On the Low-Frequency Scaling of Vector Potential Integral Equation Solutions

Vector potential integral equations (VPIEs) have recently been proposed as break-down free alternatives to field integral equations for analyzing low-frequency electromagnetic scattering problems. In this work, accuracy of VPIEs for perfect electrically conducting scatterers at low frequencies is investigated. Depending on the different representation of the vector potential formulation, four different integral equations in unknown electric current and normal component of the vector potential are obtained. To numerically solve these VPIEs, the electric current and the normal component of the vector potential are expanded using Rao-Wilton-Glisson and pulse basis functions, respectively. Inserting these expansions into two of the integral equations and using Galerkin testing yield a linear matrix system. Numerical results show that depending on the choice of VPIEs, the solution of this linear matrix system is inaccurate at low frequencies, similar to the magnetic field integral equation.