FDTD Algorithms to Solve the Wave Equation in Two and Three Dimensions

doi:10.1117/3.2250614.ch7

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.ch7

Author Affiliations +

Abstract

We now proceed to extend the 1D FDTD methodologies developed in Chapters 5 and 6 to two and three dimensions. With a few modifications and complications, the process is straightforward. Topics: • Standard and nonstandard FDTD and their errors • The computational boundary and the nonstandard Mur algorithm • Green’s function solutions and the discrete Green’s function methodology • The fuzzy grid representation • The scattered field and its nonstandard FDTD model • Validation by Mie scattering • Detailed stability analyses