A high-order locally corrected Nyström scheme for charge-current integral equations

Abstract

A high-order Nyström scheme is developed for electromagnetic (EM) scattering problems of smooth objects. The implementation is based on different well-known charge-current formulations. This study aims to develop a novel quadrature scheme to compute different singular integrals that appear on integral equation methods in EMs. The proposed quadrature scheme is used on a locally corrected Nyström method, and applied to charge-current integral equations to obtain a fast, accurate, and a low-frequency stable method to solve EM scattering problems. The proposed method allows obtaining accuracy in the range 4–10 digits in the near electric and magnetic scattered field for certain simple geometries and a wide range of frequencies. We also do a preliminary research on nonsmooth geometries obtaining a certain degree of accuracy depending on the particular charge-current integral equation used.