On Solvinging Maxwellian Eigenvalue Problems for Accelerating Cavities

We investigate algorithms for solving large sparse symmetric matrix eigenvalue problems resulting from finite element discretizations of steady state electromagnetic fields in accelerating cavities. The methods have been applied to the new design of the accelerating cavity for the PSI 590 MeV ring cyclotron. The solutions of this kind of eigenvalue problems can be polluted by so-called spurious modes if the divergencefree condition is not treated properly. In this paper we deal with a method that suppresses spurious modes by adding a penalty term to the basic quadratic form. This is the method we had the best experience with [1, 2]. The large sparse eigenvalue problems have been solved with the implicitly restarted Lanczos algorithm. Numerical results obtained on a HP Exemplar X-Class System are reported.