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Zbl 1199.78010
Greif, Chen; Schötzau, Dominik
Preconditioners for the discretized time-harmonic Maxwell equations in mixed form. (English)
[J] Numer. Linear Algebra Appl. 14, No. 4, 281-297 (2007). ISSN 1070-5325; ISSN 1099-1506/e

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 2000:: *78M10 Finite element methods (optics)
65N30 Finite numerical methods (BVP of PDE)
65F10 Iterative methods for linear systems

Keywords: time-harmonic Maxwell equations; finite element methods; saddle point linear systems; block preconditioners; Krylov subspace solvers

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