New preconditioners with two variable relaxation parameters for the discretized time-harmonic Maxwell equations in mixed form (Q1954996)

Summary: 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 [\textit{G. Cheng} et al., Comput. Phys. Commun. 180, No. 2, 192--196 (2009; Zbl 1198.65219); \textit{C. Greif} and \textit{D. Schötzau}, ETNA, Electron. Trans. Numer. Anal. 22, 114--121 (2006; Zbl 1112.65042)] and [\textit{T. Huang} et. al., Comput. Phys. Commun. 180, No. 10, 1853--1859 (2009; Zbl 1197.78068)]. Theoretical analysis shows that all eigenvalues of the preconditioned matrices are tightly clustered, and numerical tests confirm our analysis.