On the Accuracy of the ADI-FDTD Method

被引：185

作者：

Gonzalez Garcia, Salvador ^{[1
]}

Lee, Tae-Woo ^{[2
]}

Hagness, Susan C. ^{[2
]}

机构：

[1] Univ Granada, Fac Ciencias, Dept Electromagnetismo & Fis Materia, E-18071 Granada, Spain

[2] Univ Wisconsin, Dept Elect & Comp Engn, Madison, WI 53706 USA

来源：

IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS | 2002年 / 1卷

关键词：

Alternating-direction implicit (ADI) methods; finite-difference time-domain (FDTD) methods; numerical stability;

D O I：

10.1109/LAWP.2002.802583

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

We present an analytical study of the alternating-direction implicit finite-difference time-domain (ADI-FDTD) method for solving the time-varying Maxwell's equations and compare its accuracy with that of the Crank-Nicolson (CN) and Yee FDTD schemes. The closed form of the truncation error is obtained for two and three dimensions. The dependence of the truncation error on the square of the time step multiplied by the spatial derivatives of the fields is found to be a unique feature of the ADI-FDTD scheme. We illustrate the limitation on accuracy imposed by these truncation error terms by simulating a simple parallel-plate structure excited by a low-frequency voltage source. Excellent agreement is obtained between field data computed with the implicit CN scheme using time steps greatly exceeding the Courant limit and field data computed with the explicit Yee scheme. Such results are not obtained with ADI-FDTD.

引用

页码：31 / 34

页数：4

共 11 条

[1]

Ames W., 1977, NUMERICAL METHODS PA

[2] ON THE NUMERICAL INTEGRATION OF D2U-DX2+D2U-DY2=DU-D+ IMPLICIT METHODS [J].

DOUGLAS, J .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1955, 3 (01) :42-65

[3]

MITCHELL A, 1980, FINITE DIFFERENCE ME

[4] A new FDTD algorithm based on alternating-direction implicit method [J].

Namiki, T .

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 1999, 47 (10) :2003-2007

[5]

Namiki T, 2000, IEEE T MICROW THEORY, V48, P1950, DOI 10.1109/22.883876

[6] Numerical simulation using ADI-FDTD method to estimate shielding effectiveness of thin conductive enclosures [J].

Namiki, T ;

Ito, K .

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2001, 49 (06) :1060-1066

[7] Numerical simulation of microstrip resonators and filters using the ADI-FDTD method [J].

Namiki, T ;

Ito, K .

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2001, 49 (04) :665-670

[8] THE NUMERICAL SOLUTION OF PARABOLIC AND ELLIPTIC DIFFERENTIAL EQUATIONS [J].

PEACEMAN, DW ;

RACHFORD, HH .

JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1955, 3 (01) :28-41

[9]

Taflove A., 1995, COMPUTATIONAL ELECTR

[10] Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD method [J].

Zheng, FH ;

Chen, ZZ .

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, 2001, 49 (05) :1006-1009

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