DocumentCode :
1156023
Title :
Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TEz waves
Author :
Sun, Guilin ; Trueman, Christopher W.
Author_Institution :
Dept. of Electr. & Comput. Eng., Concordia Univ., Montreal, Que., Canada
Volume :
52
Issue :
11
fYear :
2004
Firstpage :
2963
Lastpage :
2972
Abstract :
Two implicit finite-difference time-domain (FDTD) methods are presented in this paper for a two-dimensional TEz wave, which are based on the unconditionally-stable Crank-Nicolson scheme. To treat PEC boundaries efficiently, the methods deal with the electric field components rather than the magnetic field. The "approximate-decoupling method" solves two tridiagonal matrices and computes only one explicit equation for a full update cycle. It has the same numerical dispersion relation as the ADI-FDTD method. The "cycle-sweep method" solves two tridiagonal matrices, and computes two equations explicitly for a full update cycle. It has the same numerical dispersion relation as the previously-reported Crank-Nicolson-Douglas-Gunn algorithm, which solves for the magnetic field. The cycle-sweep method has much smaller numerical anisotropy than the approximate-decoupling method, though the dispersion error is the same along the axes as, and larger along the 45° diagonal than ADI-FDTD. With different formulations, two algorithms for the approximate-decoupling method and four algorithms for the cycle-sweep method are presented. All the six algorithms are strictly nondissipative, unconditionally stable, and are tested by numerical computation in this paper. The numerical dispersion relations are validated by numerical experiments, and very good agreement between the experiments and the theoretical predication is obtained.
Keywords :
Maxwell equations; computational electromagnetics; electromagnetic waves; finite difference time-domain analysis; 2-D finite-difference time-domain method; Crank-Nicolson scheme; FDTD method; PEC boundary; TEz waves; approximate-decoupling method; computational electromagnetics; cycle-sweep method; numerical dispersion; perfectly electrically conducting boundary; tridiagonal matrix; Anisotropic magnetoresistance; Dispersion; Electromagnetic compatibility; Finite difference methods; Magnetic fields; Matrix decomposition; Maxwell equations; Sun; Testing; Time domain analysis; 211;Nicolson; 65; CN; Computational electromagnetics; Crank&#; FDTD; finite-difference time-domain; numerical dispersion; scheme; unconditional stability;
fLanguage :
English
Journal_Title :
Antennas and Propagation, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-926X
Type :
jour
DOI :
10.1109/TAP.2004.835142
Filename :
1353494
Link To Document :
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