  A dissipation theory is proposed for the potentials-based FDTD algorithm for
the case of inhomogeneous lossless media. We show that under the
Courant-Friedrichs-Lewy (CFL) 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.
