On the Low-Frequency Behavior of Vector Potential Integral Equations for Perfect Electrically Conducting Scatterers

Low-frequency behavior of vector potential integral equations (VPIEs) for perfect electrically conducting scatterers is investigated. Two equation sets are considered: The first set (VPIE-1) enforces the tangential component of the vector potential on the scatterer surface to be zero and uses the fundamental field relation on its normal component. The second set (VPIE-2) uses the same condition as VPIE-1 for the tangential component of the vector potential but enforces its divergence to be zero. In both sets, unknowns are the electric current and the normal component of the vector potential on the scatterer surface and are expanded using Rao-Wilton-Glisson (RWG) and pulse basis functions, respectively. To achieve a conforming discretization, RWG, scalar Buffa-Christiansen, and pulse testing functions are used. Theoretical and numerical analyses of the resulting matrix systems show that the electric current obtained by solving VPIE-1 has the wrong frequency scaling and is inaccurate at low frequencies.