A new alternating positive semidefinite splitting preconditioner for saddle point problems from time-harmonic eddy current models

被引：0
作者：
Yifen Ke
Changfeng Ma
Zhiru Ren
机构：
[1] University of Chinese Academy of Sciences,Key Laboratory of Computational Geodynamics of Chinese Academy of Sciences
[2] Fujian Normal University,College of Mathematics and Informatics & FJKLMAA
[3] Central University of Finance and Economics,School of Statistics and Mathematics
来源：
Frontiers of Mathematics in China | 2018年 / 13卷
关键词：
Time-harmonic eddy current problem; saddle point problem; alternating positive semidefinite splitting (APSS); convergence analysis; preconditioner; iteration method; 65F08; 65F10; 65F50;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Based on the special positive semidefinite splittings of the saddle point matrix, we propose a new alternating positive semidefinite splitting (APSS) iteration method for the saddle point problem arising from the finite element discretization of the hybrid formulation of the time-harmonic eddy current problem. We prove that the new APSS iteration method is unconditionally convergent for both cases of the simple topology and the general topology. The new APSS matrix can be used as a preconditioner to accelerate the convergence rate of Krylov subspace methods. Numerical results show that the new APSS preconditioner is superior to the existing preconditioners.
引用
收藏
页码：313 / 340
页数：27
相关论文
共 50 条
[1]  
Arioli M(2002)A null space algorithm for mixed finite-element approximations of Darcy’s equation Comm Numer Methods Engrg 18 645-657
[2]  
Manzini G(2009)Optimal parameters in the HSS-like methods for saddle-point problems Numer Linear Algebra Appl 16 447-479
[3]  
Bai Z Z(2012)Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models Numer Linear Algebra Appl 19 914-936
[4]  
Bai Z Z(2007)Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems IMA J Numer Anal 27 1-23
[5]  
Bai Z Z(2003)Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems SIAM J Matrix Anal Appl 24 603-626
[6]  
Golub G H(2004)Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems Numer Math 98 1-32
[7]  
Bai Z Z(2005)On generalized successive overrelaxation methods for augmented linear systems Numer Math 102 1-38
[8]  
Golub G H(2008)On parameterized inexact Uzawa methods for generalized saddle point problems Linear Algebra Appl 428 2900-2932
[9]  
Ng M K(1993)Solution of equality-constrained quadratic programming problems by a projection iterative method Rend Mat Appl 13 275-296
[10]  
Bai Z Z(2004)A preconditioner for generalized saddle point problems SIAM J Matrix Anal Appl 26 20-41
12345