On the validity of the integral equation formulation of the MEI and the extension to analyze object with impedance boundary condition

We show the validity of the assumption of the existence of the local sources. That is, from the observation that the electric and magnetic line current sources very close to the perfect electric conductor (PEC) induce the electric and magnetic local currents on the surface, the assumption is shown to be true with a new reaction integral in contrast to the original integral equation-measured equation of invariance (IE-MEI). As a natural extension, the interpretation of the new reaction integral makes it possible to analyze objects with impedance boundary conditions (IBC). The extension has the invariable feature that the procedure to solve the problem with IBC is the same for the PEC except only in the final step to obtain the current, where no noticeable increase of the CPU time is found and no extra memory is needed. As numerical examples, scattering from a circular cylinder with IBC is considered in the cases of a plane wave incidence and electric line sources very close to the cylinder. By comparison with the results of the new IE-MEI method with IBC and exact series solutions, we show the validity of the new method.