Theoretical and Numerical Study of Wave Port Boundary Conditions for Lorenz Gauge Potential-Based Finite Element Methods

The development of computational electromagnetics methods using potential-based formulations in the Lorenz gauge have been gaining interest as a way to overcome the persistent challenge of low-frequency breakdowns in traditional field-based formulations. Lorenz gauge potential-based finite element methods (FEM) have begun to be explored, but to date have only considered very simple excitations and boundary conditions. In this work, we present a theoretical and numerical study of how the widely used wave port boundary condition can be incorporated into these Lorenz gauge potential-based FEM solvers. In the course of this, we propose a new potential-based FEM approach for analyzing inhomogeneous waveguides that is in the same gauge as the 3D potential-based methods of interest to aid in verifying theoretical claims. We find that this approach has certain null spaces that are unique to the 2D setting it is formulated within that prevent it from overcoming low-frequency breakdown effects in practical applications. However, this method still is valuable for presenting numerical validation of other theoretical predictions made in this work; particularly, that any wave port boundary condition previously developed for field-based methods can be utilized within a 3D Lorenz gauge potential-based FEM solver. © 2023, Electromagnetics Academy. All rights reserved.