Closed-Form Uniform Asymptotic Expansions of Green's Functions in Layered Media

Accurate and efficient formulas for computing spatial domain Green's functions are presented in this article. To apply the formulas, we only require a set of sample points of the spectral domain Green's function on an integration path avoiding its singularities and an infinite domain tail path. Since the sampling is carried out for the integrand excluding the Bessel function, the number of sample points required is much smaller than the numerical integration method. This aspect of the proposed method, proves to be very advantageous for evaluating closed form Green's functions at large source observer distances. It is shown that, the proposed formulas provide accurate results both for the near and far-field regions as well as a wide range of material parameters such as lossless, lossy, left-handed materials as well as multi-layered substrates. Index Terms-Sommerfeld Integral, Spatial domain Green's function.0018-926X (c)

“…2 ] are directly used as end-points of PWS into the derived formulas without any restrictions on intermediate expressions as in [17]- [19].…”

Section: Statement Of the Problemmentioning

confidence: 99%

Analytical Expressions for Spatial-Domain Green’s Functions in Layered Media

Kurup

2015

“…The complex poles can be obtained through a modified vector fitting algorithm [21] or total least squares method [23], [24]. Using the following integral identity (16) the corresponding spatial-domain counterpart is obtained as (17) Finally, the closed-form representations of spatial-domain MPGF are obtained by addition of (12), (14), and (17).…”

Section: Formulationmentioning

confidence: 99%

Accurate Calculation of Mutual Coupling Between Apertures on a Large Coated Cylinder Using Mixed Potential Green's Functions

Zeng¹,

Jiang²,

et al. 2014

A rigorous approach based on the closed-form mixed potential Green's function (MPGF) is developed to evaluate mutual coupling between apertures on an electrically large cylinder with dielectric covers. An improved procedure is outlined to provide accurate values of the MPGF both in the near and far field, including the axial line region. The cylindrical functions are represented in the form of ratios to avoid the numerical instabilities, making the MPGF able to handle electrically large problems. As a result, a high degree of accuracy is ensured in the calculation of the mutual admittance between two apertures with large separation on an electrically large cylinder. This approach is validated by comparison with published data, and its ability in dealing with complex and electrically large problems is also verified.Index Terms-Cylindrically stratified media, mixed potential Green's function (MPGF), mutual coupling, rational function fitting method (RFFM).

“…To clarify these rather theoretical concepts, let us consider the integral (18) whose meaning in the Abel's sense can be easily established (5a). The partial integrals are readily evaluated as (19) And thus we have the typical divergent oscillating sequence (20) Here, the Hölder means process produces quickly the true value:…”

Section: Weighted Averages Euler and Höldermentioning

confidence: 99%

“…These algorithms are customarily included in existing software tools, either for direct use or as a benchmark to evaluate the accuracy of faster but approximate methods like the complex image formulations [10]- [15]. Today, the WA-based algorithm remains as popular as ever, as witnessed by several recently published papers [16]- [18].…”

Section: Introductionmentioning

confidence: 99%

The Weighted Averages Algorithm Revisited

Mosig

2012

The classic weighted averages (WA) algorithm for the evaluation of Sommerfeld-like integrals is reviewed and reappraised. As a result, a new version of the WA algorithm, called generalized WA, is introduced. The new version can be considered as a generalization of the well established Hölder and Cèsaro means, used to sum divergent series. Generalized WA exhibits a more compact formulation, devoid of iterative and recursive steps, and a wider range of applications. It is more robust, as it provides a unique formulation, valid for monotonic and oscillating functions. The implementation of the new version is easier and more economical in terms of basic operations. Preliminary numerical examples show that generalized WA also outperforms in terms of accuracy the classic WA algorithm, which is currently recognized as the most competitive algorithm to evaluate Sommerfeld integral tails.