Solving Maxwell eigenvalue problems for accelerating cavities

We investigate algorithms for computing steady state electromagnetic waves in cavities. The Maxwell equations for the strength of the electric field a re solved by a mixed method with quadratic finite edge (Nedelec) elements f or the field values and corresponding node-based finite elements for the La grange multiplier. This approach avoids so-called spurious modes which are introduced if the divergence-free condition for the electric field is not t reated properly. To compute a few of the smallest positive eigenvalues and corresponding eigenmodes of the resulting large sparse matrix eigenvalue pr oblems, two algorithms have been used: the implicitly restarted Lanczos alg orithm and the Jacobi-Davidson algorithm, both with shift-and-invert spectr al transformation. Two-level hierarchical basis preconditioners have been e mployed for the iterative solution of the resulting systems of equations.