Optimum design method for eigenvalue problems

This paper presents an optimum design method for an eigenvalue system in electromagnetics. For the spurious mode free analysis of the eigenvalue system, vector finite element method is adopted. In order to obtain the gradient of the objective function, which is given as a function of eigenvalues, with respect to the design variables, the eigenvalue design sensitivity analysis is proposed. The proposed method is applied to lower the cut-off frequency and to broaden the frequency range of the ridged waveguides. The numerical examples of the ridged waveguide designs show the validity of the proposed method.