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

• Published in: Journal of computational physics Vol. 218; no. 2; pp. 594 - 606
• Main Author: Remis, Rob F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.11.2006; Elsevier
• Subjects: Computational techniques; Electromagnetic fields; Electromagnetic waves; Exact sciences and technology; Finite-difference time-domain; Lossless; Mathematical analysis; Mathematical methods in physics; Maxwell equation; Maxwell’s equations; Media; Nonuniform; Physics; Stability; Two dimensional; Finite-difference time-domain; Stability; 78M20; Electromagnetic fields; 65M12; Maxwell’s equations; Tensor product; Electromagnetic waves; Inhomogeneous media; Finite difference time-domain analysis; Calculation; Maxwell's equations; Electromagnetic fields; Finite-difference time-domain; Stability; Maxwell equations; Calculation methods; 65M12; 78M20
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2006.02.022

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.