A simple technique for solvingE-field integral equations for conducting bodies at internal resonances

Abstract

A simple but effective method is presented to analyze electromagnetic radiation and scattering from condueting 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -field integral equation and hot both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -field and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> -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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> -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.