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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

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