A class of generalized shift-splitting preconditioners for nonsymmetric saddle point problems. (November 2015)

• Record Type: Journal Article
• Authors: Cao, Yang; Li, Sen; Yao, Lin-Quan
• Is Part Of: Applied mathematics letters. Volume 49(2015:Nov.)
• Page Start: 20
• Page End: 27
• Publication Date: 2015-11
• Subjects: Nonsymmetric saddle point problem -- Shift-splitting -- Convergence -- Preconditioning -- Eigenvalue; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.04.001
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, a class of generalized shift-splitting preconditioners with two shift parameters are implemented for nonsymmetric saddle point problems with nonsymmetric positive definite (1, 1) block. The generalized shift-splitting (GSS) preconditioner is induced by a generalized shift-splitting of the nonsymmetric saddle point matrix, resulting in an unconditional convergent fixed-point iteration. By removing the shift parameter in the (1, 1) block of the GSS preconditioner, a deteriorated shift-splitting (DSS) preconditioner is presented. Some useful properties of the DSS preconditioned saddle point matrix are studied. Finally, numerical experiments of a model Navier–Stokes problem are presented to show the effectiveness of the proposed preconditioners.