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

TL;DR

This paper introduces a dissipation theory for potentials-based FDTD algorithms in lossless inhomogeneous media, providing insights into energy flow and stability, and enabling the development of more reliable computational methods.

Contribution

It develops a dissipation theory showing that potentials-based FDTD in lossless media is inherently lossless under CFL conditions, offering a foundation for stable algorithm design.

Findings

FDTD equations behave as a lossless system under CFL limit.

The theory offers insights into electromagnetic energy and power flow in FDTD.

Framework for designing stable, energy-preserving FDTD algorithms.

Abstract

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.