On the high frequency behavior and stabilization of a preconditioned and resonance-free formulation

Several preconditioning techniques have been developed to control the condition number of the linear system matrices arising from the majority of the integral formulations for electromagnetics problems. The performance of these techniques is usually assessed in two regimes: (i) the case where the number of unknowns is kept constant and the frequency decreases (low-frequency regime) and (ii) the case where the frequency is kept constant and the number of unknowns increases (dense discretization regime). A third regime, however, can be identified: (iii) the case where both frequency and the number of unknowns grow since the discretization size in wavelengths is kept constant and the frequency increases (high frequency regime). This contribution will focus on formulations that are free from high-frequency resonances (combined-type equations) and are well-conditioned in both regimes (i) and (ii) and it will study and regularize their behavior in regime (iii).