Convergence of moment-method solutions of the electric field integral equation for a 2-D open cavity

We study the problem of accurate numerical determination of the radiation and scattering properties of resonant structures by estimating the cavity mode eigenvalues of the electric field integral equation for a two-dimensional open cavity. We obtain moment matrix condition number estimates for the TE and TM polarizations, and, by taking into account the quadrature error introduced by approximate numerical integration of matrix elements, we show that the number of unknowns required to accurately resolve the cavity modes scales as the square of the electrical size of the cavity.