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New modified shift-splitting preconditioners for non-symmetric saddle point problems
Arabian Journal of Mathematics ( IF 0.9 ) Pub Date : 2019-05-18 , DOI: 10.1007/s40065-019-0256-6
Mahin Ardeshiry , Hossein Sadeghi Goughery , Hossein Noormohammadi Pour

Zhou et al. and Huang et al. have proposed the modified shift-splitting (MSS) preconditioner and the generalized modified shift-splitting (GMSS) for non-symmetric saddle point problems, respectively. They have used symmetric positive definite and skew-symmetric splitting of the (1, 1)-block in a saddle point problem. In this paper, we use positive definite and skew-symmetric splitting instead and present new modified shift-splitting (NMSS) method for solving large sparse linear systems in saddle point form with a dominant positive definite part in (1, 1)-block. We investigate the convergence and semi-convergence properties of this method for nonsingular and singular saddle point problems. We also use the NMSS method as a preconditioner for GMRES method. The numerical results show that if the (1, 1)-block has a positive definite dominant part, the NMSS-preconditioned GMRES method can cause better performance results compared to other preconditioned GMRES methods such as GMSS, MSS, Uzawa-HSS and PU-STS. Meanwhile, the NMSS preconditioner is made for non-symmetric saddle point problems with symmetric and non-symmetric (1, 1)-blocks.

中文翻译:

用于非对称鞍点问题的新型改进的移位分裂预处理器

周等。和黄等。分别针对非对称鞍点问题提出了改进的移位分裂(MSS)预处理器和广义的改进移位分裂(GMSS)。他们在鞍点问题中使用了(1,1)块的对称正定和斜对称拆分。在本文中,我们使用正定和倾斜对称分裂代替,并提出了一种新的改进的移位分裂(NMSS)方法,以求解鞍点形式的大型稀疏线性系统,该线性稀疏线性系统在(1,1)块中具有占优势的正定部分。我们研究此方法对非奇异和奇异鞍点问题的收敛性和半收敛性。我们还将NMSS方法用作GMRES方法的前提。数值结果表明,如果(1,1)块具有正确定的主导部分,与其他预处理的GMRES方法(例如GMSS,MSS,Uzawa-HSS和PU-STS)相比,NMSS预处理的GMRES方法可产生更好的性能结果。同时,针对具有对称和非对称(1,1)块的非对称鞍点问题制作了NMSS预调节器。
更新日期:2019-05-18
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