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Multiplicative block preconditioner for the time-harmonic Maxwell equations

Zhuo-Hong Huang


In this paper, based on multiplicative block method, we establish a new multiplicative block preconditioner for solving symmetric, indefinite saddle point system arising from Maxwell equation in mixed form, study the spectral properties of the preconditioned matrix, and discuss the distributions of the eigenvalues and eigenvectors of the preconditioned matrix with iteration parameter. In numerical examples, we numerically compare the performance of
the multiplicative block preconditioner presented in this paper, block diagonal preconditioner established in (Greif and Schotzau, 2007) and block triangular preconditioner proposed in (Cheng, Huang and Shen, 2009), and numerically obtain the optimal parameter. Numerical experiments further verify the accuracy and practicability of the multiplicative block preconditioner.


Multiplicative block preconditioner, Computational Electromagnetics, Timeharmonic Maxwell equations, Symmetric indefinite saddle point system, BiCGSTAB method.

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