A Dissipation Theory for Potentials-Based FDTD for Lossless Inhomogeneous Media

A dissipation theory is proposed for the potentials-based finite-difference time-domain (FDTD) algorithm for the case of inhomogeneous lossless media. We show that under the Courant–Friedrichs–Lewy limit, the equations describing the time evolution of scalar and vector potentials can be seen as a lossless system. The developed theory provides insights into how electromagnetic energy and power flow are approximated in FDTD schemes. It can also be used to create new algorithms with guaranteed stability.