Towards a parallel multilevel preconditioned maxwell eigensolver

Abstract

We report on a parallel implementation of the Jacobi-Davidson (JD) to compute a few eigenpairs of a large real symmetric generalized matrix eigenvalue problem Ax = λMx, C Tx = 0. The eigenvalue problem stems from the design of cavities of particle accelerators. It is obtained by the finite element discretization of the time-harmonic Maxwell equation in weak form by a combination of Nédélec (edge) and Lagrange (node) elements. We found the Jacobi-Davidson (JD) method to be a very effective solver provided that a good preconditioner is available for the correction equations that have to be solved in each step of the JD iteration. The preconditioner of our choice is a combination of a hierarchical basis preconditioner and a smoothed aggregation AMG preconditioner. It is close to optimal regarding iteration count and scales with regard to memory consumption. The parallel code makes extensive use of the Trilinos software framework. © Springer-Verlag Berlin Heidelberg 2006.