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Preconditioners for the discretized time-harmonic Maxwell equations in mixed form. (English) Zbl 1199.78010

Summary: We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of time-harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of discrete operators, but are augmentation free and Schur complement free. We provide a complete spectral analysis, and show that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations are accompanied by numerical results that demonstrate the scalability of the proposed approach.

MSC:

78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
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