2019-07-15
A General ADE -FDTD with Crank-Nicolson Scheme for the Simulation of Dispersive Structures
By
Progress In Electromagnetics Research Letters, Vol. 86, 1-6, 2019
Abstract
A general auxiliary differential equation (ADE) finite difference time-domain (FDTD) method with Crank-Nicolson (CN) scheme is proposed to model electromagnetic wave propagation in dispersive materials in this paper. The proposed method introduces an ADE technique that establishes the relationship between the electric displacement vector and electric field intensity with a differential equation in dispersive media. The CN scheme applies only to Faraday's law, resulting in reduced memory usage and computing time. To validate the advantages of the proposed approach, two examples with plane wave propagation in dispersive media are calculated. Compared with the conventional ADE-CN-FDTD method, the results from our proposed method show its accuracy and efficiency for dispersive media simulation.
Citation
Shi-Yu Long, Wei-Jun Chen, Qi-Wen Liang, and Min Zhao, "A General ADE -FDTD with Crank-Nicolson Scheme for the Simulation of Dispersive Structures," Progress In Electromagnetics Research Letters, Vol. 86, 1-6, 2019.
doi:10.2528/PIERL19040801
References

1. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd Ed., Artech House, Boston, MA, 2005.

2. Sun, G. and C. W. Trueman, "Approximate Crank-Nicolson schemes for the 2-D finite-difference time-domain method for TEz waves," IEEE Trans. Antennas Propag., Vol. 52, No. 10, 589-590, May 2004.        Google Scholar

3. Sun, G. and C. W. Trueman, "Efficient implementations of the Crank-Nicolson schemes for the finite-difference time-domain method," IEEE Trans. Microw. Theory Tech., Vol. 54, No. 5, 2275-2284, May 2006.
doi:10.1109/TMTT.2006.873639        Google Scholar

4. Tan, E. L., "Efficient algorithms for Crank-Nicolson-based finite-difference-time domain-methods," IEEE Trans. Microw. Theory Tech., Vol. 56, No. 2, 408-413, Feb. 2006.
doi:10.1109/TMTT.2007.914641        Google Scholar

5. Sadrpour, S.-M., V. Nayyeri, M. Soleimani, and O. M. Ramahi, "A new efficient unconditionally stable finite-differnce time-domain solution of the wave equation," IEEE Trans. Antennas Propag., Vol. 65, No. 6, 3114-3121, Jun. 2017.
doi:10.1109/TAP.2017.2694468        Google Scholar

6. Chen, W.-J., P. Ma, and J. Tian, "A novel ADE-CN-FDTD with improved computational efficiency for dispersive media," IEEE Microwave and Wireless Components Letters, Vol. 28, No. 10, 849-851, Sep. 2018.
doi:10.1109/LMWC.2018.2861208        Google Scholar

7. Chen, W.-J., W. Shao, and B.-Z. Wang, "ADE-Laguerre-FDTD method for wave propagation in general dispersive materials," IEEE Microwave and Wireless Components Letters, Vol. 23, No. 5, 228-230, May 2013.
doi:10.1109/LMWC.2013.2253310        Google Scholar

8. Rouf, H. K., F. Costen, and S. G. Garcia, "3D Crank-Nicolson finite difference time domain method for dispersive media," Electron. Lett., Vol. 45, No. 19, 961-962, Sep. 2009.
doi:10.1049/el.2009.1940        Google Scholar