Accelerating the convergence of series representing the free space periodic Green's function

Singh, Surendra; Richards, W.; Zinecker, J.R.; Wilton, Donald R.

doi:10.1109/8.60985

Cited by 160 publications

(85 citation statements)

References 3 publications

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“…In particular, the infinite array periodic GF for electric source and electric observation point located at the same height , when the source is a unitary pulse in with unit Fourier transform, is (28) where for the sake of simplicity and . If the current generator has unit amplitude, then the expression for the spectral dyadic GF is: (29) where (30) (31) and are the impedances at the section in the equivalent circuit of Fig. 15, and they are equal to the parallel of the input impedances, for the TM and TE th mode respectively, when looking in each one of the two media.…”

Section: Discussionmentioning

confidence: 99%

“…The followed procedure, described in detail in [28], closely resembles the one presented by Wilton in [29] and is based on the Kummer transformation. However, while in [29] the acceleration method was developed for the case of scalar free-space GF, in [28] it has been extended to the dyadic multilayer GF. Moreover, geometrical symmetries are exploited in the calculation of the coupling between basis and test functions.…”

Section: B Efficiency Of the 3d Implementationmentioning

confidence: 99%

See 1 more Smart Citation

Multimode Equivalent Networks for the Design and Analysis of Frequency Selective Surfaces

Monni

Gerini

Neto

et al. 2007

IEEE Trans. Antennas Propagat.

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Section: Discussionmentioning

confidence: 99%

Section: B Efficiency Of the 3d Implementationmentioning

confidence: 99%

Multimode Equivalent Networks for the Design and Analysis of Frequency Selective Surfaces

Monni

Gerini

Neto

et al. 2007

IEEE Trans. Antennas Propagat.

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“…Among the analytical ones, Poisson's formula and Kummer's decompositions [9] represent the most commonly adopted approaches. Numerical acceleration techniques like the Shanks' transformations [10] or the ρ algorithm [11] may also be necessary to further accelerate the result. Improved convergence can be obtained by applying the Ewald's transformation [12].…”

Section: Introductionmentioning

confidence: 99%

Integral-Equation Analysis of Frequency Selective Surfaces Using Ewald Transformation and Lattice Symmetry

Su¹,

Xu²,

He³

et al. 2011

PIER

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Abstract-In this paper, we present the space-domain integralequation method for the analysis of frequency selective surfaces (FSS), consisting of an array of periodic metallic patches or a metal screens perforated periodically with arbitrarily shaped apertures. The computation of the spatial domain Green's function is accelerated by the Ewald transformation. The geometric model is simplified by the lattice symmetry, so that the unknowns are greatly reduced. Time of filling MOM matrix and solving linear system is dramatically reduced. Our technique shows much higher efficiency when compared with the available commercial software and the existing methods published.

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“…Shank's [5], Chebyshev-Toeplitz, ρ [6], θ and Levin's transforms are some of the general algorithms while Kummer, Poisson [7] and Ewald's transforms belong to the second category. Among these methods Shanks' transformation can efficiently evaluate the periodic Green's function of planar stratified media, like the one shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

Computation of Periodic Green's Functions in Layered Media Using Complex Images Technique

Bahadori

Alaeian²,

Faraji‐Dana³

2011

PIER

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Abstract-In this paper, a new method based on the complex images technique has been presented to efficiently compute the Green's functions required in a Mixed Potential Integral Equation (MPIE) analysis of a periodic structure located on a layered medium. This method leads to a closed-form representation of the Green's functions of these periodic structures given in terms of slowly convergent series valid for sub-wavelength as well as super-wavelength cell sizes for all source-point to field-point distances. Comparison between the results obtained by the proposed method and those obtained through other numerical methods verifies its accuracy. Fast convergence, simple final form and versatility of the proposed method are its main advantages which make it suitable for the analysis of the periodic structures using the integral equation techniques.

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Accelerating the convergence of series representing the free space periodic Green's function

Cited by 160 publications

References 3 publications

Multimode Equivalent Networks for the Design and Analysis of Frequency Selective Surfaces

Multimode Equivalent Networks for the Design and Analysis of Frequency Selective Surfaces

Integral-Equation Analysis of Frequency Selective Surfaces Using Ewald Transformation and Lattice Symmetry

Computation of Periodic Green's Functions in Layered Media Using Complex Images Technique

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