,Li C K.Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices[J].Mathematics of Computation,2007,76(257):287-298.
[12] Ke Y F,Ma C F.The dimensional splitting iteration methods for solving saddle point problems arising from time-harmonic eddy current models[J].Appl.Math.Comput.,2017,303:146-164.
[13] Ren Z R,Cao Y.An alternating positive-semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models[J].IMA J.Numer.Anal.,2016,36:922-946.
[14] 关新,时谐涡旋电流问题中线性方程组的预处理方法[D].上海:华东师范大学,2013.
[1] 于春肖, 苑润浩, 穆运峰. 新预处理ILUCG法求解稀疏病态线性方程组[J]. 计算数学, 2014, 35(1): 21-27.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10