Electric Field-Based Surface Integral Constraints for Helmholtz Decompositions of the Current on a Conductor

A new formulation for electromagnetic scattering from perfect electric conductors is presented. The new EFIE-hd formulation is based on the electric field integral equation (EFIE) and incorporates a Helmholtz decomposition (HD) of the current. Instead of using specialized basis functions, the HD is obtained by imposing appropriate surface integral constraints. It is shown that this strategy allows for the use of a locally corrected Nyström discretization method for the resulting formulation. Numerical examples are provided to demonstrate that the EFIE-hd is frequency stable and provides accurate solutions for the electric and magnetic fields at both high and low frequencies for simply connected structures. Examples for multiply connected structures are also provided.