Preconditioners And Their Analyses For Edge Element Saddle-point Systems Arising From Time-harmonic Maxwell Equations

We propose and analyze new preconditioners for the saddle-point systems arising from the edge element discretization of the time-harmonic Maxwell equations.The preconditioners come from a formula giving the inverse of the coefficient matrix of the saddle-point system with vanishing,and non-vanishing wave numbers,and are gener-alizations of the preconditioner in[9].we show theoretically and numerically that the conjugate gradient method(CG)with these new preconditioners can be applied effi-ciently when the wave number(k)is not too large(roughly k ? 4 numerically).The spectral behaviors of the resulting preconditioned systems for the new and some existing preconditioners are analyzed and compared,and numerical experiments are presented to demonstrate and compare the efficiencies of these preconditioners.