Computationally efficient solution for finding the current density on the illuminated and shadow sides of an infinitely thin circular disk

Background. The article is devoted to the development of a computationally efficient numerical solution to the diffraction problem on an infinitely thin ideally conducting circular disk. The main attention is paid to the problem of finding the distribution of the surface current density on each side of the disk separately, which has remained undiscovered in other well-known studies. The aim of this paper is to eliminate this disadvantage by forming a computationally efficient algorithmic solution based on the method of moments and allowing numerically to set a smooth approximation of the surface current density on the illuminated and shadow sides of an infinitely thin ideally conducting circular disk. Methods. The solution is formed by the Galerkin method when determining the desired approximation of the surface current density on the disk. The solution is based on the formation of a smooth vector function given by the sum of global curl-free and curl basis functions relative to the disk. The corresponding basis functions are formed from the modifications of Bessel functions of the first kind and Zernike polynomials proposed in the paper. Results. The operability of the proposed solution is verified on test examples for a disk at different diameter-to-wavelength ratios. The comparison was made with the solution of a similar problem in the Ansoft HFSS CAD system. Conclusion. The obtained results allow us to conclude that the proposed solution is preferable and are the basis for further generalization of the results to more complex geometric structures when using the conformal mapping method.