A spectral collocation method for acoustic scattering by multiple elastic plates

Colbrook, Matthew J.; Ayton, Lorna J.

doi:10.1016/j.jsv.2019.114904

Cited by 19 publications

(13 citation statements)

References 28 publications

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“…where a constant stiffness has been chosen so that we were able to validate the results with the methods of [9]. We consider a plane wave incident field of angle π/4 and k 0 = 10.…”

Section: Extension To Multiple Platesmentioning

confidence: 99%

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics

Colbrook

Kisil

2020

Proc. R. Soc. A.

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Many problems in fluid mechanics and acoustics can be modelled by Helmholtz scattering off poro-elastic plates. We develop a boundary spectral method, based on collocation of local Mathieu function expansions, for Helmholtz scattering off multiple variable poro-elastic plates in two dimensions. Such boundary conditions, namely the varying physical parameters and coupled thin-plate equation, present a considerable challenge to current methods. The new method is fast, accurate and flexible, with the ability to compute expansions in thousands (and even tens of thousands) of Mathieu functions, thus making it a favourable method for the considered geometries. Comparisons are made with elastic boundary element methods, where the new method is found to be faster and more accurate. Our solution representation directly provides a sine series approximation of the far-field directivity and can be evaluated near or on the scatterers, meaning that the near field can be computed stably and efficiently. The new method also allows us to examine the effects of varying stiffness along a plate, which is poorly studied due to limitations of other available techniques. We show that a power-law decrease to zero in stiffness parameters gives rise to unexpected scattering and aeroacoustic effects similar to an acoustic black hole metamaterial.

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“…where a constant stiffness has been chosen so that we were able to validate the results with the methods of [9]. We consider a plane wave incident field of angle π/4 and k 0 = 10.…”

Section: Extension To Multiple Platesmentioning

confidence: 99%

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics

Colbrook

Kisil

2020

Proc. R. Soc. A.

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“…Dzieciuch wrote the first code for the normal mode model approximated by Chebyshev polynomials [ 17 ]. In 2019, Colbrook et al used the boundary-based collocation spectral method to solve the two-dimensional acoustic scattering problem [ 18 ]. In the same year, Wise et al used the Fourier spectral collocation method to solve the distribution of sound sources.…”

Section: Introductionmentioning

confidence: 99%

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

Wang

Zhu

et al. 2021

Entropy

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The accuracy and efficiency of sound field calculations highly concern issues of hydroacoustics. Recently, one-dimensional spectral methods have shown high-precision characteristics when solving the sound field but can solve only simplified models of underwater acoustic propagation, thus their application range is small. Therefore, it is necessary to directly calculate the two-dimensional Helmholtz equation of ocean acoustic propagation. Here, we use the Chebyshev–Galerkin and Chebyshev collocation methods to solve the two-dimensional Helmholtz model equation. Then, the Chebyshev collocation method is used to model ocean acoustic propagation because, unlike the Galerkin method, the collocation method does not need stringent boundary conditions. Compared with the mature Kraken program, the Chebyshev collocation method exhibits a higher numerical accuracy. However, the shortcoming of the collocation method is that the computational efficiency cannot satisfy the requirements of real-time applications due to the large number of calculations. Then, we implemented the parallel code of the collocation method, which could effectively improve calculation effectiveness.

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“…Our goal in this article is to extend this analysis to linked boundary conditions. A key tool in our analysis is the unified transform (also known as the Fokas method), a novel transform for analyzing boundary value problems for linear (and integrable nonlinear) partial differential equations (PDEs) 7–19 . An excellent pedagogical review of this method can be found in the paper of Deconinck et al 20 …”

Section: Introductionmentioning

confidence: 99%

Kernel density estimation with linked boundary conditions

et al. 2020

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Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking the values of the unknown target density function at the boundaries. We provide a kernel density estimator (KDE) that successfully incorporates this linked boundary condition, leading to a non-self-adjoint diffusion process and expansions in nonseparable generalized eigenfunctions. The solution is rigorously analyzed through an integral representation given by the unified transform (or Fokas method). The new KDE possesses many desirable properties, such as consistency, asymptotically negligible bias at the boundaries, and an increased rate of approximation, as measured by the AMISE. We apply our method to the motivating example in biology and provide numerical experiments with synthetic data, including comparisons with state-of-theart KDEs (which currently cannot handle linked boundary constraints). Results suggest that the new method is fast and accurate. Furthermore, we demonstrate how to build statistical estimators of the boundary conditions satisfied by the target function without a priori knowledge. Our analysis can also be extended to more general This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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A spectral collocation method for acoustic scattering by multiple elastic plates

Cited by 19 publications

References 28 publications

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics

A Mathieu function boundary spectral method for scattering by multiple variable poro-elastic plates, with applications to metamaterials and acoustics

A High-Efficiency Spectral Method for Two-Dimensional Ocean Acoustic Propagation Calculations

Kernel density estimation with linked boundary conditions

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