On the spectrum of the electric field integral equation and the convergence of the moment method

Existing convergence estimates for numerical scattering methods based on bo undary integral equations are asymptotic in the limit of vanishing discreti zation length, and break down as the electrical size of the problem grows. In order to analyse the efficiency and accuracy of numerical methods for th e large scattering problems of interest in computational electromagnetics, we study the spectrum of the electric field integral equation (EFIE) for an infinite, conducting strip for both the TM (weakly singular kernel) and TE polarizations (hypersingular kernel). Due to the self-coupling of surface wave modes, the condition number of the discretized integral equation incre ases as the square root of the electrical size of the strip for both polari zations. From the spectrum of the EFIE, the solution error introduced by di scretization of the integral equation can also be estimated. Away from the edge singularities of the solution, the error is second order in the discre tization length for low-order bases with exact integration of matrix elemen ts, and is first order if an approximate quadrature rule is employed. Compa rison with numerical results demonstrates the validity of these condition n umber and solution error estimates. The spectral theory offers insights int o the behaviour of numerical methods commonly observed in computational ele ctromagnetics. Copyright (C) 2001 John Wiley & Sons, Ltd.