MULTILEVEL METHODS APPLIED TO THE DESIGN OF RESONANT CAVITIES

An application of multilevel (ML) methods to compute the modes and eig envalues of resonant cavities is presented, The involved methods inclu de an ML eigenvalue solver, an ML mode separation technique, a boundar y treatment method, and a subspace continuation technique (SCT) for se quences of problems. In the presented numerical experiments, an asympt otic convergence factor of order 0.1 is obtained for ML cycles on all fine levels, while performing only a few relaxations per cycle. This f actor is obtained for a rectangular cavity as well as for cavities hav ing reentrant corners, holes and narrow regions, and presenting cluste rs of close and equal eigenvalues. A second order scheme is obtained f or the computed eigenvalues and modes with an amount of work of order O(qN) for q modes of size N on the finest level, The SCT is illustrate d on a moving boundary problem, where solutions change fast at a small boundary change, Such computations are applied to the design of new m icrowave selective devices.