This article proposes a new scheme of real-coefficient fitting both Green's function and its gradient with Fast Fourier Transform (RFGG-FG-FFT) for combined field integral equation (CFIE) to compute the conducting object's electromagnetic scattering, which improves original fitting both Green's function and its gradient with Fast Fourier Transform (FGG-FG-FFT) on efficiency. Firstly, based on Moore-Penrose generalized inverse, an equivalent form of fitting matrix equation is obtained containing the property of Green's function's integral proved by addition theorem. Based on this property, with truncated Green's function new fitting technique is presented for computing fitting coefficients with real value expression, which is different from complex value expression by the original fitting technique in FGG-FG-FFT. Numerical analysis of error shows that new fitting technique has the same accuracy, but only one half of sparse matrices' storage compared to the original fitting technique in FGG-FG-FFT. Finally, the new scheme combining FGG-FG-FFT and new fitting technique is constructed. Some examples show that the new scheme is accurate and effective compared to FGG-FG-FFT and p-FFT.
1. Harrington, R. F., Field Computation by Moment Methods, Oxford University Press Oxford, England, 1996.
2. 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
3. Nie, X.-C., J. L.-W. Li, and N. Yuan, "Precorrected-FFT algorithm for solving combined field integral equations in electromagnetic scattering," Journal of Electromagnetic Waves and Applications, Vol. 16, No. 8, 574-577, 2002. doi:10.1163/156939302X00697
4. 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
5. 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
6. 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
7. Xie, J. Y., H. X. Zhou, X. Mu, G. Hua, W. D. Li, and W. Hong, "p-FFT and FG-FFT with real coefficients algorithm for the EFIE," J. Southeast Univ., Vol. 30, No. 3, 267-270, Sep. 2014.
8. Abramowitz, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.
9. 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
11. 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
12. Stratton, J. A., Electromagnetic Theory, McGraw-Hill Book Company, New York, 1941.
13. Frigo, M. and S. Johnson, FFTW Manual, [Online]. Available: http://www.fftw.org/.
14. 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