COMBINED FIELD-ONLY BOUNDARY INTEGRAL EQUATIONS FOR ELECTROMAGNETIC SCATTERING

We present a novel boundary integral equation (BIE) formulation for electromagnetic scattering by 3D perfectly electrically conducting (PEC) obstacles, combining the advantages of both field-only and combined-field approaches. Our formulation exploits the property that the three components of the scattered electric field are radiative solutions of the Helmholtz equation. This fact allows for straightforward boundary integral representations derived from scalar Green’s identities. Imposing the PEC boundary conditions results in a BIE system solely involving standard Helmholtz integral operators and scalar surface unknowns. To ensure the well- posedness of the formulation, we incorporate the combined field methodology [3] within this field- only BIE framework [5]. The resulting BIE system can be further reduced to a single scalar BIE by exploiting the system’s low-rank structure, and can be efficiently solved using existing Helmholtz BIE solvers. This results in a significant departure from conventional electromagnetic BIEs, which often suffer from well- documented numerical challenges due to the involved evaluation of electric and magnetic field integral operators. We analyze the well-posedness of our formulation for spheres and showcase its broader applicability through a variety of numerical examples on more general geometries.