A Local Positive (Semi)Definite Shift-Splitting Preconditioner for Saddle Point Problems with Applications to Time-Harmonic Eddy Current Models

被引：5

作者：

Cao, Yang ^{[1
]}

Ren, Zhi-Ru ^{[2
]}

机构：

[1] Nantong Univ, Sch Transportat & Civil Engn, Nantong 226019, Peoples R China

[2] Cent Univ Finance & Econ, Sch Stat & Math, Beijing 100081, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2020年 / 10卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Saddle point problem; splitting iteration; preconditioning; convergence; time-harmonic eddy current model; ITERATION METHODS; HSS PRECONDITIONER; SEMIDEFINITE; FORMULATION; ALGORITHMS; SYSTEMS;

D O I：

10.4208/eajam.150319.200619

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A local positive (semi)definite shift-splitting preconditioner for non-Hermitian saddle point problems arising in finite element discretisations of hybrid formulations of time-harmonic eddy current models is constructed. The convergence of the corresponding iteration methods is proved and the spectral properties of the associated preconditioned saddle point matrices are studied. Numerical experiments show the efficiency of the proposed preconditioner for Krylov subspace methods.

引用

页码：135 / 157

页数：23

共 47 条

[1]

[Anonymous], 2003, Iterative Methods for Sparse Linear Systems, DOI DOI 10.1137/1.9780898718003

[2]

[Anonymous], 1971, Iterative Solution of Large Linear Systems

[3] New modified shift-splitting preconditioners for non-symmetric saddle point problems [J].

Ardeshiry, Mahin ;

Goughery, Hossein Sadeghi ;

Pour, Hossein Noormohammadi .

ARABIAN JOURNAL OF MATHEMATICS, 2020, 9 (02) :245-257

[4]

ARROW K. J., 1958, Studies in Linear and Non-Linear Programming

[5] Residual reduction algorithms for nonsymmetric saddle point problems [J].

Bacuta, Constantin ;

McCracken, Brendan ;

Shu, Lu .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (06) :1614-1628

[6]

Bai ZZ, 2007, IMA J NUMER ANAL, V27, P1, DOI [10.1093/imanum/drl017, 10.1093/imanum/dr1017]

[7]

Bai ZZ, 2006, J COMPUT MATH, V24, P539

[8] Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models [J].

Bai, Zhong-Zhi .

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2012, 19 (06) :914-936

[9] Eigenvalue estimates for saddle point matrices of Hermitian and indefinite leading blocks [J].

Bai, Zhong-Zhi .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 237 (01) :295-306

[10] On preconditioned MHSS iteration methods for complex symmetric linear systems [J].

Bai, Zhong-Zhi ;

Benzi, Michele ;

Chen, Fang .

NUMERICAL ALGORITHMS, 2011, 56 (02) :297-317

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