FDTD Algorithms for the 1D Equation

doi:10.1117/3.2250614.ch5

Book: Computing the Flow of Light: Nonstandard FDTD Methodologies for Photonics Design

Author(s): James B. Cole, Saswatee Banerjee

Published: 2017

https://doi.org/10.1117/3.2250614.ch5

Author Affiliations +

Abstract

In Chapter 3 we developed the basic concepts of standard and nonstandard finite difference models with respect to the simple harmonic oscillator. We now extend these developments to the next level of complexity, the 1D wave equation, and thereby set the stage to deal with the 2D and 3D wave equations and with Maxwell’s equations. FDTD algorithms to solve the 1D wave equation may seem simple, but in fact there are many ‘devils in the details’ that must be smitten before FDTD can be used to solve interesting problems. Dealing with these ‘devils’ in one dimension will make it easier to handle them later on in two and three. Topics: • Standard and nonstandard FDTD for the wave equation in different forms • Accuracy and stability • Other constraints