Numerical stability of nonorthogonal FDTD methods

Author

Gedney, Stephen D. ; Roden, J. Alan

Author_Institution

Dept. of Electr. Eng., Kentucky Univ., Lexington, KY, USA

Volume

48

Issue

2

fYear

2000

fDate

2/1/2000 12:00:00 AM

Firstpage

231

Lastpage

239

Abstract

In this paper, a sufficient test for the numerical stability of generalized grid finite-difference time-domain (FDTD) schemes is presented. It is shown that the projection operators of such schemes must be symmetric positive definite. Without this property, such schemes can exhibit late-time instabilities. The origin and the characteristics of these late-time instabilities are also uncovered. Based on this study, nonorthogonal grid FDTD schemes (NFDTD) and the generalized Yee (GY) methods are proposed that are numerically stable in the late time for quadrilateral prism elements, allowing these methods to be extended to problems requiring very long-time simulations. The study of numerical stability that is presented is very general and can be applied to most solutions of Maxwell´s equations based on explicit time-domain schemes

Keywords

Maxwell equations; electromagnetic field theory; finite difference time-domain analysis; numerical stability; Maxwell´s equations; generalized Yee method; generalized grid finite-difference time-domain schemes; late-time instabilities; nonorthogonal FDTD methods; numerical stability; projection operators; quadrilateral prism elements; symmetric positive definite operators; Electromagnetic analysis; Finite difference methods; Helium; Integral equations; Interpolation; Maxwell equations; Numerical stability; Passive circuits; Testing; Time domain analysis;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/8.833072

Filename

833072