Richard B. Lehoucq
Sandia National Laboratories, MS 1110, P.O.Box 5800, Albuquerque, NM 87185-1110.
We present a new approach for computing guided waves of optical fibers. We review the standard approaches and discuss our formulation that results in a non-symmetric generalized eigenvalue problem. The resulting non-symmetric generalized eigenvalue problem may be solved with two different methods. The first method combines a spectral transformation with an implicitly restarted block Arnoldi method. The resulting sets of linear equations are solved with a direct method. The second method transforms the generalized eigenvalue problem to a standard eigenvalue problem and also uses an implicitly restarted block Arnoldi method. We present computational results comparing the two methods and show that a block approach leads to a more efficient method.