Analysis of a Multigrid Algorithm for Time Harmonic Maxwell Equations

This paper considers a multigrid algorithm suitable for efficient solution of indefinite linear systems arising from finite element discretization of time harmonic Maxwell equations. In particular, a “backslash” multigrid cycle is proven to converge at rates independent of refinement level if certain indefinite block smoothers are used. The method of analysis involves comparing the multigrid error reduction operator with that of a related positive definite multigrid operator. This idea has previously been used in multigrid analysis of indefinite second order elliptic problems. However, the Maxwell application involves a non-elliptic indefinite operator. With the help of a few new estimates, the earlier ideas can still be applied. Some numerical experiments with lowest order Nedelec elements are also reported.