Generalized combined field integral equations for the iterative solution of the three-dimensional Maxwell equations

The construction of new second-kind Fredholm integral equations for the numerical solution of problems of high-frequency electromagnetic scattering by a perfect conductor is proposed. These formulations are characterized by some eigenvalue clusterings. They are especially well adapted to Krylov subspace iterative solvers. Their derivation is based on the incorporation of a sufficiently accurate approximation of the exact operator linking the Cauchy data of the scattering boundary-value problem to the classical integral relations. This operator is related to the concept of the On-Surface Radiation Condition (OSRC). These formulations can be considered as a natural generalization of the well-known Brakhage–Werner and combined field integral equations. The efficiency of the approach is established through an analytical and numerical study in the spherical case.