Point-based discretization of the mixed-potential RWG MoM via the Nystrom method

Summary form only given. Enforcing continuity of the approximated field between elements of the mesh can improve accuracy of a numerical solution as well as conditioning of its impedance matrix (M. Shafieipour, et. al., IEEE Trans. Antennas Propag., 99, 1-11, 2013). In the class of low-order solutions, Rao-Wilton-Glisson (RWG) basis functions are widely used in the numerical solution of electromagnetic scattering problems and they have been recently suggested in conjunction with first-order Locally Corrected Nystrom (LCN) method when solution of the Electric Field Integral Equation (EFIE) is perused (M. Shafieipour, et. al., IEEE Trans. Antennas Propag., 99, 1-11, 2013), resulting in a current-continuity-enforcing point-based discretization scheme (RWG-via-LCN) which can efficiently be accelerated by the Multilevel Fast Multipole Algorithm (MLFMA). However, it is known that the LCN method suffers from low-frequency breakdown (J. C. Young, et. al., IEEE Antennas. Wireless. Propag. Lett., 11, 846-849, 2012) when trying to solve for the EFIE as LCN discretizes the vector-potential EFIE as opposed to the mixed-potential EFIE. In this work we show that the RWG-via-LCN method inherits the low-frequency breakdown from the LCN method. As a remedy, we introduce a new RWGvia-LCN scheme which is a mixture of zerothand first-order discretization of the EFIE and we show that it is equivalent to the mixed-potential RWG MoM. The new method preserves all advantages of the RWG-via-LCN method (i.e. point-based and current-continuity-enforcing) and at the same time enjoys a wide-band solution and is computationally more efficient as it uses zeroth-order EFIE to compute the scalar potential contribution.