Boundary integral solutions of three dimensional acoustic radiation problems

Meyer, William L.; Bell, W.; Zinn, B. T.; Stallybrass, M.P.

doi:10.1016/0022-460x(78)90504-7

Cited by 176 publications

(59 citation statements)

References 8 publications

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“…[1][2][3]14,39 It is clear that the requirement for η is such that it should be complex with nonzero imaginary part to yield a unique solution for Eq. (24).…”

Section: The Burton and Miller Methodsmentioning

confidence: 99%

The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter

Marburg

2016

J. Comp. Acous.

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The phenomenon of irregular frequencies or spurious modes when solving the Kirchhoff-Helmholtz integral equation has been extensively studied over the last six or seven decades. A class of common methods to overcome this phenomenon uses the linear combination of the Kirchhoff-Helmholtz integral equation and its normal derivative. When solving the Neumann problem, this method is usually referred to as the Burton and Miller method. This method uses a coupling parameter which, theoretically, should be complex with nonvanishing imaginary part. In practice, it is usually chosen proportional or even equal to i/k. A literature review of papers about the Burton and Miller method and its implementations revealed that, in some cases, it is better to use −i/k as coupling parameter. The better choice depends on the specific formulation, in particular, on the harmonic time dependence and on the fundamental solution or Green's function, respectively. Surprisingly, an unexpectedly large number of studies is based on the wrong choice of the sign in the coupling parameter. Herein, it is described which sign of the coupling parameter should be used for different configurations. Furthermore, it will be shown that the wrong sign does not just make the solution process inefficient but can lead to completely wrong results in some cases.

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“…[1][2][3]14,39 It is clear that the requirement for η is such that it should be complex with nonzero imaginary part to yield a unique solution for Eq. (24).…”

Section: The Burton and Miller Methodsmentioning

confidence: 99%

The Burton and Miller Method: Unlocking Another Mystery of Its Coupling Parameter

Marburg

2016

J. Comp. Acous.

View full text Add to dashboard Cite

show abstract

“…All but the last of these references seem to have been unaware of the difficulties with the methods at the characteristic wavenumbers. The computational performance of elementary methods is compared with various alternative methods in Schenck [75], Meyer et al [60], Sayhi et al [74], for example. Because of the perceived computational difficulties, research has generally moved away from the elementary methods and towards alternative methods.…”

Section: Elementary Methodsmentioning

confidence: 99%