A High-Order Locally Corrected Nyström Scheme for Charge-Current Integral Equations

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.