Efficient computation of Sommerfeld integral tails – methods and algorithms

Michalski, Krzysztof A.; Mosig, J. R.

doi:10.1080/09205071.2015.1129915

Cited by 103 publications

(54 citation statements)

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“…In Figures 2 and 3 are plotted far-field patterns for the seawater and gold problems, respectively, computed by rigorous integration of Sommerfeld integrals (Michalski, 1998;Michalski & Mosig, 2016b) (solid line) and by the second-order saddle-point method (MSP2) of the present paper (dashed line), although these two results are visually indistinguishable. The fields are computed at a fixed radial distance of k 0 r =100 for elevation angles between 0 ∘ (the z axis) and 90 ∘ (the surface) and are plotted normalized to the maximum values using decibel (dB) scale, with the sin and cos functions set to unity.…”

Section: Sample Numerical Results and Validationmentioning

confidence: 86%

On the Far‐Zone Electromagnetic Field of a Horizontal Electric Dipole Over an Imperfectly Conducting Half‐Space With Extensions to Plasmonics

Michalski

Lin

2018

Radio Science

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Second‐order asymptotic formulas for the electromagnetic fields of a horizontal electric dipole over an imperfectly conducting half‐space are derived using the modified saddle‐point method. Application examples are presented for ordinary and plasmonic media, and the accuracy of the new formulation is assessed by comparisons with two alternative state‐of‐the‐art theories and with the rigorous results of numerical integration.

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Section: Sample Numerical Results and Validationmentioning

confidence: 86%

On the Far‐Zone Electromagnetic Field of a Horizontal Electric Dipole Over an Imperfectly Conducting Half‐Space With Extensions to Plasmonics

Michalski

Lin

2018

Radio Science

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“…However, for a finite scatterer the spectral domain is continuous and now the poles and oscillations along the branch cuts are hard to discretize (Dilz and Beurden 2016, 2017). Deformations of the Sommerfeld integration path to a complex-plane path (Ruiter 1981; Newman and Forrai 1987; Hochman and Leviatan 2010; Michalski and Mosig 2016) can help to evade these poles and branch cuts. In Dilz and Beurden (2017) an algorithm for two-dimensional electromagnetic scattering with TE polarization in a multilayered medium is presented, where both contrast-current density and scattered field are represented on a path in the complex plane of the spectral domain.…”

Section: Introductionmentioning

confidence: 99%

A 3D spatial spectral integral equation method for electromagnetic scattering from finite objects in a layered medium

2018

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The generalization of a two-dimensional spatial spectral volume integral equation to a three-dimensional spatial spectral integral equation formulation for electromagnetic scattering from dielectric objects in a stratified dielectric medium is explained. In the spectral domain, the Green function, contrast current density, and scattered electric field are represented on a complex integration manifold that evades the poles and branch cuts that are present in the Green function. In the spatial domain, the field-material interactions are reformulated by a normal-vector field approach, which obeys the Li factorization rules. Numerical evidence is shown that the computation time of this method scales as on the number of unknowns. The accuracy of the method for three numerical examples is compared to a finite element method reference.

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“…The classical layer Green functions and associated Sommerfeld integrals automatically enforce the relevant transmission conditions on the unbounded flat surfaces and thus reduce the scattering problems to integral equations on the obstacles and/or defects (cf. [19,24]). The Sommerfeld integrals amount to singular Fourier integrals [8,25] whose evaluation is generally quite challenging.…”

Section: Introductionmentioning

confidence: 99%

Windowed Green function method for the Helmholtz equation in the presence of multiply layered media

Bruno

Pérez‐Arancibia

2017

Proc. R. Soc. A.

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This paper presents a new methodology for the solution of problems of two-and threedimensional acoustic scattering (and, in particular, two-dimensional electromagnetic scattering) by obstacles and defects in presence an arbitrary number of penetrable layers. Relying on use of certain slow-rise windowing functions, the proposed Windowed Green Function approach (WGF) efficiently evaluates oscillatory integrals over unbounded domains, with high accuracy, without recourse to the highly expensive Sommerfeld integrals that have typically been used to account for the effect of underlying planar multi-layer structures. The proposed methodology, whose theoretical basis was presented in the recent contribution (SIAM J. Appl. Math. 76(5), p. 1871, 2016), is fast, accurate, flexible, and easy to implement. Our numerical experiments demonstrate that the numerical errors resulting from the proposed approach decrease faster than any negative power of the window size. In a number of examples considered in this paper the proposed method is up to thousands of times faster, for a given accuracy, than corresponding methods based on use of Sommerfeld integrals.

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Efficient computation of Sommerfeld integral tails – methods and algorithms

Cited by 103 publications

References 100 publications

On the Far‐Zone Electromagnetic Field of a Horizontal Electric Dipole Over an Imperfectly Conducting Half‐Space With Extensions to Plasmonics

On the Far‐Zone Electromagnetic Field of a Horizontal Electric Dipole Over an Imperfectly Conducting Half‐Space With Extensions to Plasmonics

A 3D spatial spectral integral equation method for electromagnetic scattering from finite objects in a layered medium

Windowed Green function method for the Helmholtz equation in the presence of multiply layered media

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