Journal of the Institute of Electronics Engineers of Korea TC (대한전자공학회논문지TC)

The Institute of Electronics and Information Engineers (대한전자공학회)
권호 표지

Reduction Method of Anisotropy Error in Two Dimensional ADI-FDTD Method

2차원 ADI-FDTD 수치해석에서 이방성 오차의 감소방안

  • Kim, Jong-Sung (Department of Communications Engineering, Kyungsung University) ;
  • Kong, Ki-Bok (School of Engineering, Information and Communications University)
  • 김종성 (경성대학교 멀티미디어통신공학과) ;
  • 공기복 (한국정보통신대학교 공학부)
  • Published : 2007.10.25
Download PDF
⟨ Previous Next ⟩

Abstract

A new adaptive alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method is proposed to obtain isotropic wave propagation for all directional angles. We add the square terms of time-step multiplied by the spatial derivatives of x and y as a perturbed term to the conventional ADI-FDTD and can find the optimization coefficient of square terms of time-step to generate the minimum anisotropy. The new ADI-FDTD is also stable, even when its time-step is greater than the Courant-Friedrich-Levy (CFL) limit. The characteristic equation of the dispersion relation governing the new method is derived and compared with the theoretical and numerical results for the conventional ADI-FDTD and perturbed ADI-FDTD methods.

공간상의 전자파 전파에서 모든 각도에서 동일한 전송속도를 갖는 ADI-FDTD 해석방법을 제안한다. 이는 기존의 ADI-FDTD 방법에서 시간 간격의 2차항에 x, y 에 공간 미분이 곱해진 항을 추가하고, 이에 대한 최적의 상수를 구하여 구현 하였다. 새로운 ADI-FDTD 는 CFL 안정도 조건을 초과하는 시간 간격에 대해서도 안정적인 특성을 나타낸다. 이 방법에 대한 분산 관계식을 구한 후 이를 수치적인 결과와 비교하여 제안하는 방법이 기존의 방법에 비해서 나타나는 장점, 즉 등방성 전파 및 수치적 오차의 감소를 수치적 예를 통하여 검증하였다.

Keywords

References

  1. A Taflove, Computational Electrodynamics., Norwood, MA: Artech House, 1995
  2. T. Namiki, 'A New FDTD Algorithm Based on Alternating-Direction Implict Method', IEEE Trans. Microwave Theory Tech., Vol. 47, No. 10,pp. 2003-2007, Oct. 1999 https://doi.org/10.1109/22.795075
  3. F. Zheng, Z. Chen, and J. Zhang, 'A Finite-Difference Time-Domain Method Without the Courant Stability Conditions', IEEE Microwave Guided Wave Letters, Vol.9, No.11, 441-443, Nov.1009 https://doi.org/10.1109/75.808026
  4. S. G. Garcia, and T. W. Lee, and S. C. Hagness, 'On the Accuracy of the ADI-FDTD Method,' IEEE Antennas and Wireless Propagation Letters, Vol. 1, pp.31-34, 2002 https://doi.org/10.1109/LAWP.2002.802583
  5. J. Chen, Zhu Wang, and Yinchao Chen, 'Higher-order alternative direction implicit FDTD method,' Electronics Letters, Vol. 38, No. 22, pp.1321-1322, October, 2002 https://doi.org/10.1049/el:20020911
  6. Muhu Wang, Zhu Wang, and Ji Chen, 'A Parameter Optimized ADI-FDTD Method,' IEEE Antennas and Wireless Propagation Letters, Vol.2, pp.118-121, 2003 https://doi.org/10.1109/LAWP.2003.815283
  7. An Ping Zhao, 'Improvement on the Numerical Dispersion of 2-D ADI-FDTD with Artificial Anisotropy,' IEEE Microwave and Wireless Components Letters, Vol.14, No.6, pp.292-294, July 2005
  8. S. Wang, F. L. Teixeria, and J. Chen, 'An Iterative ADI-FDTD With Reduced Splitting Error,' IEEE Microwave and Wireless Components Letters, Vol. 15, No.2, pp.92-94, Feb. 2005 https://doi.org/10.1109/LMWC.2004.842835
  9. I. Ahmed, and Z. Chen, 'Error Reduced ADI-FDTD Method,' IEEE Antennas and Wireless Propagation Letters, Vol. 4, pp.323- 325, Jul. 2005 https://doi.org/10.1109/LAWP.2005.855630
  10. K W. Mortan and D. F. Mayer, Numerical Solution of Partial Differential Equations. Cambridge University Press, 1994
  11. G. Sun, and C. W. Trueman, 'Analysis and Numerical Experiments on the Numerical Dispersion of Two-Dimensional ADI-FDTD,' IEEE Antennas and Wireless Propagation Letters, Vol. 2, pp.78-81, 2003 https://doi.org/10.1109/LAWP.2003.814771