A Simple Technique for Solving E-Field Integral Equations for Conducting Bodies at Internal Resonances

A simple but effective method is presented to analyze electromagnetic radiation and scattering from conducting bodies at frequencies corresponding to internal resonances of a cavity of the same shape. The advantage of this technique is that it requires only the E-field integral equation and not both E-field and H-field as required by the combined fields formulation. It is shown theoretically that this method produces a solution with minimum norm and converges monotonically as the order of the approximation is increased. The minimum norm solution for the current density given by the E-field integral equation is not the correct current density as there is a portion of the resonant current that exists on the body. However, the minimum norm solution indeed provides the true scattering fields. This technique may also be utilized for obtaining a minimum norm solution for nearly singular and singular matrix equations. Examples are presented to illustrate the application of this technique.