An IE-FFT Algorithm to Analyze PEC Objects for MFIE Formulation

  • Received : 2018.03.15
  • Accepted : 2018.09.28
  • Published : 2019.01.31


An IE-FFT algorithm is implemented and applied to the electromagnetic (EM) solution of perfect electric conducting (PEC) scattering problems. The solution of the method of moments (MoM), based on the magnetic field integral equation (MFIE), is obtained for PEC objects with closed surfaces. The IE-FFT algorithm uses a uniform Cartesian grid to apply a global fast Fourier transform (FFT), which leads to significantly reduce memory requirement and speed up CPU with an iterative solver. The IE-FFT algorithm utilizes two discretizations, one for the unknown induced surface current on the planar triangular patches of 3D arbitrary geometries and the other on a uniform Cartesian grid for interpolating the free-space Green's function. The uniform interpolation of the Green's functions allows for a global FFT for far-field interaction terms, and the near-field interaction terms should be adequately corrected. A 3D block-Toeplitz structure for the Lagrangian interpolation of the Green's function is proposed. The MFIE formulation with the IE-FFT algorithm, without the help of a preconditioner, is converged in certain iterations with a generalized minimal residual (GMRES) method. The complexity of the IE-FFT is found to be approximately $O(N^{1.5})$and $O(N^{1.5}logN)$ for memory requirements and CPU time, respectively.


Fast Fourier Transform (FFT);Integral Equation (IE);Method of Moments (MoM)


  1. R. F. Harrington, Field Computation by Moment Methods. New York, NY: The Macmillan Company, 1968.
  2. R. E. Hodges and Y. Rahmat-Samii, "The evaluation of MFIE integrals with the use of vector triangle basis functions," Microwave and Optical Technology Letters, vol. 14, no. 1, pp. 9-14, 1997.<9::AID-MOP4>3.0.CO;2-P
  3. O. Ergul and L. Gurel, "Improved testing of the magneticfield integral equation," IEEE Microwave and Wireless Components Letters, vol. 15, no. 10, pp. 615-617, 2005.
  4. J. M. Song and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microwave and Optical Technology Letters, vol. 10, no. 1, pp. 14-19, 1995.
  5. S. M. Seo and J. F. Lee, "A single-level low rank IE-QR algorithm for PEC scattering problems using EFIE formulation," IEEE Transactions on Antennas and Propagation, vol. 52, no. 8, pp. 2141-2146, 2004.
  6. K. Zhao, M. N. Vouvakis, and J. F. Lee, "Application of the multilevel adaptive cross-approximation on ground plane designs," in Proceedings of 2004 International Symposium on Electromagnetic Compatibility (EMC), Silicon Valley, CA, 2004, pp. 124-127.
  7. J. R. Phillips and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 16, no. 10, pp. 1059-1072, 1997.
  8. E. Bleszynski, M. Bleszynski, and T. Jaroszewicz, "AIM: adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Science, vol. 31, no. 5, pp. 1225-1251, 1996.
  9. S. M. Seo, C. Wang, and J. F. Lee, "Analyzing PEC scattering structure using an IE-FFT algorithm," ACES Journal (The Applied Computational Electromagnetic Society Journal), vol. 24, no. 2, pp. 116-128, 2009.
  10. S. Rao, D. Wilton, and A. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Transactions on Antennas and Propagation, vol. 30, no. 3, pp. 409-418, 1982.
  11. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: The Johns Hopkins University Press, 1996.