A well-conditioned, Hermitian, positive definite, combined field integral equation for simply and multiply connected geometries

We present a new preconditioner for the combined field integral equation (CFIE) that gives rise to a Hermitian, positive definite system of linear equations. Differently from other Calderón strategies, this scheme necessitates a standard discretization of the electric field integral equation (EFIE) with Rao-Wilton-Glisson (RWG) basis functions (i.e., no dual EFIE matrix required), is free from spurious resonances, and is stable down to the static limit for both simply and multiply connected geometries. The fact that the new system matrix is Hermitian, positive definite, and well-conditioned makes it amenable for fast iterative and direct solvers. Numerical results demonstrate the effectiveness of the proposed approach.