TY - JOUR
T1 - Shift-splitting preconditioners for saddle point problems
AU - Cao, Yang
AU - Du, Jun
AU - Niu, Qiang
N1 - Funding Information:
This work is supported by the National Natural Science Foundation of China (Nos. 11301290 , 11301420 ).
PY - 2014/12/15
Y1 - 2014/12/15
N2 - In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners.
AB - In this paper, we first present a shift-splitting preconditioner for saddle point problems. The preconditioner is based on a shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration. Based on the idea of the splitting, we further propose a local shift-splitting preconditioner. Some properties of the local shift-splitting preconditioned matrix are studied. These preconditioners extend those studied by Bai, Yin and Su for solving non-Hermitian positive definite linear systems (Bai et al., 2006). Finally, numerical experiments of a model Stokes problem are presented to show the effectiveness of the proposed preconditioners.
KW - Convergence
KW - Preconditioning
KW - Saddle point problem
KW - Shift-splitting
UR - http://www.scopus.com/inward/record.url?scp=84902256961&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2014.05.017
DO - 10.1016/j.cam.2014.05.017
M3 - Article
AN - SCOPUS:84902256961
SN - 0377-0427
VL - 272
SP - 239
EP - 250
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -