Integration of \(hp\)-adaptivity and a two-grid solver for electromagnetic problems (Q2384206)

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.