Integration of hp-adaptivity and a two grid solver for electromagnetic problems

We present implementation details and analyze convergence of a two grid solver forming the core of a fully automatic hp-adaptive strategy for electromagnetic problems. The solver delivers a solution for a fine grid obtained from an arbitrary coarse hp grid by a global hp-refinement. The classical V-cycle algorithm combines an overlapping block Jacobi smoother with optimal relaxation, and a direct solve on the coarse grid. A theoretical analysis of the two grid solver is illustrated with numerical experiments. Several electromagnetic applications show the efficiency of combining the fully automatic hp-adaptive strategy with the two grid solver.