A Robust Method for the Computation of Green's Functions in Stratified Media

Polimeridis, Athanasios G.; Yioultsis, Traianos V.; Tsiboukis, T.D.

doi:10.1109/tap.2007.900258

Cited by 31 publications

(23 citation statements)

References 20 publications

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“…2) is lossless, since this is the worst case scenario for the convergence of the series (1) [ (18)]. Also in this section, we will compare the CPU times employed in the computation of via (5) …”

Section: Numerical Resultsmentioning

confidence: 99%

“…And that same 2-D Green's function with 1-D periodicity has also been used in the analysis of the scattering of plane waves from 1-D periodic arrays of lossy strips in free space [3]. Recently, several authors have shown that the nonperiodic Green's functions of multilayered media can be expressed in closed form as linear combinations of spherical and cylindrical waves in homogeneous media [4], [5]. According to this, the 3-D Green's functions of multilayered media with 2-D periodicity can be easily obtained in terms Manuscript of both 3-D homogeneous Green's functions with 2-D periodicity and 2-D homogeneous Green's functions with 2-D periodicity [6], [7].…”

Section: Introductionmentioning

confidence: 99%

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An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

Fructos

Boix

Mesa

et al. 2008

IEEE Trans. Antennas Propagat.

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This paper presents an algorithm for the acceleration of the series involved in the computation of 2-D homogeneous Green's functions with 1-D and 2-D periodicities. The algorithm is based on an original implementation of the spectral Kummer-Poisson's method, and it can be applied to the efficient computation of a wide class of infinite series. In the algorithm the number of asymptotic terms retained in Kummer's transformation is externally controlled so that any of the series that has to be accelerated is split into one series with exponential convergence and another series with algebraic convergence of arbitrarily large order. Numerical simulations have shown that there is an "optimum" number of asymptotic terms retained in Kummer's transformation for which the CPU time needed in the summation of the series is minimized. The CPU times required by Ewald's method for the evaluation of 2-D Green's functions with 1-D and 2-D periodicities have been compared with those required by the present algorithm, and the algorithm has been found to be between 1.2 and 3 times faster than Ewald's method when working in "optimum" operation conditions.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

Fructos

Boix

Mesa

et al. 2008

IEEE Trans. Antennas Propagat.

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“…Instead, application of one of the extrapolation techniques allows us to infer the limit value in (7) by calculating just a few partial integrals . As mentioned in the introduction, WA is a generalization of the Euler transformation, which instead of simple means uses weighted means of consecutive partial sums (8) where are the weights to be chosen. Since , (8) can be written in a following form: (9) Obviously, the optimal solution would come from the annihilation of the remainders of the linearly transformed sequence by imposing an appropriate ratio of the weights (10) In this point the WA method could be considered complete if the remainders were explicitly known, which is, unfortunately, not the case for the sequences of our interest.…”

Section: A Partition-extrapolation Methods Involving Wa Techniquementioning

confidence: 99%

Efficient Algorithms for Computing Sommerfeld Integral Tails

Golubovic

Polimeridis

Mosig

2012

IEEE Trans. Antennas Propagat.

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Abstract-Sommerfeld-integrals (SIs) are ubiquitous in the analysis of problems involving antennas and scatterers embedded in planar multilayered media. It is well known that the oscillating and slowly decaying nature of their integrands makes the numerical evaluation of the SI real-axis tail segment a very time consuming and computationally expensive task. Therefore, SI tails have to be specially treated. In this paper we compare two recently developed techniques for their efficient numerical evaluation. First, a partition-extrapolation method, in which the integration-then-summation procedure is combined with a new version of the weighted averages (WA) extrapolation technique, is summarized. The previous variants of WA technique are also discussed. Then, a review of double-exponential (DE) quadrature formulas for direct integration of the SI tails is presented. The efficient way of implementing the algorithms, their pros and cons, as well as comparisons of their performance are discussed in detail.

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“…Recently, a novel approach was proposed for extracting the surface wave poles by the rational function fitting method (RFFM) in the planar stratified media [17][18][19]. In this approach, the spectrum of the Green's functions was fitted via the RFFM, based on the vector fitting algorithm (VECTFIT) presented in [20,21], after the extraction of the quasistatic part of the spectrum.…”

Section: Introductionmentioning

confidence: 99%

An Efficient Method for the Computation of Mixed Potential Green's Functions in Cylindrically Stratified Media

Ye¹,

Xiao²,

Qiu³

et al. 2012

PIER

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Abstract-Closed-form mixed potential Green's functions (MPGFs) for cylindrically stratified media are derived in terms of quasistaticwave and surface-wave contributions. In order to avoid possible overflow/underflow problems in the numerical calculations of special cylindrical functions such as Bessel and Hankel functions, a novel form of the spectral-domain MPGFs is developed. Then, a twolevel methodology is used for the approximation of the spectraldomain MPGFs. In the first step, the qusistatic components are extracted from the spectral-domain MPGFs, and then transformed into the space domain with the use of the Sommerfeld identity and its derivatives. In the second step, the remaining parts of the spectral-domain MPGFs are approximated in terms of pole-residue expressions via the rational function fitting method (RFFM). The proposed method is efficient and fully automatic, which avoids an analytical cumbersome extraction of the surface wave poles (SWPs), prior to the spectrum fitting. In addition, this method can evaluate the spatial-domain MPGFs accurately and efficiently for both the nearand far-fields. Finally, numerical results for the spatial-domain MPGFs of a two-layer structure are presented and discussed.

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A Robust Method for the Computation of Green's Functions in Stratified Media

Cited by 31 publications

References 20 publications

An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

An Efficient Approach for the Computation of 2-D Green's Functions With 1-D and 2-D Periodicities in Homogeneous Media

Efficient Algorithms for Computing Sommerfeld Integral Tails

An Efficient Method for the Computation of Mixed Potential Green's Functions in Cylindrically Stratified Media

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