A hybrid uniform geometrical theory of diffraction–moment method for efficient analysis of electromagnetic radiation/scattering from large finite planar arrays

Çivi, Özlem Aydın; Pathak, P.H.; Chou, Hsi‐Tseng; Nepa, Paolo

doi:10.1029/1999rs001922

Cited by 64 publications

(50 citation statements)

References 17 publications

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“…66 60. Convergence of the Ewald sums in (18) with (28) and (33) (28) and (33), respectively. One term (n = 0) in G spatial is sufficient for excellent accuracy.…”

Section: Intentionally Left Blankmentioning

confidence: 97%

“…Civi also solves a truncated array of short dipole antennas each modeled with a single basis function [28]. Unlike Neto and Cucini, Civi solves for the total current on the array.…”

Section: Work Pertaining To Seamsmentioning

confidence: 99%

“…The convergence properties of G spectral and G spatial , in (28) and (33), respectively, are analyzed here. First we derive the so called "optimum" Ewald splitting parameter E 0 , and then we show that in some specific important cases this choice leads to a high-frequency breakdown.…”

Section: Asymptotic Convergence Of G Spectral and G Spatialmentioning

confidence: 99%

“…When truncating the two series in (28) and (33) as P Q q=−Q and P N n=−N , respectively, resulting in a total number of terms 2Q + 1 and 2N + 1, the optimum Ewald splitting parameter E 0 , minimizes the total number (2Q + 1) + (2N + 1) of necessary q, n-terms.…”

Section: The Optimum Ewald Splitting Parameter Ementioning

confidence: 99%

“…The total number of terms needed is determined by observing that to obtain roughly the same number of significant digits of accuracy in each sum in (28) and (33), the asymptotic approximation of their terms in (34) and (35), respectively, must have the same exponential factor e −σ 2 , and thus we set…”

Section: The Optimum Ewald Splitting Parameter Ementioning

confidence: 99%

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Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Johnson¹,

Warne²,

Jorgenson³

et al. 2006

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In this LDRD we examine techniques to analyze the electromagnetic scattering from structures that are nearly periodic. Nearly periodic could mean that one of the structure's unit cells is different from all the others -a defect. It could also mean that the structure is truncated, or butted up against another periodic structure to form a seam. Straightforward electromagnetic analysis of these nearly periodic structures requires us to grid the entire structure, which would overwhelm today's computers and the computers in the foreseeable future. In this report we will examine various approximations that allow us to continue to exploit some aspects of the structure's periodicity and thereby reduce the number of unknowns required for analysis. We will use the Green's Function Interpolation with a Fast Fourier Transform (GIFFT) to examine isolated defects both in the form of a source dipole over a meta-material slab and as a rotated dipole in a finite array of dipoles. We will look at the numerically exact solution of a one-dimensional seam. In order to solve a two-dimensional seam, we formulate an efficient way to calculate the Green's function of a 1d array of point sources. We next formulate ways of calculating the far-field due to a seam and due to array truncation based on both array theory and high-frequency asymptotic methods. We compare the high-frequency and GIFFT results. Finally, we use GIFFT to solve a simple, two-dimensional seam problem.3

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“…66 60. Convergence of the Ewald sums in (18) with (28) and (33) (28) and (33), respectively. One term (n = 0) in G spatial is sufficient for excellent accuracy.…”

Section: Intentionally Left Blankmentioning

confidence: 97%

“…Civi also solves a truncated array of short dipole antennas each modeled with a single basis function [28]. Unlike Neto and Cucini, Civi solves for the total current on the array.…”

Section: Work Pertaining To Seamsmentioning

confidence: 99%

Section: Asymptotic Convergence Of G Spectral and G Spatialmentioning

confidence: 99%

Section: The Optimum Ewald Splitting Parameter Ementioning

confidence: 99%

Section: The Optimum Ewald Splitting Parameter Ementioning

confidence: 99%

See 3 more Smart Citations

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Johnson¹,

Warne²,

Jorgenson³

et al. 2006

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Uniform Geometrical Theory of Diffraction

Pathak

2005

Encyclopedia of RF and Microwave Engineering

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Keller's geometrical theory of diffraction (GTD) [1,2] constitutes a major breakthrough for solving problems of electromagnetic (EM) radiation and scattering at high frequencies. The GTD can also be applied to solving acoustic and elastic wave problems; however, only the EM case is discussed here. Recently, the development of fast solvers for signifi‐cantly increasing the efficiency of numerical methods in solving large problems has met with some success. However, for truly large problems, asymptotic high‐frequency methods in general, and especially ray methods such as the GTD and its uniform version, still remain the most useful analysis tools.

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An efficient synthesis approach for electromagnetic near‐ and far‐field contoured patterns using alternative narrow‐beam field functions transformed from the radiations of linearly excited array antennas with least computational complexity

Chou

2015

Radio Science

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This paper presents an effective scheme to accelerate the computational efficiency in synthesizing the electromagnetic contoured patterns spanned by the radiations of phased array antennas, which is applicable to synthesize both the near-and far-field patterns. The core concept is to adapt/create closed-form and simple formulations with least computational unknowns to be used in the iterative synthesis procedure. The efficiency is assured by avoiding the cumbersome numerical integration/summation for the radiation fields in the synthesis procedure. Thus, the scheme first transforms the conventional field basis functions (FBFs) defined by the radiations of every array elements into a set of global FBFs arising from the radiations of a set of overlapped virtual arrays, where each of the virtual arrays is properly excited by a Gaussian taper to avoid the ray caustic problems encountered in the asymptotic evaluations. The new FBFs (NFBFs) created by this transformation have radiation fields focused in narrow spans in contrast to the wide patterns of conventional FBFs and may reduce the number of FBFs in the computation if a small coverage area is considered. Furthermore, the closed-form formulations of global NFBFs are obtained by asymptotic evaluation and may dramatically reduce the computational time. This approach is implemented with the use of successive projection method, which also provides closed-form formulations to update the excitations in each iterative step, to synthesize the near-and far-field contoured patterns to demonstrate the feasibility and efficiency.

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A hybrid uniform geometrical theory of diffraction–moment method for efficient analysis of electromagnetic radiation/scattering from large finite planar arrays

Cited by 64 publications

References 17 publications

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Analysis of electromagnetic scattering by nearly periodic structures: an LDRD report.

Uniform Geometrical Theory of Diffraction

An efficient synthesis approach for electromagnetic near‐ and far‐field contoured patterns using alternative narrow‐beam field functions transformed from the radiations of linearly excited array antennas with least computational complexity

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