On the Spectral Behavior and Normalization of a Resonance-Free and High-Frequency Stable Integral Equation

Abstract

The CFIE used for solving scattering and radiation problems, although a resonance-free formulation, suffers from an ill-conditioning that strongly depends on the frequency and discretization density, both in the low- and high-frequency regime, resulting in slow convergence rates for iterative solvers. This work presents a new preconditioning scheme for the CFIE that cures the low- and the high-frequency as well as the dense discretization breakdown. The new preconditioner for the CFIE is based on a spherical harmonics analysis and the proper regularization with Helmholtz-type operators. Numerical results have been obtained to prove the effectiveness of this new formulation in real scenarios.