TY - JOUR
T1 - A modified generalized shift-splitting preconditioner for nonsymmetric saddle point problems
AU - Huang, Zheng Ge
AU - Wang, Li Gong
AU - Xu, Zhong
AU - Cui, Jing Jing
N1 - Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.
PY - 2018/5/1
Y1 - 2018/5/1
N2 - For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSS) preconditioner as well as the MGSS iteration method is derived in this paper, which generalize the modified shift-splitting (MSS) preconditioner and the MSS iteration method newly developed by Huang and Su (J. Comput. Appl. Math. 317:535–546, 2017), respectively. The convergent and semi-convergent analyses of the MGSS iteration method are presented, and we prove that this method is unconditionally convergent and semi-convergent. Meanwhile, some spectral properties of the preconditioned matrix are carefully analyzed. Numerical results demonstrate the robustness and effectiveness of the MGSS preconditioner and the MGSS iteration method and also illustrate that the MGSS iteration method outperforms the generalized shift-splitting (GSS) and the generalized modified shift-splitting (GMSS) iteration methods, and the MGSS preconditioner is superior to the shift-splitting (SS), GSS, modified SS (M-SS), GMSS and MSS preconditioners for the generalized minimal residual (GMRES) method for solving the nonsymmetric saddle point problems.
AB - For the nonsymmetric saddle point problems with nonsymmetric positive definite (1,1) parts, the modified generalized shift-splitting (MGSS) preconditioner as well as the MGSS iteration method is derived in this paper, which generalize the modified shift-splitting (MSS) preconditioner and the MSS iteration method newly developed by Huang and Su (J. Comput. Appl. Math. 317:535–546, 2017), respectively. The convergent and semi-convergent analyses of the MGSS iteration method are presented, and we prove that this method is unconditionally convergent and semi-convergent. Meanwhile, some spectral properties of the preconditioned matrix are carefully analyzed. Numerical results demonstrate the robustness and effectiveness of the MGSS preconditioner and the MGSS iteration method and also illustrate that the MGSS iteration method outperforms the generalized shift-splitting (GSS) and the generalized modified shift-splitting (GMSS) iteration methods, and the MGSS preconditioner is superior to the shift-splitting (SS), GSS, modified SS (M-SS), GMSS and MSS preconditioners for the generalized minimal residual (GMRES) method for solving the nonsymmetric saddle point problems.
KW - Convergence
KW - Modified generalized shift-splitting
KW - Nonsymmetric saddle point problem
KW - Semi-convergence
KW - Spectral properties
UR - https://www.scopus.com/pages/publications/85023207701
U2 - 10.1007/s11075-017-0377-y
DO - 10.1007/s11075-017-0377-y
M3 - 文章
AN - SCOPUS:85023207701
SN - 1017-1398
VL - 78
SP - 297
EP - 331
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 1
ER -