Spectral properties of primal-based penalty preconditioners for saddle point problems

Authors:
Shu-Qian Shen;Ting-Zhu Huang;Er-Jie Zhong
Affiliations:
School of Mathematics and Computational Sciences, China University of Petroleum, Dongying, Shandong, 257061, PR China and School of Applied Mathematics, University of Electronic Science and Techno ...;School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

For large and sparse saddle point linear systems, this paper gives further spectral properties of the primal-based penalty preconditioners introduced in [C.R. Dohrmann, R.B. Lehoucq, A primal-based penalty preconditioner for elliptic saddle point systems, SIAM J. Numer. Anal. 44 (2006) 270-282]. The regions containing the real and non-real eigenvalues of the preconditioned matrix are obtained. The model of the Stokes problem is supplemented to illustrate the theoretical results and to test the quality of the primal-based penalty preconditioner.