A stable higher order TDIE solver using a separable approximation for convolution with the retarded potential

Since the initial development of Time-Domain Integral Equations (TDIEs), the issue of instability has limited their use by computational practitioners. Significant progress notwithstanding, there is still a need for theoretical understanding of the causes of instability, their remedies (in the continuous case) and solution schemes applicable to electrically large, complex structures. It was in an attempt to remedy this that a method based on a separable approximation for the convolution with the retarded potential was recently developed. In this work, we seek to reformulate the Time Domain Electric Field Integral Equation (TDEFIE) in a manner than can be shown to produce bounded currents. We also present a number of results using the non-augmented TDEFIE to demonstrate the method´s effectiveness on higher order surfaces.