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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: geranmayeh@temf.tu-darmstadt.de
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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

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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