Modified block preconditioners for the discretized time-harmonic Maxwell equations in mixed form

Abstract

In this paper, building on the previous work by Greif and Schötzau [Preconditioners for the discretized time-harmonic Maxwell equations in mixed form, Numer. Linear Algebra Appl. 14 (2007) 281–297] and Benzi and Olshanskii [An augmented lagrangian-based approach to the Oseen problem, SIAM J. Sci. Comput. 28 (2006) 2095–2113], we present the improved preconditioning techniques for the iterative solution of the saddle point linear systems, which arise from the finite element discretization of the mixed formulation of the time-harmonic Maxwell equations. The modified block diagonal and triangular preconditioners considered are based on augmentation with using the symmetric nonsingular weighted matrix. We discuss the spectral properties of the preconditioned matrix in detail and generalize the results of the above-mentioned paper by Greif and Schötzau. Numerical experiments are given to demonstrate the efficiency of the presented preconditioners.