Singular value decomposition of integral equations of EM and applications to the cavity resonance problem

The use of the method of moments (MM) based on the electric-field integral equation is considered for conducting bodies with closed regions. For such a calculation, the scattered field is theoretically well defined, but numerical problems have been found near resonant frequencies. To study these problems, the use of the singular value decomposition (SVD) in MM calculations is developed, and the reason the SVD is the appropriate tool for the numerical analysis of any MM calculation (even when the matrix equation is to be solved by an iterative technique) is shown. In particular, the SVD casts a MM calculation into a diagonal form, which allows a careful numerical analysis. The problems near resonance are found to be due to the creation of an approximate impedance matrix Z, which has the wrong resonant frequency (i.e., it is not consistent with that of the radiation problem). One numerical method that avoids these difficulties by using the SVD is discussed, and other more efficient ways of avoiding the usual numerical difficulties are suggested