Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 564132, 7 pages.

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

Shi-Liang Wu, Feng Chen, and Xiao-Qi Niu

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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.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 564132, 7 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357179945

Digital Object Identifier
doi:10.1155/2012/564132

Mathematical Reviews number (MathSciNet)
MR2898082

Zentralblatt MATH identifier
1244.76094

Citation

Wu, Shi-Liang; Chen, Feng; Niu, Xiao-Qi. A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow. J. Appl. Math. 2012, Special Issue (2012), Article ID 564132, 7 pages. doi:10.1155/2012/564132. https://projecteuclid.org/euclid.jam/1357179945


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