New block triangular preconditioner for linear systems arising from the discretized time-harmonic Maxwell equations

Abstract

In this paper, based on the preconditioners presented by Rees and Greif [T. Rees, C. Greif, A preconditioner for linear systems arising from interior point optimization methods, SIAM J. Sci. Comput. 29 (2007) 1992–2007], we present a new block triangular preconditioner applied to the problem of solving linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations ( k = 0 ) in electromagnetic problems, since linear systems arising from the corresponding equations and methods have the same matrix block structure. Similar to spectral distribution of the preconditioners presented by Rees and Greif, this paper analyzes the corresponding spectral distribution of the new preconditioners considered in this paper. From the views of theories and applications, the presented preconditioners are as efficient as the preconditioners presented by Rees and Greif to apply. Moreover, numerical experiments are also reported to illustrate the efficiency of the presented preconditioners.