An Algorithm of 3-D ADI-R-FDTD Based on Non-Zero Divergence Relationship


Article Preview

In this letter, an alternating-direction reduced finite-difference time-domain (ADI-R-FDTD) method is presents. It is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with alternating-direction finite-difference time-domain (ADI-FDTD) method in 3 dimensions case, and the expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the ADI-FDTD method is combined with the reduced finite-difference time-domain (R-FDTD) method. In the proposed method, the memory requirement of ADI-R-FDTD is reduced by1/12 of the memory requirement of ADI-FDTD averagely in 3D case. The formulation is presented and the accuracy and efficiency of the proposed method is verified by comparing the results with the conventional results.



Advanced Materials Research (Volumes 317-319)

Edited by:

Xin Chen




X. H. Jin et al., "An Algorithm of 3-D ADI-R-FDTD Based on Non-Zero Divergence Relationship", Advanced Materials Research, Vols. 317-319, pp. 1172-1176, 2011

Online since:

August 2011




[1] Singh. G, Eng Leong Tan, Zhi Ning Chen, A Split-step FDTD Method for 3-D Maxwell's Equations in General Anisotropic Media, IEEE Transactions on Antennas and Propagation, vol. 58, pp.3647-3657, (2010).


[2] Takefumi Namiki, A New FDTD Algorithm Based on Alternating-Direction Implicit Method, IEEE Transactions onf Microwave Theory and Techniques, vol. 47, pp.2003-2007, (1999).


[3] Eng Leong Tan, Acceleration of LOD-FDTD Method Using Fundamental Scheme on Graphics Processor Units, IEEE Microwave and Wireless Components Letters, vol. 20, pp.648-650, (2010).


[4] F. Zheng, Z. Chen, and J. Zhang, A finite-difference time-domain method without the Courant stability conditions, IEEE Microw. Guided Wave Lett., vol. 9, pp.441-443, (1999).


[5] Rouf H. K, Costen F, Garcia D. G, Reduction of numerical errors in frequency dependent ADI-FDTD, IEEE Electronics Letters, vol. 46, pp.489-490, (2010).


[6] G. D. Kondylis, F. D. Flaviis, G. J. Pottie, T. Itoh, A memory-efficient formulation of the finite-difference time-domain method for the solution of Maxwell equation, IEEE Trans. MTT, vol. 49(7), pp.1310-1320, (2001).


[7] B. Liu, B. Q. Gao, W. Tan, and W. Ren, A New FDTD Algorithm-ADI/R-FDTD, in Electromagnetic Compatibility, 2002 3rd International Symposium on, May 21-24, 2002, pp.250-253.


[8] Fenghua Zheng, Zhizhang Chen, Jiazong Zhang. Toward the Development of a Three-Dimensional Unconditionally Stable Finite-Difference Time-Domain Mehtod, IEEE Transactions on Microwave Theory and Techniques, vol. 48(9), pp.1550-1558.