• 论文 • 上一篇    下一篇

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   

  1. 上海交通大学数学科学学院, 上海 200240
  • 收稿日期:2017-05-24 出版日期:2018-09-15 发布日期:2018-08-08
  • 通讯作者: 王增琦,Email:wangzengqi@sjtu.edu.cn.
  • 基金资助:

    国家自然科学基金(11371022)资助项目.

刘忠祥, 王翠薇, 王增琦. 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.

Liu Zhongxiang, Wang Cuiwei, Wang Zengqi. 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.

THE IMPROVEMENT OF BLOCK ALTERNATING IMPLICIT ITERATION METHODS FOR SADDLE-POINT PROBLEMS FROM TIME-HARMONIC EDDY CURRENT MODELS

Liu Zhongxiang, Wang Cuiwei, Wang Zengqi   

  1. Shanghai Jiao Tong University, School of Mathematical Sciences, Shanghai 200240, China
  • Received:2017-05-24 Online:2018-09-15 Published:2018-08-08
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.
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.

MR(2010)主题分类: 

()
[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] 吴敏华, 李郴良. 求解带Toeplitz矩阵的线性互补问题的一类预处理模系矩阵分裂迭代法[J]. 计算数学, 2020, 42(2): 223-236.
[2] 曹阳, 陈莹婷. 正则化HSS预处理鞍点矩阵的特征值估计[J]. 计算数学, 2020, 42(1): 51-62.
[3] 王丽, 罗玉花, 王广彬. 求解加权线性最小二乘问题的一类预处理GAOR方法[J]. 计算数学, 2020, 42(1): 63-79.
[4] 张纯, 贾泽慧, 蔡邢菊. 广义鞍点问题的改进的类SOR算法[J]. 计算数学, 2020, 42(1): 39-50.
[5] 戴平凡, 李继成, 白建超. 解线性互补问题的预处理加速模Gauss-Seidel迭代方法[J]. 计算数学, 2019, 41(3): 308-319.
[6] 闫熙, 马昌凤. 求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析[J]. 计算数学, 2019, 41(1): 37-51.
[7] 潘春平, 王红玉, 曹文方. 非Hermitian正定线性方程组的外推的HSS迭代方法[J]. 计算数学, 2019, 41(1): 52-65.
[8] 李郴良, 田兆鹤, 胡小媚. 一类弱非线性互补问题的广义模系矩阵多分裂多参数加速松弛迭代方法[J]. 计算数学, 2019, 41(1): 91-103.
[9] 骆其伦, 黎稳. 二维Helmholtz方程的联合紧致差分离散方程组的预处理方法[J]. 计算数学, 2017, 39(4): 407-420.
[10] 施章磊, 李维国. 矩阵广义逆硬阈值追踪算法与稀疏恢复问题[J]. 计算数学, 2017, 39(2): 189-199.
[11] 周海林. 线性子空间上求解矩阵方程组A1XB1=C1,A2XB2=C2的迭代算法[J]. 计算数学, 2017, 39(2): 213-228.
[12] 柯艺芬, 马昌凤. 椭圆PDE-约束优化问题的一个预条件子[J]. 计算数学, 2017, 39(1): 70-80.
[13] 温朝涛, 陈小山. 矩阵极分解新的数值方法[J]. 计算数学, 2017, 39(1): 23-32.
[14] 刘丽华, 马昌凤, 唐嘉. 求解广义鞍点问题的一个新的类SOR算法[J]. 计算数学, 2016, 38(1): 83-95.
[15] 潘春平. 关于Katz指标的二级分裂迭代方法[J]. 计算数学, 2015, 37(4): 390-400.
阅读次数
全文


摘要