Construction principles of multigrid smoothers for Curl-Curl equations

The construction principle for multigrid smoothers for discrete Curl-Curl equations consists in the inclusion of an additional zero divergence constraint. This principle is shown to hold for established schemes such as Hiptmair´s hybrid smoother and it is used to construct a new smoother starting from a mixed formulation using a Lagrange multiplier formulation, where a zero divergence constraint leads to a grad-div augmented system. The convergence properties of this system are compared to the nonaugmented system and to the hybrid scheme using Gauss-Seidel iterations for different curl-curl systems arising from various electrodynamical problems.