A general class of shift-splitting preconditioners for non-Hermitian saddle point problems with applications to time-harmonic eddy current models

被引：13

作者：

Cao, Yang ^{[1
]}

机构：

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

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2019年 / 77卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Non-Hermitian saddle point problem; Time-harmonic eddy current model; Shift-splitting iteration; Preconditioning; Convergence; ITERATIVE METHODS; FORMULATION; SYSTEMS;

D O I：

10.1016/j.camwa.2018.10.046

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Based on a general splitting of the (1,1) leading block matrix, we first construct a general class of shift-splitting (GCSS) preconditioners for non-Hermitian saddle point problems. Convergence conditions of the corresponding matrix splitting iteration methods and preconditioning properties of the GCSS preconditioned saddle point matrices are analyzed. Then the GCSS preconditioner is specifically applied to the non-Hermitian saddle point problems arising from the finite element discretizations of the hybrid formulations of the time-harmonic eddy current models. With suitable choices of the splittings, the new GCSS preconditioners are easier to implement and have faster convergence rates than the existing shift-splitting preconditioner and its modified variant. Two numerical examples are presented to verify the theoretical results and show effectiveness of the new proposed preconditioners. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：1124 / 1143

页数：20

共 33 条

[11] A preconditioner for generalized saddle point problems [J].

Benzi, M ;

Golub, GH .

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2004, 26 (01) :20-41

[12] Parameter estimates for the Relaxed Dimensional Factorization preconditioner and application to hemodynamics [J].

Benzi, Michele ;

Deparis, Simone ;

Grandperrin, Gwenol ;

Quarteroni, Alfio .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2016, 300 :129-145

[13] RMCP: Relaxed Mixed Constraint Preconditioners for saddle point linear systems arising in geomechanics [J].

Bergamaschi, Luca ;

Martinez, Angeles .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2012, 221 :54-62

[14] Mixed systems of algebraic equations in computational electromagnetism [J].

Bossavit, A .

COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 1998, 17 (1-3) :59-63

[15] A class of generalized shift-splitting preconditioners for nonsymmetric saddle point problems [J].

Cao, Yang ;

Li, Sen ;

Yao, Lin-Quan .

APPLIED MATHEMATICS LETTERS, 2015, 49 :20-27

[16] A relaxed deteriorated PSS preconditioner for nonsymmetric saddle point problems from the steady Navier-Stokes equation [J].

Cao, Yang ;

Dong, Jun-Liang ;

Wang, Yu-Ming .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 273 :41-60

[17] Shift-splitting preconditioners for saddle point problems [J].

Cao, Yang ;

Du, Jun ;

Niu, Qiang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 272 :239-250

[18] A weighted nodal-radial point interpolation meshless method for 2D solid problems [J].

Cao, Yang ;

Yao, Lin-Quan ;

Yi, Shi-Chao .

ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS, 2014, 39 :88-100

[19] A RELAXED HSS PRECONDITIONER FOR SADDLE POINT PROBLEMS FROM MESHFREE DISCRETIZATION [J].

Cao, Yang ;

Yao, Linquan ;

Jiang, Meiqun ;

Niu, Qiang .

JOURNAL OF COMPUTATIONAL MATHEMATICS, 2013, 31 (04) :398-421

[20]

Grief C., 2006, ELECTRON T NUMER ANA, V22, P11

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