New technique for kernel regularization of surface integral equations in electromagnetics

Integral equation method is widely used for solution of electromagnetic boundary value problems, in the form of volume and surface integral equations (SIE), for the volume conductivity or polarization currents, or surface magnetic or electric currents, respectively. However, it is problematic to apply two-dimensional SIE for structures of complicated shapes as their kernels have nonintegrable singularities. The paper introduces a new method of reducing such singularities. This method is based upon three points. The first is the presentation of surface current though some new surface potentials. The second is the application of the vector integral theorems and the transfer of the differential operators from kernels to the introduced potentials. The third is the application of the inverse operator-function. It enables one to obtain the integrable, either logarithmic-singular or regular kernels.