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

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 num erical methods for guided wave and resonator analysis. It amounts to a nume rical search for the singularities of a matrix valued function of wave numb er or frequency. If a larger number of eigenvalues is required, such a proc edure is often unreliable and inefficient. The present paper derives a nove l approach, which by investigation of the full matrix function, instead of a scalar characteristic equation, assures reliable detection of large numbe rs of arbitrarily distributed simple or degenerated eigenvalues. The new Mu ltiple Eigenvalue Search Algorithm allows for a sampling step width larger than the eigenvalue separation. As a side effect it thereby leads to a subs tantial reduction of numerical effort. Copyright (C) 1999 John Wiley & Sons , Ltd.