Journal of Applied Mathematics
Volume 2012 (2012), Article ID 564132, 7 pages
http://dx.doi.org/10.1155/2012/564132
Research Article

A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow

Shi-Liang Wu,1,2 Feng Chen,1 and Xiao-Qi Niu1

1School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China
2College of Mathematics, Chengdu University of Information Technology, Chengdu 610255, China

Received 21 November 2011; Accepted 11 January 2012

Academic Editor: Kok Kwang Phoon

Copyright © 2012 Shi-Liang Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented. The relationship between the two different formulations spectrum of the SIMPLE preconditioned matrix is established by using the theory of matrix eigenvalue, and some corresponding results in recent article by Li and Vuik (2004) are extended.