A modified relaxed splitting preconditioner for generalized saddle point problems from the incompressible Navier-Stokes equations

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• 作者：Hong-Tao Fan^a ; ^{fanht14@lzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Xin-Yun Zhu^b ; ^{zhu_x@utpb.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Generalized saddle point problems ; Modified relaxed splitting preconditioner ; Matrix splitting ; Eigenvalue distribution ; Navier&ndash ; Stokes equations
• 刊名：Applied Mathematics Letters
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：55
• 期：Complete
• 页码：18-26
• 全文大小：812 K

文摘

Based on a new matrix splitting of the original coefficient matrix, a modified relaxed splitting (MRS) preconditioner for generalized saddle point problems from the incompressible Navier–Stokes equations is considered. The eigenvalue distribution and an upper bound of the degree of the minimal polynomial of the preconditioned matrix are studied. The proposed preconditioner is closer to the original matrix than the generalized relaxed splitting (GRS) preconditioner in the sense of certain norm, which straightforwardly results in a MRS iteration method. Finally, numerical results are given to demonstrate the theoretical analysis. The results show that this novel preconditioner is competitive with and more effective than some of the best existing preconditioners.