away from the true growth rate L 5r2 to the slower rate of L 1r2 . For W s 2.2, the condition number grows as L 3r2 as L Ž . becomes large, as predicted by Eq. 20 .
CONCLUSION
We have obtained estimates of the eigenvalues of resonant and near-resonant modes for a two-dimensional open cavity in order to study the conditioning and solution accuracy of the method of moments for this structure. For the TE polarization, if the aspect ratio of the cavity is held constant, the condition number of the moment matrix near low-order resonances increases with the 3r2 power of the electrical size of the cavity. For the TM polarization, the condition number is proportional to the square of the electrical size. Resonant and near-resonant cavity modes also lead to increased sensitivity to discretization error. The self coupling of the modes includes the quadrature error arising from approximate integration of the singularity of the kernel, whereas the cross coupling arises from the tails of the kernel, for which the quadrature error is generally much smaller. Since small cavity mode eigenvalues are caused by a near cancellation of the cross coupling and the self coupling, the relative effect of the quadrature error is large. The number of unknowns required to accurately model the scattering behavior of the cavity increases as the square of the electrical size. Alternately, the order of the quadrature rule must increase with the square of the electrical size.