Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 617390, 13 pages
http://dx.doi.org/10.1155/2012/617390
Research Article

New Preconditioners with Two Variable Relaxation Parameters for the Discretized Time-Harmonic Maxwell Equations in Mixed Form

Yuping Zeng1,2 and Chenliang Li2

1Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Jiangsu, Nanjing 210046, China
2School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guangxi, Guilin 541004, China

Received 4 May 2012; Revised 3 July 2012; Accepted 4 July 2012

Academic Editor: Ion Zaballa

Copyright © 2012 Yuping Zeng and Chenliang Li. 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 provide new preconditioners with two variable relaxation parameters for the saddle point linear systems arising from finite element discretization of time-harmonic Maxwell equations in mixed form. The new preconditioners are of block-triangular forms and Schur complement-free. They are extensions of the results in Cheng et al., 2009, Grief and Schötzau, 2007, and Huang et al., 2009. Theoretical analysis shows that all eigenvalues of the preconditioned matrices are tightly clustered, and numerical tests confirm our analysis.