Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems (Q557926)

The authors investigate different eigensolvers to compute a small number (5-10) of the smallest eigenvalues of the homogeneous Helmholtz equation discretized by the finite element method. The practical background of this problem originates in accelerator physics where the lowest eigenmodes of resonant rf (radio frequency) accelerating structures are of central interest in the design phase. Discretization by finite elements leads to a real symmetric generalized matrix eigenvalue problem. Different eigenvalue solvers and preconditioners are carefully described and compared for a realistic, practical application problem. These are especially the Jacobi-Davidson algorithm, the locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm and a multilevel preconditioner which combines a hierarchical basis and a smoothed aggregation algebraic multigrid (AMG) preconditioner. As a result of the extensive study the Jacobi-Davidson algorithms turns out to be superior to LOBPCG for the given Maxwell eigenvalue problem. The well-compiled study gives important information for further research not only in the field of Maxwell's eigenvalue problem.