Numerical method for calculating surface current density on a two-dimensional scatterer with smooth contour

A numerical method is presented for finding the surface current density on a two-dimensional smooth scatterer. This method is an improved version on a method which one of the authors presented as an adjoint method to the conventional mode-matching method for finding the scattered field. After formulating the problem, the method is interpreted as being adjoint to the conventional mode-matching method, and it is shown that the method yields a sequence of approximate current densities converging to the true density in the mean squares sense. Next the improved method is proposed and the fact that this method yields a sequence of approximate solutions which converges to the true density uniformly on the contour of the scatterer is proven. It is then stated that the method is an adjoint one to the mode-matching method with a smoothing procedure, which is proposed as a powerful numerical method for the scattered field. Numerical results of some sample calculations are attached to show the effectiveness of the new method.