Two-grid methods for time-harmonic Maxwell equations

In this paper, we develop several two-grid methods for the Nédélec edge finite element approximation of the time-harmonic Maxwell equations. We first present a two-grid method that uses a coarse space to solve the original problem and then use a fine space to solve a corresponding symmetric positive definite problem. Then, we present two types of iterative two-grid methods, one is to add the kernel of the curl-operator in the fine space to a coarse mesh space to solve the original problem and the other is to use an inner iterative method for dealing with the kernel of the curl-operator in the fine space and the coarse space, separately. We provide the error estimates for the first two methods and present numerical experiments to show the efficiency of our methods.