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Zbl 1197.78068
Huang, Ting-Zhu; Zhang, Li-Tao; Gu, Tong-Xiang; Zuo, Xian-Yu
New block triangular preconditioner for linear systems arising from the discretized time-harmonic Maxwell equations. (English)
[J] Comput. Phys. Commun. 180, No. 10, 1853-1859 (2009). ISSN 0010-4655

Summary: Based on the preconditioners presented by {\it T. Rees} and {\it C. Greif} [SIAM J. Sci. Comput. 29, No.~5, 1992--2007 (2007; Zbl 1155.65048)], we present a new block triangular preconditioner applied to the problem of solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations $(k=0)$ in electromagnetic problems, since linear systems arising from the corresponding equations and methods have the same matrix block structure. Similar to spectral distribution of the preconditioners presented by Rees and Greif, this paper analyzes the corresponding spectral distribution of the new preconditioners considered in this paper. From the views of theories and applications, the presented preconditioners are as efficient as the preconditioners presented by Rees and Greif to apply. Moreover, numerical experiments are also reported to illustrate the efficiency of the presented preconditioners.

MSC 2000:: *78M99 Basic mathematical methods in optics
65F08

Keywords: Maxwell equations; saddle point problem; Krylov subspace method; block preconditioner

Citations: Zbl 1155.65048

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