Potential-Based Time Domain Integral Equations Free From Interior Resonances

Potential-based integral equations are being explored to develop numerical methods that avoid low-frequency breakdown issues so that they can analyze multiscale structures that are becoming increasingly important in electromagnetic engineering. This work continues the development of potential-based time domain integral equations by presenting three new formulations in the Lorenz gauge that do not support interior resonances. These modifications allow the methods to be applied to deeply multiscale structures of practical importance that contain significantly subwavelength- and wavelength-sized geometric features. Appropriate marching-on-in-time discretization schemes are developed for each formulation that fully conform to the temporal Sobolev space properties of the integral equations. It is shown that following this approach leads to a discrete system with improved stability properties. Further, it is demonstrated that this new system can produce accurate results over broad bandwidths and analyze deeply multiscale systems that previous potential-based time domain integral equations could not.