Numerical solution of acoustic problems by integral equations

Reut, Z.

doi:10.1016/0022-460x(89)90646-9

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Acoustic Solution1

Burton and Miller1

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2000

2007

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Cited by 2 publications

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“…The advantage of the CNDF is that there is no need for internal arbitrary points. The disadvantage is that the normal derivative of the surface integral contains highly singular integrands, which require specific integration schemes (Reut, 1989).…”

Section: Acoustic Solutionmentioning

confidence: 99%

Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

Denli¹,

Sun²

2007

The Shock and Vibration Digest

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Section: Acoustic Solutionmentioning

confidence: 99%

Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

Denli¹,

Sun²

2007

The Shock and Vibration Digest

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“…Amini and Harris (1990) gave a comparison between the RBM and the direct Burton and Miller form. Reut (1985) has developed a Burton and Miller formulation which is called Composite Normal Derivative Overlapping Relation (CONDOR), based in part upon Terai (1980). Ursell (1973Ursell ( , 1978 noted that g k (x, y) can be replaced by any fundamental solution to the Helmholtz equation in the exterior domain B + which satisfies the radiation condition.…”

Section: Burton and Millermentioning

confidence: 99%

A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

Zaman

2000

SQU Journal for Science

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This is a review presenting an overview of the developments in boundary integral formulations of the acoustic scattering problems. Generally, the problem is formulated in one of two ways viz. Green’s representation formula, and the Layer-theoretic formulation utilizing either a simple-layer or a double-layer potential. The review presents and expounds the major contributions in this area over the last four decades. The need for a robust and improved formulation of the exterior scattering problem (Neumann or Dirichlet) arose due to the fact that the classical formulation failed to yield a unique solution at (acoustic) wave-numbers which correspond to eigenvalues (eigenfrequencies) of the corresponding interior scattering problem. Moreover, this correlation becomes more pronounced as the wave-numbers become larger i.e. as the (acoustic) frequency increases. The robust integral formulations which are discussed here yield Fredholms integral equations of the second kind which are more amenable to computation than the first kind. However, the integral equation involves a hypersingular kernel which creates ill-conditioning in the final matrix representation. This is circumvented by a regularisation technique. An extensive useful list of references is also presented here for researchers in this area.

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Numerical solution of acoustic problems by integral equations

Cited by 2 publications

References 6 publications

Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

Structural-Acoustic Optimization of Composite Sandwich Structures: A Review

A Comprehensive Review of Boundary Integral Formulations of Acoustic Scattering Problems

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