A reliable and efficient numerical method for indirect eigenvalue problems arising in waveguide and resonator analysis

摘要

The solution of an indirect (also referred to as non-algebraic or nonlinear) eigenvalue problem is the final step of a variety of well established numerical methods for guided wave and resonator analysis. It amounts to a numerical search for the singularities of a matrix valued function of wave number or frequency. lf a larger number of eigenvalues is required, such a procedure is often unreliable and inefficient. The present paper derives a novel approach, which by investigation of the full matrix function, instead of a scalar characteristic equation, assures reliable detection of large numbers of arbitrarily distributed simple or degenerated eigenvalues. The new Multiple Eigenvalue Search Algorithm allows for a sampling step width larger than the eigenvalue separation. As a side effect it thereby leads to a substantial reduction of numerical effort.