Accuracy and convergence of the time domain wave equation methods

Time-domain electrodynamics is formally described either by Maxwell’s equations or by the wave equation. In the former case, the system state is described by the field vectors E and H, while the electromagnetic potentials are the usual choice in the latter case. Here, we investigate the accuracy and the convergence of the time domain wave equation method based on the scalar wave potentials in the treatment of edges and corners. Comparisons are provided with the commonly used finite-difference time domain (FDTD) method based on Yee’s discretization and with the time domain transmission-line matrix (TLM) method.