volume | PIER Journals

Abstract

This article proposes a computational scheme for a combined field integral equation to compute electromagnetic scattering, which is Reduced order Fitting Green's function's Gradient and Fitting Green's function with Fast Fourier Transform (ROF). This new scheme can greatly reduce computation time compared to integral equation Fast Fourier Transform (IE), as well as Fitting Green's function's Gradient and Fitting Green's function with Fast Fourier Transform (FGG). Firstly, based on the property of Green's functions' integral under special condition, real-coefficient fitting method is utilized to replace the original complex values expression of combination coefficients with the real values. Secondly, a cross-shaped grid named as reduced order grid is presented to reduce computation time for modified near-field coupling impedance. Thirdly, by combining real-coefficient fitting method and reduced order grid, a new scheme of ROF is achieved. Finally, some examples verify ROF, which has advantages, such as higher efficiency than that of IE based on original grid and FGG based on cross-shaped grid, being not sensitive to grid spacing, and keeping the same precision as that of IE based on original grid.

1. Harrington, R. F., Field Computation by Moment Methods, Oxford University Press Oxford, 1996.

2. Engheta, N., W. D. Murthy, V. Rokhlin, and M. S. Vassiliou, "The fast multipole method (FMM) for electromagnetic scattering problems," IEEE Trans. Antennas Propag., Vol. 40, No. 6, 634-641, Jun. 1992.
doi:10.1109/8.144597 Google Scholar

3. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propag. Magn., Vol. 35, No. 3, 7-12, Jun. 1993.
doi:10.1109/74.250128 Google Scholar

4. Song, J., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, Oct. 1997.
doi:10.1109/8.633855 Google Scholar

5. Chew, W. C., J. M. Jin, E. Michielssen, and J. M. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, 2001.

6. Jiang, L.-J. and W. C. Chew, "A mixed-form fast multipole algorithm," IEEE Trans. Antennas Propag., Vol. 53, No. 12, 4145-4156, Dec. 2005.
doi:10.1109/TAP.2005.859915 Google Scholar

7. Bleszynski, M., E. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Sci., Vol. 31, No. 5, 1225-1251, Sep.-Oct. 1996.
doi:10.1029/96RS02504 Google Scholar

8. Nie, X. C., L. W. Li, N. Yuan, T. S. Yeo, and Y. B. Gan, "Precorrected-FFT algorithm for solving combined field integral equations in electromagnetic scattering," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 8, 1171-1187, Jan. 2002.
doi:10.1163/156939302X00697 Google Scholar

9. Mo, S. S. and J.-F. Lee, "A fast IE-FFT algorithm for solving PEC scattering problems," IEEE Trans. Magn., Vol. 41, No. 5, 1476-1479, May 2005.
doi:10.1109/TMAG.2005.844564 Google Scholar

10. Kong, W. B., H. X. Zhou, K. L. Zheng, and W. Hong, "Analysis of multiscale problems using the MLFMA With the assistance of the FFT-based method," IEEE Trans. Antennas Propag., Vol. 63, No. 9, 4184-4188, Sep. 2015.
doi:10.1109/TAP.2015.2444442 Google Scholar

11. Xie, J. Y., H. X. Zhou, W. Hong, W. D. Li, and G. Hua, "A highly accurate FGG-FG-FFT for the combined field integral equation," IEEE Trans. Antennas Propag., Vol. 61, No. 9, 4641-4652, Sep. 2013.
doi:10.1109/TAP.2013.2267652 Google Scholar

12. Sun, H.-L., C. M. Tong, P. Peng, G. X. Zou, and G. L. Tian, "Real-coefficient FGG-FG-FFT for the combined field integral equation," Progress In Electromagnetics Research M, Vol. 54, 19-27, 2017.
doi:10.2528/PIERM16112202 Google Scholar

13. Rao, S. M., D. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818 Google Scholar

14. Yang, K. and A. E. Yilmaz, "Comparison of pre-corrected FFT/adaptive integral method matching schemes," Microw. and Opt. Tech. Lett., Vol. 53, No. 6, 1368-1372, Jun. 2011.
doi:10.1002/mop.26006 Google Scholar

15. Saad, Y., Iterative Methods for Sparse Linear Systems, PWS Publishing Company, 1996.

16. Frigo, M. and S. Johnson, "FFTW manual,", [Online]. Available from: http://www.fftw.org/. Google Scholar

17. Xie, J. Y., H. X. Zhou, W. D. Li, and W. Hong, "IE-FFT for the combined field integral equation applied to electrically large objects," Microw. and Opt. Tech. Lett., Vol. 54, No. 4, 891-896, Apr. 2012.
doi:10.1002/mop.26697 Google Scholar

18. Chen, S.-W., F. Lu, and Y. Ma, "Fitting Green’s function FFT acceleration applied to anisotropic dielectric scattering problems," International Journal of Antennas and Propag., Vol. 2, 1-8, Dec. 2015. Google Scholar

Dr. Hua-Long Sun

Dr. Chuang Ming Tong

Dr. Qi Liu

Dr. Gao Xiang Zou