Subspace iteration search method for generalized eigenvalue problems with sparse complex unsymmetric matrices in finite-element analysis of waveguides

In this paper, a numerical method for the robust computation of the number of eigenvalues within a closed contour of a generalized complex eigenvalue problem is presented. As a result of this computation, it is possible to perform a systematic search for the eigenvalues, ensuring that no eigenvalues are forgotten, and to optimize their calculation. Application is made to the finite-element modal analysis of inhomogeneous waveguides.