Application of Kummer's Transformation to the Efficient Computation of the 3-D Green's Function With 1-D Periodicity

Fructos, A.L.; Boix, Rafael R.; Mesa, Francisco

doi:10.1109/tap.2009.2036188

Cited by 14 publications

(12 citation statements)

References 29 publications

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“…The most effective algorithm for this case has recently been developed in [8]. The convergence rate of the difference series in our approach will be the same as that in [8], and therefore the effectiveness of both approaches is similar.…”

Section: Discussionmentioning

confidence: 96%

“…As shown in the recent study [8], the Kummer's method of high order applied for the Green's functions represented by the series of elementary functions works more effectively than for the series consisting of special functions. Therefore, we can conclude that our modification using elementary functions in the spectral representation of the 2-D Green's function is more effective than the modifications of the Kummer's method [9], [10], and [5] using the series of Hankel functions and modified Bessel functions.…”

Section: Discussionmentioning

confidence: 97%

“…Meanwhile, the authors of [5] have demonstrated in their subsequent paper [8] that the use of series of elementary functions in the Kummer's method of high order yields more efficient algorithms than those of the similar methods using series of special functions such as Hankel functions. That fact means that there is a possibility of further enhancement of the effectiveness in calculation of the 2-D Green's function for 1-D periodic structures compared to the methods proposed in [9], [10], and [5].…”

Section: Introductionmentioning

confidence: 99%

“…The feature and novelty of the approach proposed here consists in such a transformation of the auxiliary series constructed of asymptotic terms of high order of the original series in the Kummer's method that the new auxiliary series keeping the same behavior of its terms allows its summation in closed form unlike the existing realizations, e.g. [8].…”

Section: Introductionmentioning

confidence: 99%

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A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

Skobelev¹

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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A new modification of the Kummer's method of Mth order for 2≤M≤6 is proposed for efficient computation of the 2-D Green's function for 1-D periodic structures in homogeneous media. The modification consists in transformation of the auxiliary series constructed of asymptotic terms of the original spectral series into a new series which, unlike the previous one, allows its summation in closed form. The new representation of the Green's functions consists of a rapidly converging difference series whose terms decay as q -(M+1) , as well a new rigorous expression for the sum of the transformed auxiliary series.

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Section: Discussionmentioning

confidence: 96%

Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

Skobelev¹

2011

2011 XXXth URSI General Assembly and Scientific Symposium

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“…This is done by accelerating the convergence of series summation appearing in the elements of the Galerkin matrix using an asymptotic approximation to the Bessel and Green's functions, followed by an approximation of the infinite summation of each leading term with the fast convergent series. Similar fast convergent series have been used recently for the evaluation of periodic Green's function [14]. Thus, this technique involving asymptotic approximation followed by use of fast convergent series is very simple to understand and apply to different problems in electromagnetics.…”

Section: Introductionmentioning

confidence: 99%

Efficient and Accurate Approximation of Infinite Series Summation Using Asymptotic Approximation and Fast Convergent Series

Jain¹,

Song²

2012

PIER M

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We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green's function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green's function, and the summation of the leading terms is carried out using the fast convergent series. Research M, Vol. 22, 191-203, 2012 EFFICIENT Abstract-We present an approach for very quick and accurate approximation of infinite series summation arising in electromagnetic problems. This approach is based on using asymptotic expansions of the arguments and the use of fast convergent series to accelerate the convergence of each term. It has been validated by obtaining very accurate solution for propagation constant for shielded microstrip lines using spectral domain approach (SDA). In the spectral domain analysis of shielded microstrip lines, the elements of the Galerkin matrix are summations of infinite series of product of Bessel functions and Green's function. The infinite summation is accelerated by leading term extraction using asymptotic expansions for the Bessel function and the Green's function, and the summation of the leading terms is carried out using the fast convergent series.

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Frequency Selective Surfaces

2022

Electromagnetic Shielding

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A methodology is presented for the design synthesis of metamaterials that act as thin multifrequency artificial magnetic conductors. These structures are realized by placing a frequency-selective surface above a conventional prefect electric conductor, separated by a thin dielectric layer. The frequency-selective surface design is optimized using a microgenetic algorithm to operate at multiple, narrow frequency bands. Two examples of genetically engineered multiband high-impedance frequency-selective surfaces (that is, artificial magnetic conductors) are presented and discussed.

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Application of Kummer's Transformation to the Efficient Computation of the 3-D Green's Function With 1-D Periodicity

Cited by 14 publications

References 29 publications

A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

A modification of the kummer's method for efficient computation of the 2-D Green's functions for 1-D periodic structures

Efficient and Accurate Approximation of Infinite Series Summation Using Asymptotic Approximation and Fast Convergent Series

Frequency Selective Surfaces

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