The Lagrange Interpolation Method for the Cavity Eigenvalue Problem with Electric Field Integral Equation

Calculating the eigenmodes and eigenfrequencies of a perfect electric conductor cavity is one of the classical problems in electromagnetics. When we use the electric field integral equation (EFIE) to solve the problem, we will get a nonlinear eigenvalue problem because the frequency is the argument of the exponential function of the free space Green's function. A nonlinear eigenvalue problem is usually not easy to solve. In this work, a simple and iterative method is proposed for the EFIE eigenvalue problem. By using the Lagrange interpolation of the Green's function, the nonlinear eigenvalue problem can be transformed to a polynomial eigenvalue problem, which is then rearranged to the generalized eigenvalue problem. By solving the generalized eigenvalue problem iteratively, the resonance frequencies and modes of a cavity can be obtained. The method is applicable to arbitrarily shaped cavities and the numerical computation is easy to carry out. For demonstrating the accuracy and the feasibility of the method, several numerical results are presented.