In this paper, the fast Fourier transform (FFT) to perform spatial convolutions of the time domain discrete Green's functions (DGF) method related to the analysis of the antenna with more than one dimension has been proposed. For this aim, the discrete Green's functions and the currents on the antenna have been appropriately defined periodic so as to use the zero padded fast Fourier transform. The computational complexity of this approach is O(NwNxNyNz log(NxNyNz)), contrary to O(NwNx2Ny2Nz2)for direct implementation of the convolutions. Simulation results demonstrate the great efficiency of the FFTbased spatial convolutions in the modeling of planar antennas.
2. Yang, S. W., Y. K. Chen, and Z. P. Nie, "Simulation of time modulated linear antenna arrays using the FDTD method," Progress In Electromagnetics Research, Vol. 98, 175-190, 2009.
3. Li, J., L. X. Guo, and H. Zeng, "FDTD investigation on bistatic scattering from a target above two-layered rough surface using UPML absorbing condition," Progress In Electromagnetics Research, Vol. 88, 197-211, 2008.
4. Noroozi, Z. and F. Hojjat-Kashani, "Three dimensional FDTD analysis of the dual-band implantable antenna for continuous glucose monitoring," Progress In Electromagnetics Research Letters, Vol. 28, 9-12, 2012.
5. Dzulkipli, N. I., M. H. Jamaluddin, R. Ngah, M. R. Kamarudin, N. Seman, and M. K. A. Rahim, "Mutual coupling analysis using FDTD for dielectric resonator antenna reflectarray radiation prediction," Progress In Electromagnetics Research B, Vol. 41, 121-136, 2012.
6. Vazquez, J. and C. G. Parini, "Discrete Green's function formulation of FDTD method for Electromagnetics modelling," Electronics Letters, Vol. 35, No. 7, 554-555, 1999.
7. Vazquez, J. and C. G. Parini, "Antenna modelling using discrete Green's function formulation of FDTD method," Electronics Letters, Vol. 35, No. 13, 1033-1034, 1999.
8. Kastner, R., "A Multidimensional z-transform evaluation of the discrete finite difference time domain Green's function," IEEE Trans. on Antennas and Propag., Vol. 54, No. 4, 1215-1222, Apr. 2006.
9. Jeng, S. K., "An analytical expression for 3-D dyadic FDTD-compatible Green's function in in¯nite free space via z-transform and partial difference operators," IEEE Trans. on Antennas and Propag., Vol. 59, No. 4, 1347-1355, Apr. 2011.
10. Stefanski, T. P., "Implementation of FDTD-compatible Green's function on heterogeneous CPU-GPU parallel processing system," Progress In Electromagnetics Research, Vol. 135, 297-316, 2013.
11. Ma, W., M. R. Rayner, and C. G. Parini, "Disctere Green's function formulation of the FDTD method and its application in antenna modeling," IEEE Trans. on Antennas and Propag., Vol. 53, No. 1, 339-364, Jan. 2005.
12. Cottee, A., W. Ma, M. R. Rayner, and C. G. Parini, "Application of the DGF-FDTD technique to log periodic antennas," Int. Conf. on Antennas and Propagation, 553-556, UK, Apr. 2003.
13. Sirenko, K. , V. Pazynin, Y. K. Sirenko, and H. Bagci, "An FFT-accelerated FDTD scheme with exact absorbing conditions for characterizing axially symmetric resonant structures," Progress In Electromagnetics Research, Vol. 111, 331-364, 2011.
14. Zhuang, W., Z. Fan, D.-Z. Ding, and Y. An, "Fast analysis and design of frequency selective surface using the GMRESR-FFT method," Progress In Electromagnetics Research B, Vol. 12, 63-80, 2009.
15. Capozzoli, A., C. Curcio, and A. Liseno, "NUFFT-accelerated plane-polar (also phaseless) near-field/far-field transformation," Progress In Electromagnetics Research M, Vol. 27, 59-73, 2012.