Implicit ID-FDTD Algorithm Based on Crank-Nicolson Scheme: Dispersion Relation and Stability Analysis

Author

Kim, Hyun ; Koh, Il-Suek ; Yook, Jong-Gwan

Author_Institution

Dept. of Electr. & Electron. Eng., Yonsei Univ., Seoul, South Korea

Volume

59

Issue

6

fYear

2011

fDate

6/1/2011 12:00:00 AM

Firstpage

2259

Lastpage

2267

Abstract

A new implicit isotropic-dispersion finite difference time domain (ID-FDTD) algorithm is proposed, which is formulated based on the Crank-Nicolson (CN) implicit scheme. The update equation of the new scheme is given for a three dimension (3D) problem and a general lossy medium including electric and magnetic losses. The dispersion relation of the CN ID-FDTD scheme is obtained based on the eigen-analysis technique. Also, the unconditional stability is mathematically proved by using the energy method. For a practical application, a maximum time-limit is proposed for free space. To validate the proposed scheme, a 2D cavity problem is considered. The electric fields inside the cavity, which are calculated by the proposed, conventional CN FDTD schemes, and the exact solution, are compared.

Keywords

eigenvalues and eigenfunctions; finite difference time-domain analysis; stability; Crank-Nicolson scheme; dispersion relation; eigen-analysis technique; implicit ID-FDTD algorithm; isotropic-dispersion finite difference time domain algorithm; stability analysis; Dispersion; Equations; Finite difference methods; Mathematical model; Optimized production technology; Three dimensional displays; Time domain analysis; Crank-Nicolson (CN) implicit scheme; energy method; isotropic-dispersion finite difference (ID-FD) equation; low dispersion scheme;

fLanguage

English

Journal_Title

Antennas and Propagation, IEEE Transactions on

Publisher

ieee

ISSN

0018-926X

Type

jour

DOI

10.1109/TAP.2011.2143684

Filename

5752237