The Wiener-Hopf Method in Electromagnetics

Daniele, Vito; Zich, R.E.

doi:10.1049/sbew503e

Cited by 101 publications

(97 citation statements)

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“…A convention is introduced here to distinguish the additive and the multiplicative factorisation by using a superscript and subscript notation (e.g K(α) = K − (α) + K + (α) for additive Wiener-Hopf splitting and K(α) = K − (α)K + (α) for multiplicative factorisation). For more details on the scalar factorisation see (Noble 1958;Daniele & Zich 2014).…”

Section: Approximate Wiener-hopf Factorisationmentioning

confidence: 99%

Aerodynamic noise from rigid trailing edges with finite porous extensions

Kisil

Ayton

2017

J. Fluid Mech.

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This paper investigates the effects of finite flat porous extensions to semi-infinite impermeable flat plates in an attempt to control trailing-edge noise through bio-inspired adaptations. Specifically the problem of sound generated by a gust convecting in uniform mean steady flow scattering off the trailing edge and permeable-impermeable junction is considered. This setup supposes that any realistic trailing-edge adaptation to a blade would be sufficiently small so that the turbulent boundary layer encapsulates both the porous edge and the permeable-impermeable junction, and therefore the interaction of acoustics generated at these two discontinuous boundaries is important. The acoustic problem is tackled analytically through use of the Wiener-Hopf method. A two-dimensional matrix Wiener-Hopf problem arises due to the two interaction points (the trailing edge and the permeable-impermeable junction). This paper discusses a new iterative method for solving this matrix Wiener-Hopf equation which extends to further two-dimensional problems in particular those involving analytic terms that exponentially grow in the upper or lower half planes. This method is an extension of the commonly used "pole removal" technique and avoids the needs for full matrix factorisation. Convergence of this iterative method to an exact solution is shown to be particularly fast when terms neglected in the second step are formally smaller than all other terms retained. The new method is validated by comparing the iterative solutions for acoustic scattering by a finite impermeable plate against a known solution (obtained in terms of Mathieu functions). The final acoustic solution highlights the effects of the permeable-impermeable junction on the generated noise, in particular how this junction affects the far-field noise generated by high-frequency gusts by creating an interference to typical trailing-edge scattering. This effect results in partially porous plates predicting a lower noise reduction than fully porous plates when compared to fully impermeable plates.

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Section: Approximate Wiener-hopf Factorisationmentioning

confidence: 99%

Aerodynamic noise from rigid trailing edges with finite porous extensions

Kisil

Ayton

2017

J. Fluid Mech.

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“…However, the Wiener‐Hopf kernel can require a sophisticated scalar factorization (Bates & Mittra, ; Kobayashi, ). Moreover, the Wiener‐Hopf (WH) technique is applied for the PEC right‐angled wedge (Daniele & Zich, ) but without reporting numerical results. However, the above bibliographic references are used to validate and test the procedure proposed in this work.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper the formulation of the problem is obtained by applying the GWHT. Efficient approximate solutions are obtained via the factorization technique known as Fredholm factorization (Daniele & Lombardi, ; Daniele & Zich, ). A preliminary work on this approach for the considered problem has been presented in Daniele (), Daniele (), and Daniele et al ().…”

Section: Introductionmentioning

confidence: 99%

The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 1. Formulation and Validation

2017

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Complex scattering problems are often made by composite structures where wedges and penetrable substrates may interact at near field. In this paper (Part 1) together with its companion paper (Part 2) we study the canonical problem constituted of a Perfectly Electrically Conducting (PEC) wedge lying on a grounded dielectric slab with a comprehensive mathematical model based on the application of the Generalized Wiener‐Hopf Technique (GWHT) with the help of equivalent circuital representations for linear homogenous regions (angular and layered regions). The proposed procedure is valid for the general case, and the papers focus on E‐polarization. The solution is obtained using analytical and semianalytical approaches that reduce the Wiener‐Hopf factorization to integral equations. Several numerical test cases validate the proposed method. The scope of Part 1 is to present the method and its validation applied to the problem. The companion paper Part 2 focuses on the properties of the solution, and it presents physical and engineering insights as Geometrical Theory of Diffraction (GTD)/Uniform Theory of Diffraction(UTD) coefficients, total far fields, modal fields, and excitation of surface and leaky waves for different kinds of source. The structure is of interest in antenna technologies and electromagnetic compatibility (tip on a substrate with guiding and antenna properties).

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“…The study of PDEs is a vast and expanding area of research [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. This paper concerns the Wiener-Hopf method, which is used for a broad collection of PDEs [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Combining Rational Approximation with Asymptotic Wiener–Hopf Factorization Algorithm for Matrix Functions: Implementation and Testing

Rougerie¹,

Kisil²

2017

J Appl Computat Math

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This paper discusses how an asymptotic Wiener-Hopf factorization can be implemented for a wide class of functions. Asymptotic Wiener-Hopf factorization was discussed [19] and the convergence for matrices sufficiently close to the identity matrix is shown. We demonstrate how the algorithm can be successfully implemented with the help of the rational approximations. The idea is to simplify the matrix first by rationally approximating and then perform the approximate factorisation. There is no compromise in accuracy since the factorisation is approximate anyway and rational approximations are very precise usually. There is also a mapping of real line discussed and implemented to make the rational approximation more optimal. The code is tested against some easy examples which are calculated by hand. The use of this code is illustrated with some more complicated matrix functions motivated by applications. The method has been implemented for 2 × 2 and 4 × 4 matrices but can easy be adapted for any size matrix. The code will be made available with the publication of this paper. We note that to date there are very few implemented Wiener-Hopf factorisation available due to instabilities, so this paper will make an important contribution to this area.

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The Wiener-Hopf Method in Electromagnetics

Cited by 101 publications

References 0 publications

Aerodynamic noise from rigid trailing edges with finite porous extensions

Aerodynamic noise from rigid trailing edges with finite porous extensions

The Electromagnetic Field for a PEC Wedge Over a Grounded Dielectric Slab: 1. Formulation and Validation

Combining Rational Approximation with Asymptotic Wiener–Hopf Factorization Algorithm for Matrix Functions: Implementation and Testing

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