Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems

Authors:
Peter Arbenz;Roman Geus
Affiliations:
Institute of Computational Science, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland;Institute of Computational Science, Swiss Federal Institute of Technology, CH-8092 Zurich, Switzerland
Venue:
Applied Numerical Mathematics - 6th IMACS International symposium on iterative methods in scientific computing
Year:
2005

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Abstract

We investigate eigensolvers for computing a few of the smallest eigenvalues of a generalized eigenvalue problem resulting from the finite element discretization of the time independent Maxwell equation. Various multilevel preconditioners are employed to improve the convergence and memory consumption of the Jacobi-Davidson algorithm and of the locally optimal block preconditioned conjugate gradient (LOBPCG) method. We present numerical results of very large eigenvalue problems originating from the design of resonant cavities of particle accelerators.