Simultaneous multigrid techniques for the computation of close frequency eigenmodes in resonant cavities

Simultaneous adaptive multigrid (MG) methods for the computation of the modes and eigenvalues of resonant cavities are presented. The methods couple an MG eigenvalue solver and an MG mode separation technique which is an MG generalization of the known Rayleigh Ritz Projection. The coupling is possible due to the simultaneous processing of all desired modes. The simultaneous approximation and separation allows to separate efficiently the modes on coarse grids and to monitor the stability of the algorithm. A boundary treatment method is introduced in the simultaneous techniques for the treatment of complex shapes of real devices. A subspace continuation technique (SCT) is used for sequences of eigenvalue problems. The MG techniques show to be much more efficient than classical and improved single level techniques. Numerical experiments which illustrate the efficiency of the simultaneous techniques are shown for resonant cavities presenting close eigenvalues and special boundary difficulties.