A modified new matrix splitting preconditioner for double saddle point problems

被引：2

作者：

Li, Jun ^{[1
]}

机构：

[1] Northwest Normal Univ, Coll Math & Stat, Lanzhou 730070, Peoples R China

来源：

JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS | 2024年 / 41卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Double saddle point problems; Matrix splitting; Preconditioning; Spectral properties; GMRES method; SIMPLIFIED HSS PRECONDITIONER;

D O I：

10.1007/s13160-023-00581-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a new matrix splitting (NS) is given based on the coefficient matrix of the double saddle point problems, and a modified new matrix splitting (MNS) preconditioner is also proposed. Theoretical analysis proves that the iteration method produced by the MNS preconditioner is convergent with any positive parameters under assumed conditions and the eigenvalues of the MNS preconditioned matrix are located in a positive interval. Numerical examples verify the efficiency of the proposed preconditioner.

引用

页码：85 / 103

页数：19

共 22 条

[11] Huang N., ARXIV
[12] Spectral analysis of the preconditioned system for the 3 x 3 block saddle point problem
Huang, Na
Ma, Chang-Feng
[J]. NUMERICAL ALGORITHMS, 2019, 81 (02) : 421 - 444
[13] A practical formula for computing optimal parameters in the HSS iteration methods
Huang, Yu-Mei
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 255 : 142 - 149
[14] Alternating positive semidefinite splitting preconditioners for double saddle point problems
Liang, Zhao-Zheng
Zhang, Guo-Feng
[J]. CALCOLO, 2019, 56 (03)
[15] A generalized variant of simplified HSS preconditioner for generalized saddle point problems
Liao, Li-Dan
Zhang, Guo-Feng
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 346 : 790 - 799
[16] Schur complement systems in the mixed-hybrid finite element approximation of the potential fluid flow problem
Maryska, J
Rozlozník, M
Tuma, M
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 22 (02) : 704 - 723
[17] A variant of relaxed alternating positive semi-definite splitting preconditioner for double saddle point problems
Meng, Lingsheng
Li, Jun
Miao, Shu-Xin
[J]. JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 2021, 38 (03) : 979 - 998
[18] A PRECONDITIONED NULLSPACE METHOD FOR LIQUID CRYSTAL DIRECTOR MODELING
Ramage, Alison
Gartland, Eugene C., Jr.
[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2013, 35 (01) : B226 - B247
[19] Improved splitting preconditioner for double saddle point problems arising from liquid crystal director modeling
Ren, Bi-Cong
Chen, Fang
Wang, Xiao-Liang
[J]. NUMERICAL ALGORITHMS, 2022, 91 (03) : 1363 - 1379
[20] Saad Y., 2003, Iterative Methods for Sparse Linear Systems

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