Analysis and Regularization of the TD-EFIE Low-Frequency Breakdown

Low-frequency breakdown phenomenon plaguing marching-on-in-time solutions of time domain electric field integral equations is analyzed and cured. A theoretical analysis of the breakdown identifies deficiencies in the treatments proposed to date. A scheme for eliminating low frequency breakdown phenomena that leverages hierarchical regularization is presented. It applies to arbitrary meshes and gives rise to linear systems that are better conditioned than those obtained with standard loop-star/tree bases. The scheme's analytical properties and numerical results demonstrate its efficacy in accelerating the iterative solution of the time domain electric field integral equations.