Preconditioners for the discretized time‐harmonic Maxwell equations in mixed form

We introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time‐harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the 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.