Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-18T14:59:07.410Z Has data issue: false hasContentIssue false
  • English
  • Français

Space-FFT-accelerated marching-on-in-degree methods for finite periodic structures

Published online by Cambridge University Press:  19 June 2009

Amir Geranmayeh ,
Wolfgang Ackermann  and
Thomas Weiland
Amir Geranmayeh*
Affiliation:
Institut Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt Schlossgartenstr. 8, 64289 Darmstadt, Germany. Phone: +49 6151164661; Fax: +49 6151164611
Wolfgang Ackermann
Affiliation:
Institut Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt Schlossgartenstr. 8, 64289 Darmstadt, Germany. Phone: +49 6151164661; Fax: +49 6151164611
Thomas Weiland
Affiliation:
Institut Theorie Elektromagnetischer Felder (TEMF), Technische Universitaet Darmstadt Schlossgartenstr. 8, 64289 Darmstadt, Germany. Phone: +49 6151164661; Fax: +49 6151164611
*
Corresponding author: A. Geranmayeh Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A fast, yet unconditionally stable, solution of time-domain electric field integral equations (TD EFIE) pertinent to the scattering analysis of uniformly meshed and/or periodic conducting structures is introduced. A one-dimensional discrete fast Fourier transform (FFT)-based algorithm is proffered to expedite the calculation of the recursive spatial convolution products of the Toeplitz–block–Toeplitz retarded interaction matrices in a new marching-without-time-variable scheme. Additional saving owing to the system periodicity is concatenated with the Toeplitz properties due to the uniform discretization in multi-level sense. The total computational cost and storage requirements of the proposed method scale as O(Nt2Nslog Ns) and O(Nt Ns), respectively, as opposed to O(Nt2Ns2) and O(NtNs2) for classical marching-on-in-order methods, where Nt and Ns are the number of temporal and spatial unknowns, respectively. Simulation results for arrays of plate-like and cylindrical scatterers demonstrate the accuracy and efficiency of the technique.

Keywords

Time-domain integral equation methodsMarching-on-in-order schemesLaguerre polynomialsMulti-level Toeplitz matricesFast Fourier transform
Type
Original Article
Information
International Journal of Microwave and Wireless Technologies , Volume 1 , Special Issue 4: European Microwave Week 2008 , August 2009 , pp. 331 - 337
Copyright
Copyright © Cambridge University Press and the European Microwave Association 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Yilmaz, A.E.; Jin, J.M.; Michielssen, E.: A parallel FFT accelerated transient field-circuit simulator. IEEE Trans. Microw. Theory Tech., 53 (2005), 2851–2865, doi:10.1109/TMTT.2005.854260.CrossRefGoogle Scholar
[2]Geranmayeh, A.; Ackermann, W.; Weiland, T.: Temporal discretization choices for stable boundary element methods in electromagnetic scattering problems. Appl. Numer. Math., 59 (2009), 5–27, doi:10.1016/j.apnum.2008.12.026.CrossRefGoogle Scholar
[3]Yu, W.; Fang, D.; Zhou, C.: Marching-on-in-degree based time domain magnetic field integral equation methods for bodies of revolution. IEEE Microw. Wirel. Compon. Lett., 17 (2007), 813–815, doi:10.1109/LMWC.2007.910455.CrossRefGoogle Scholar
[4]Chung, Y.S. et al. : Solution of time domain electric field integral equation using Laguerre polynomials. IEEE Trans. Antennas Propag., 52 (2004), 2319–2328, doi:10.1109/TAP.2004.835248.CrossRefGoogle Scholar
[5]Ji, Z.; Sarkar, T.K.; Jung, B.H.; Yuan, M.; Salazar-Palma, M.: Solving time domain electric field integral equation without the time variable. IEEE Trans. Antennas Propag., 54 (2006), 258–262, doi:10.1109/TAP.2005.861515.Google Scholar
[6]Jung, B.H.; Ji, Z.; Sarkar, T.K.; Salazar-Palma, M.; Yuan, M.: A comparison of marching-on in time method with marching-on in degree method for the TDIE solver. Prog. Electromagn. Res., 70 (2007), 281–296, doi:10.2528/PIER07013002.CrossRefGoogle Scholar
[7]Aygun, K.; Fischer, B.C.; Meng, J.; Shanker, B.; Michielssen, E.: A fast hybrid field-circuit simulator for transient analysis of microwave circuits. IEEE Trans. Microw. Theory Tech., 52 (2004), 573–583, doi:10.1109/TMTT.2003.821929.CrossRefGoogle Scholar
[8]Hu, J.L.; Chan, C.H.; Xu, Y.: A fast solution of the time domain integral equation using fast Fourier transformation. Microw. Opt. Technol. Lett., 25 (2000), 172–175.3.0.CO;2-P>CrossRefGoogle Scholar
[9]Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T.: A new fast time domain integral equation solution algorithm. IEEE Antennas Propag. Soc. Int. Symp. Dig., 4 (2001), 176–180, doi:10.1109/APS.2001.959427.Google Scholar
[10]Yilmaz, A.E.; Weile, D.S.; Jin, J.M.; Michielssen, E.: A fast Fourier transform accelerated marching-on-in-time algorithm for electromagnetic analysis. Electromagnetics 21 (2001), 181–197, doi:10.1080/02726340116903.CrossRefGoogle Scholar
[11]Bleszynski, E.; Bleszynski, M.; Jaroszewicz, T.: Block–Toeplitz fast integral equation solver for large finite periodic and partially periodic antenna arrays, in Proc. IEEE Topical Conf. Wireless Communication Technology, Honolulu, HI, 2003, 28–32, doi:10.1109/WCT.2003.1321590.CrossRefGoogle Scholar
[12]Barrowes, B.E.; Teixeira, F.L.; Kong, J.A.: Fast algorithm for matrix–vector multiply of asymmetric multilevel block–Toeplitz matrices in 3-D scattering. Microw. Opt. Technol. Lett., 31 (2001), 28–32, doi:10.1002/mop.1348.CrossRefGoogle Scholar
[13]Yilmaz, A.E.; Weile, D.S.; Jin, J.M.; Michielssen, E.: A hierarchical FFT algorithm (HIL-FFT) for the fast analysis of transient electromagnetic scattering phenomena. IEEE Trans. Antennas Propag., 50 (2002), 971–982, doi:10.1109/TAP.2002.802094.CrossRefGoogle Scholar
[14]Geranmayeh, A.; Ackermann, W.; Weiland, T.: FFT-accelerated marching-on-in-order methods, in Proc. 38th European Microwave Conference (EuMC’08), 2008, vol. 11, 511–514, doi:10.1109/EUMC.2008.4751501.CrossRefGoogle Scholar
[15]Geranmayeh, A.; Ackermann, W.; Weiland, T.: Hybrid planar surface elements, in Proc. 13th Biennial IEEE Conf. Electromanetic Field Computation (CEFC'08), Athens, Greece, 2008, vol. PC3, 242.Google Scholar
[16]Bindiganavale, S.S.; Volakis, J.L.; Anastassiu, H.: Scattering from planar structures containing small features using the adaptive integral method (AIM). IEEE Trans. Antennas Propag., 46 (1998), 1867–1878, doi:10.1109/8.743831.CrossRefGoogle Scholar
[17]Yilmaz, A.E.; Jin, J.M.; Michielssen, E.: Time domain adaptive integral method for surface integral equations. IEEE Trans. Antennas Propag., 52 (2004), 2692–2708, doi:10.1109/TAP.2004.834399.CrossRefGoogle Scholar
[18]Geranmayeh, A.; Ackermann, W.; Weiland, T.: Toeplitz property on order indices of Laguerre expansion methods, In IEEE MTT-S Int. Microwave Symp. (IMS'09) Digest, 2009, vol. 1, 1–4.Google Scholar