Stability of FDTD on nonuniform grids for Maxwell's equations in lossless media

Authors:
Rob F. Remis
Affiliations:
Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Laboratory of Electromagnetic Research, Mekelweg, Delft, The Netherlands
Venue:
Journal of Computational Physics
Year:
2006

Citing 4
Cited 1

A convergence analysis of Yee's scheme on nonuniform grids

SIAM Journal on Numerical Analysis
Application of the difference Gaussian rules to solution of hyperbolic problems

Journal of Computational Physics
Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain

SIAM Journal on Numerical Analysis
On the stability of the finite-difference time-domain method

Journal of Computational Physics

On the relation between FDTD and Fibonacci polynomials

Journal of Computational Physics

Quantified Score

Hi-index	31.45

Visualization

Abstract

In this paper we present practical stability conditions for the finite-difference time-domain method on nonuniform tensor product grids (Yee grids). These stability conditions apply to Maxwell's equations for inhomogeneous and lossless media. Rectangular domains are considered and the conditions are expressed in terms of the minimum spatial stepsizes of the grid and the maximum electromagnetic wave speed in the configuration. The maximum wave speed is known as soon as the media are specified, while the minimum spatial stepsizes are known after the configuration has been discretized. For two-dimensional configurations we present a number of numerical examples which illustrate the effectiveness of the proposed stability conditions.