Vol. 58
Latest Volume
All Volumes
PIERM 126 [2024] PIERM 125 [2024] PIERM 124 [2024] PIERM 123 [2024] PIERM 122 [2023] PIERM 121 [2023] PIERM 120 [2023] PIERM 119 [2023] PIERM 118 [2023] PIERM 117 [2023] PIERM 116 [2023] PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2017-07-04
ROF for the Combined Field Integral Equation
By
Progress In Electromagnetics Research M, Vol. 58, 87-96, 2017
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.
Citation
Hua-Long Sun, Chuang Ming Tong, Qi Liu, and Gao Xiang Zou, "ROF for the Combined Field Integral Equation," Progress In Electromagnetics Research M, Vol. 58, 87-96, 2017.
doi:10.2528/PIERM17032403
References

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.