CMP-based discretization of the combined field integral equation

Combined field integral equation (CFIE) solvers are widely used for analyzing electromagnetic interactions with perfect electrically conducting (PEC) closed surfaces because, unlike electric field equation (EFIE) solvers, they do not suffer from internal resonance problems. However, they are unbounded as their EFIE components contain a hypersingular term. This renders the matrix systems resulting from discretization of CFIEs ill-conditioned, and their iterative solution inefficient or even impossible when the discretization is dense across part of, or the entire, surface. The unbounded nature of EFIEs can be remedied by leveraging the well-known Calderon identities. However, since Calderon-preconditioned EFIEs exhibit the same resonances as magnetic field integral equations (MFIEs), CFIEs obtained by combining them are not resonance-free. In this work, the Calderon multiplicative preconditioner (CMP) is combined with the localization technique to render CFIEs bounded and resonance-free. The proposed technique easily can be implemented in existing (fast) method-of-moments (MOM) codes. Numerical results show that the iterative solution of the preconditioned CFIE-MOM system converges rapidly regardless the discretization density and frequency of excitation.