Lorenz Gauge Potential-Based Time Domain Integral Equations for Analyzing Subwavelength Penetrable Regions

Potential-based integral equations are being explored to develop numerical methods that avoid low frequency breakdown issues so that they can analyze multiscale and subwavelength structures that are becoming increasingly important in electromagnetic engineering. This work continues the development of potential-based time domain integral equations by presenting a new formulation in the Lorenz gauge that is applicable to penetrable regions. An appropriate marching-on-in-time discretization scheme is developed that fully conforms to the spatial and 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 for objects that are significantly smaller than a wavelength where previous methods have failed.