A Stabilized and Well-Conditioned Marching-on-in Degree Method for Transient Analysis of Dielectric Objects

This paper presents a solver for addressing the challenges of low frequency instability and high-order oscillation in dielectric scattering problems. The proposed solver effectively mitigates dense-mesh issues and eliminates the impact of smaller $s$ values, which is realized by canceling the scalar component of the $\mathcal{L}$ operator. Additionally, we employ the radial integration to ensure the stability of higher-order temporal functions. Numerical examples validate the accuracy and effectiveness of the algorithm.