A clarification of nonexistence problems with the superposition method

Wilton, D.T.; Mathews, I. C.; Jeans, Richard

doi:10.1121/1.408140

Cited by 24 publications

(12 citation statements)

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“…10 As a remedy to this, we consider another set of point sources, s m,2 displaced inward from the sphere's surface by d 2 ¼ 0.0072 m. Then we consider the composite Green's functions of the form s m ¼ ð1 þ 1000i=kÞ s m;1 þ ð1 À 1000i=kÞ s m;2 :…”

Section: Numerical Examplesmentioning

confidence: 99%

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Scattering from a finite cylinder near an interface

Fawcett

2014

The Journal of the Acoustical Society of America

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In this paper, a Boundary Integral Equation Method (BIEM) is described for the computation of scattering from a finite, rigid, cylinder near a pressure release interface. The cylinder lies parallel or tilted with respect to the interface plane so that the azimuthal symmetry of the problem is destroyed. The scattering solution is first described in terms of an azimuthally symmetric free space solution. The multiple interactions of the scattered field with the interface are accounted for by an azimuthal-conversion matrix. In Sec. III, the method of this paper is benchmarked using wavefield superposition for a sphere near a pressure-release surface. Computed scattered spectra are shown for a finite cylinder, parallel and tilted with respect to the interface, and for a variety of source/receiver geometries. The differences resulting from not including multiple target/interface interactions (single scatter solution) and from including all interactions are presented. The problem of irregular frequencies for the single-scatter and the fully coupled BIEM are discussed and numerically examined.

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Section: Numerical Examplesmentioning

confidence: 99%

“…In this paper, we use the method of virtual sources or wavefield superposition. [9][10][11] A set of 301 point sources of the form S 1 ðr; z; h : r 0 ; z 0 ; h 0 Þ ¼ À 1 4p…”

Section: Numerical Examplesmentioning

confidence: 99%

Scattering from a finite cylinder near an interface

Fawcett

2014

The Journal of the Acoustical Society of America

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“…Although the formulations circumvent the singularity presented in the integral equation in BEM, it does surfer from the problem of non-uniqueness of solutions at some critical wave numbers [2] . By combining the single-layer and double-layer with a complex constant α, the hybrid-layer potential integral formulations were produced to solve the non-uniqueness problem.…”

Section: Theoretical Formulationmentioning

confidence: 99%

Wave superposition based sound field reconstruction

Chen

Yang

2008

J. Shanghai Jiaotong Univ. (Sci.)

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In order to overcome the obstacle of singular integral in boundary element method (BEM), we presented an efficient sound field reconstruction technique based on the wave superposition method (WSM). Its principle includes three steps: first, the sound pressure field of an arbitrary shaped radiator is measured with a microphone array; then, the exterior sound field of the radiator is computed backward and forward using the WSM; at last, the final results are visualized in terms of sound pressure contours or animations. With these visualized contours or animations, noise sources can be easily located and quantified; also noise transmission path can be found out. By numerical simulation and experimental results, we proved that the technique are suitable and accurate for sound field reconstruction. In addition, we presented a sound field reconstruction system prototype on the basis of this technique. It makes a foundation for the application of wave superposition in the sound field reconstruction in industry situations.

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“…However, the resolution of the nonuniqueness problem in the WSM was questioned by other researchers. For example Wilton et al 52 and Leblanc et al 53 presented that the WSM is not free of the nonuniqueness problem and they showed that the nonuniqueness problem still exists at critical frequencies. Ochmann 7 also discussed that the nonuniqueness problem occurs in the WSM if the inner surface is closed.…”

Section: Wave Superposition Methodsmentioning

confidence: 99%

Review: The Use of Equivalent Source Method in Computational Acoustics

Lee

2017

J. Comp. Acous.

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This paper reviews the equivalent source method (ESM), an attractive alternative to the standard boundary element method (BEM). The ESM has been developed under different names: method of fundamental solutions, wave superposition method, equivalent source method, etc. However, regardless of the method name, the basic concept is very similar; that is to use auxiliary points called equivalent sources to reconstruct the acoustic pressure for radiation or scattering problems. The strength of the equivalent sources are then determined via various approaches such that the boundary conditions on the boundary surface are satisfied. This paper reviews several frequencydomain and time-domain ESMs. There are several distinct advantages in these types of methods: (1) the method is a meshless approach so that it is easy and simple to implement; (2) it does not have a numerical singularity problem that occurs in the BEM; (3) the number of equivalent sources can be fewer than the number of surface collocation points so that the matrix size is reduced and a fast computation is achieved for large problems. The main issue of the ESM is that there is no rule to find out the optimal number and position of equivalent sources. In addition, the ESM suffers from the numerical instability that is associated with the ill-conditioned matrix. Some guidelines have been suggested in terms of finding the number and position of the sources, and several numerical techniques have been developed to resolve the numerical instability. This paper reviews the common theories, numerical issues and challenges of the ESM, and it summarizes recent developments and applications of the ESM to aircraft noise.

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A clarification of nonexistence problems with the superposition method

Cited by 24 publications

References 0 publications

Scattering from a finite cylinder near an interface

Scattering from a finite cylinder near an interface

Wave superposition based sound field reconstruction

Review: The Use of Equivalent Source Method in Computational Acoustics

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