An Iterative Wiener--Hopf Method for Triangular Matrix Functions with Exponential Factors

Kisil, Anastasia V.

doi:10.1137/17m1136304

Cited by 25 publications

(39 citation statements)

References 41 publications

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“…This is unlike other methods such as rational approximation and "pole removal" rely on taking non-zero imaginary part in k 0 . In this paper we also found that the results converge faster for large |k 0 | (which is equivalent to larger L) as was is found in (Kisil 2017).…”

Section: Convergencesupporting

confidence: 82%

“…In the case when k 0 has a small imaginary part the convergence analysis follows almost unchanged as in (Kisil 2017). This gives that convergence occurs for large enough |k 0 |, and is faster the larger |k 0 | is.…”

Section: Convergencementioning

confidence: 84%

“…The convergence of the proposed procedure was considered in (Kisil 2017). It gave some of the sufficient conditions for convergence but not the necessary conditions.…”

Section: Convergencementioning

confidence: 99%

“…In this paper the class of matrix (1.1) is more general than is considered in that paper. Two main differences are that: we have no common strip of analyticity in (1.1) and A, B and C do not belong to the classes described in (Kisil 2017). With respect to the later, on the application of Liouville's theorem the entire functions are constant rather than zero, this is discussed in Section 4.1.…”

Section: Convergencementioning

confidence: 99%

“…Importantly, this method is entirely algorithmic and bypasses the need to construct a multiplicative matrix factorisation. Theoretical aspect of this method were addressed in (Kisil 2017). We validate the method by considering the two-dimensional Wiener-Hopf problem of the scattering of a sound wave by a finite impermeable plate, which has a known solution (McLachlan 1964).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Convergencesupporting

confidence: 82%

Section: Convergencementioning

confidence: 84%

“…The convergence of the proposed procedure was considered in (Kisil 2017). It gave some of the sufficient conditions for convergence but not the necessary conditions.…”

Section: Convergencementioning

confidence: 99%

Section: Convergencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Aerodynamic noise from rigid trailing edges with finite porous extensions

Kisil

Ayton

2017

J. Fluid Mech.

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On Iterative Procedure for a Vectorial Wiener-Hopf Problem with Oscillating Terms

Dubatovskaya,

Livasov,

Mishuris

2024

Analysis Without Borders

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Scattering by two staggered semi-infinite cracks on square lattice: an application of asymptotic Wiener–Hopf factorization

Maurya

Sharma

2019

Z. Angew. Math. Phys.

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Scattering of time-harmonic plane wave by two parallel semi-infinite rows, but with staggered edges, is considered on square lattice. The condition imposed on the semi-infinite rows is a discrete analogue of Neumann boundary condition. A physical interpretation assuming an out-of-plane displacement for the particles arranged in the form of a square lattice and interacting with nearest-neighbours, associates the scattering problem to lattice wave scattering due to the presence of two staggered but parallel crack tips. The discrete scattering problem is reduced to the study of a pair of Wiener-Hopf equation on an annulus in complex plane, using Fourier transforms. Due to the offset between the crack edges, the Wiener-Hopf kernel, a 2 × 2 matrix, is not amenable to factorization in a desirable form and an asymptotic method is adapted. Further, an approximation in the far field is carried out using the stationary phase method. A graphical comparison between the far-field approximation based on asymptotic Wiener-Hopf method and that obtained by a numerical solution is provided. Also included is a graphical illustration of the low frequency approximation, where it has been found that the numerical solution of the scattering problem coincides with the well known formidable solution in the continuum framework.

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An Iterative Wiener--Hopf Method for Triangular Matrix Functions with Exponential Factors

Cited by 25 publications

References 41 publications

Aerodynamic noise from rigid trailing edges with finite porous extensions

Aerodynamic noise from rigid trailing edges with finite porous extensions

On Iterative Procedure for a Vectorial Wiener-Hopf Problem with Oscillating Terms

Scattering by two staggered semi-infinite cracks on square lattice: an application of asymptotic Wiener–Hopf factorization

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