Vol. 139
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2013-05-05
Applications of the Discrete Green's Function in the Finite-Difference Time-Domain Method
By
Progress In Electromagnetics Research, Vol. 139, 479-498, 2013
Abstract
In this paper, applications of the discrete Green's function (DGF) in the three-dimensional (3-D) finite-difference time-domain (FDTD) method are presented. The FDTD method on disjoint domains was developed employing DGF to couple the subdomains as well as to compute the electromagnetic field outside these subdomains. Hence, source and scatterer are simulated in separate subdomains and updating of vacuum cells, being of little interest from a user point of view, can be avoided. In the developed method, the field radiated by a single subdomain is computed as a convolution of DGF with equivalent current sources measured over two displaced Huygens surfaces. Therefore, the computed electromagnetic field is compatible with the FDTD grid and can be applied as an incident wave in a coupled total-field/scattered-field (TFSF) subdomain. In the developed method, the DGF waveforms are truncated using the Hann's window and windowing parameters assuring accuracy of computations are pointed out. The error of the field computations varies between -90 dB and -40 dB depending on the DGF length and excitation waveform. However, if the DGF length is equal to the number of iterations in a simulation, the presented DGF applications return the same results as the direct FDTD method.
Citation
Tomasz P. Stefanski, "Applications of the Discrete Green's Function in the Finite-Difference Time-Domain Method," Progress In Electromagnetics Research, Vol. 139, 479-498, 2013.
doi:10.2528/PIER13032906
References

1. Vazquez, J. and C. G. Parini, "Discrete Green's function formulation of FDTD method for electromagnetic modelling," Electron. Lett., Vol. 35, No. 7, 554-555, 1999.
doi:10.1049/el:19990416

2. Holtzman, R. and R. Kastner, "The time-domain discrete Green's function method (GFM) characterizing the FDTD grid boundary," IEEE Trans. Antennas Propag., Vol. 49, No. 7, 1079-1093, 2001.
doi:10.1109/8.933488

3. Holtzman, R., R. Kastner, E. Heyman, and R. W. Ziolkowski, "Stability analysis of the Green's function method (GFM) used as an ABC for arbitrarily shaped boundaries," IEEE Trans. Antennas Propag., Vol. 50, No. 7, 1017-1029, 2002.
doi:10.1109/TAP.2002.802272

4. Jeng, S.-K., "An analytical expression for 3-D dyadic FDTD-compatible Green's function in infinite free space via z-transform and partial difference operators," IEEE Trans. Antennas Propag., Vol. 59, No. 4, 1347-1355, 2011.
doi:10.1109/TAP.2011.2109363

5. Taflove, A. and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd edition, Artech House, Boston, 2005.

6. Xiao, S.-Q., Z. Shao, and B.-Z. Wang, "Application of the improved matrix type FDTD method for active antenna analysis," Progress In Electromagnetics Research, Vol. 100, 245-263, 2010.
doi:10.2528/PIER09112204

7. Lee, K. H., I. Ahmed, R. S. M. Goh, E. H. Khoo, E. P. Li, and T. G. G. Hung, "Implementation of the FDTD method based on Lorentz-Drude dispersive model on GPU for plasmonics applications," Progress In Electromagnetics Research, Vol. 116, 441-456, 2011.

8. Kong, L.-Y., J. Wang, and W.-Y. Yin, "A novel dielectric conformal FDTD method for computing SAR distribution of the human body in a metallic cabin illuminated by an intentional electromagnetic pulse (IEMP)," Progress In Electromagnetics Research, Vol. 126, 355-373, 2012.
doi:10.2528/PIER11112702

9. Xiong, R., B. Chen, J.-J. Han, Y.-Y. Qiu, W. Yang, and Q. Ning, "Transient resistance analysis of large grounding systems using the FDTD method," Progress In Electromagnetics Research, Vol. 132, 159-175, 2012.

10. 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, 9-21, 2012.
doi:10.2528/PIERL11070113

11. Wahl, P., D. S. Ly Gagnon, C. Debaes, J. Van Erps, N. Vermeulen, D. A. B. Miller, and H. Thienpont, "B-calm: An open-source multi-gpu-based 3D-FDTD with multi-pole dispersion for plasmonics," Progress In Electromagnetics Research, Vol. 138, 467-478, 2013.

12. Ma, W., M. R. Rayner, and C. G. Parini, "Discrete Green's function formulation of the FDTD method and its application in antenna modeling," IEEE Trans. Antennas Propag., Vol. 53, No. 1, 339-346, 2005.
doi:10.1109/TAP.2004.838797

13. Vazquez, J. and C. G. Parini, "Antenna modelling using discrete Green's function formulation of FDTD method," Electron. Lett., Vol. 35, No. 13, 1033-1034, 1999.
doi:10.1049/el:19990741

14. Holtzman, R., R. Kastner, E. Heyman, and R. W. Ziolkowski, "Ultra-wideband cylindrical antenna design using the Green's function method (GFM) as an absorbing boundary condition (ABC) and the radiated field propagator in a genetic optimization," Microw. Opt. Tech. Lett., Vol. 48, No. 2, 348-354, 2006.
doi:10.1002/mop.21346

15. Mirhadi, S., M. Soleimani, and A. Abdolali, "An FFT-based approach in acceleration of discrete Green's function method for antenna analysis," Progress In Electromagnetics Research M, Vol. 29, 17-28, 2013.

16. Tan, T. and M. Potter, "Optimized analytic field propagator (O-AFP) for plane wave injection in FDTD simulations," IEEE Trans. Antennas Propag., Vol. 58, No. 3, 824-831, 2010.
doi:10.1109/TAP.2009.2039310

17. Merewether, D. E. and R. Fisher, "An application of the equivalence principle to the finite-difference analysis of EM fields inside complex cavities driven by large apertures," Proc. IEEE Antennas Propag. Soc. Int. Symp., 495-498, 1982.

18. Schneider, J. B. and K. Abdijalilov, "Analytic field propagation TFSF boundary for FDTD problems involving planar interfaces: PECs, TE, and TM," IEEE Trans. Antennas Propag., Vol. 54, No. 9, 2531-2542, 2006.
doi:10.1109/TAP.2006.880757

19. Chew, W. C., "Electromagnetic theory on a lattice," Journal of Applied Physics, Vol. 75, No. 10, 4843-4850, 1994.
doi:10.1063/1.355770

20. Clemens, M. and T. Weiland, "Discrete electromagnetism with the finite integration technique," Progress In Electromagnetics Research, Vol. 32, 65-87, 2001.
doi:10.2528/PIER00080103

21. Schuhmann, R. and T. Weiland, "Conservation of discrete energy and related laws in the finite integration technique," Progress In Electromagnetics Research, Vol. 32, 301-316, 2001.
doi:10.2528/PIER00080112

22. Bossavit, A., "Generalized finite differences' in computational electromagnetics," Progress In Electromagnetics Research, Vol. 32, 45-64, 2001.
doi:10.2528/PIER00080102

23. Teixeira, F. L., "Geometric aspects of the simplicial discretization of Maxwell's equations," Progress In Electromagnetics Research, Vol. 32, 171-188, 2001.
doi:10.2528/PIER00080107

24. Mouysset, V. P., A. Mazet, and P. Borderies, "Efficient treatment of 3D time-domain electromagnetic scattering scenes by disjointing sub-domains and with consistent approximations," Progress In Electromagnetics Research, Vol. 71, 41-57, 2007.
doi:10.2528/PIER07013005

25. De Hon, B. P. and J. M. Arnold, "Stable FDTD on disjoint domains - A discrete Green's function diakoptics approach," Proc. The 2nd European Conf. on Antennas and Propag. (EuCAP), 1-6, 2007.

26. Murbach, M., E. Cabot, E. Neufeld, M.-C. Gosselin, A. Christ, K. P. Pruessmann, and N. Kuster, "Local SAR enhancements in anatomically correct children and adult models as a function of position within 1.5T MR body coil," Progress in Biophysics and Molecular Biology, Vol. 107, No. 3, 428-433, 2011.
doi:10.1016/j.pbiomolbio.2011.09.017

27. Benkler, S., N. Chavannes, and N. Kuster, "Novel FDTD Huygens source enables highly complex simulation scenarios on ordinary PCs," Proc. IEEE Antennas Propag. Soc. Int. Symp., 1-4, 2009.

28. Stefanski, T. P., "Discrete Green's function approach to disjoint domain simulations in 3D FDTD method," Electron. Lett., Vol. 49, No. 9, 597-599, 2013.
doi:10.1049/el.2012.4462

29. Merewether, D. E., R. Fisher, and F. W. Smith, "On implementing a numeric Huygen's source scheme in a finite difference program to illuminate scattering bodies," IEEE Trans. Nucl. Sci., Vol. 27, No. 6, 1829-1833, 1980.
doi:10.1109/TNS.1980.4331114

30. Martin, T., "An improved near- to far-zone transformation for the finite-difference time-domain method," IEEE Trans. Antennas Propag., Vol. 46, No. 9, 1263-1271, 1998.
doi:10.1109/8.719968

31. Stefanski, T. P., "Fast implementation of the FDTD-compatible Green's function on multicore processor," IEEE Antennas Wireless Propag. Lett., Vol. 11, 81-84, 2012.
doi:10.1109/LAWP.2012.2183632

32. Stefanski, T. P. and K. Krzyzanowska, "Implementation of FDTD-compatible Green's function on graphics processing unit," IEEE Antennas Wireless Propag. Lett., Vol. 11, 1422-1425, 2012.
doi:10.1109/LAWP.2012.2229380

33. 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.

34. Oppenheim, A. V., R. W. Schafer, and J. R. Buck, Discrete-time Signal Processing, 2nd edition, Prentice-Hall, Englewood Cliffs, 1999.

35. Lei, J.-Z., C.-H. Liang, and Y. Zhang, "Study on shielding effectiveness of metallic cavities with apertures by combining parallel FDTD method with windowing technique," Progress In Electromagnetics Research, Vol. 74, 85-112, 2007.
doi:10.2528/PIER07041905

36. Stefanski, T. P., "Accuracy of the discrete Green's function ormulation of the FDTD method," IEEE Trans. Antennas Propag., Vol. 61, 829-835, 2013.
doi:10.1109/TAP.2012.2224837

37. Laakso, T. I., V. Valimaki, M. Karjalainen, and U. K. Laine, "Splitting the unit delay," IEEE Signal Proc. Mag., Vol. 13, No. 1, 30-60, 1996.
doi:10.1109/79.482137

38. Schneider, J. B. and C. L. Wagner, "FDTD dispersion revisited: Faster-than-light propagation," IEEE Microwave and Guided Wave Lett., Vol. 9, No. 2, 54-56, 1999.
doi:10.1109/75.755044

39. Olkkonen, J. T. and H. Olkkonen, "Fractional delay filter based on the B-spline transform," IEEE Signal Proc. Lett., Vol. 14, No. 2, 97-100, 2007.
doi:10.1109/LSP.2006.882103

40. Olkkonen, J. T. and H. Olkkonen, "Fractional time-shift B-spline filter," IEEE Signal Proc. Lett., Vol. 14, No. 10, 688-691, 2007.
doi:10.1109/LSP.2007.896402