The Wave-Matching Boundary Integral Equation — An energy approach to Galerkin BEM for acoustic wave propagation problems

Hargreaves, Jonathan A.; Lam, Y. W.

doi:10.1016/j.wavemoti.2018.07.003

Cited by 6 publications

(21 citation statements)

References 62 publications

(176 reference statements)

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“…[8] and the HF-BEM scheme in ref. [20] are extremely similar. All wave propagation operations are represented by matrix multiplications.…”

Section: Algorithm Structurementioning

confidence: 84%

“…Such behaviour could reasonably be termed a shadow wave. In the 'Wave-Matching' BEM [20], distinction between incoming and outgoing sound causes these to arise separately from reflections. A shadow wave cancels out the incoming wave, then a reflected wave is radiated with amplitude and phase dependent on the boundary condition.…”

Section: Visibility and Shadow Regionsmentioning

confidence: 99%

“…These are included by allowing |𝜒| > 1, as is done in ref. [20], which makes the surfacenormal components of 𝐤 ̂− and 𝐤 ̂+ imaginary.…”

Section: Solution By Marching On In Reflection Ordermentioning

confidence: 99%

“…[8] implements directional sources and receivers for SB-GA, while ref. [20] only implements omnidirectional sources and receivers, but the directional source framework demonstrated in ref. [9] could be readily added.…”

Section: Algorithm Structurementioning

confidence: 99%

“…[24] with the equivalent 2D versions derived in section 4.2.2 of ref. [20]. If that were done, then both algorithms would take the following structure:…”

Section: Algorithm Structurementioning

confidence: 99%

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A comparison between the high-frequency Boundary Element Method and Surface-Based Geometrical Acoustics

Hargreaves

2023

inter noise

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The audible frequency range covers many octaves in which the wavelength changes from being large with respect to dominant features of a space to being comparatively much smaller. This makes numerical prediction of a space's acoustic response, e.g. for auralisation, extremely challenging if all frequencies are to be represented accurately. Different classes of algorithm give the best balance of accuracy to computational cost in different frequency bands - 'wave solvers' such as Boundary Element Method (BEM) at low frequencies and Geometrical Acoustics (GA) methods at high frequencies. But combining their output data can be an awkward process due to their very different formulations. This is particularly important for early reflections, which give crucial spatial perceptual cues. Hence there is a need for a unified full audible bandwidth algorithm for early reflections. This paper will describe ongoing research to develop such an algorithm by exploiting synergies between high-frequency BEM and GA. It will describe how appropriately chosen oscillatory basis functions in BEM can produce leading-order GA behaviour at high frequencies and explore how interactions between these compare to the same interactions arising in a surface-based Geometrical Acoustics scheme.

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“…[8] and the HF-BEM scheme in ref. [20] are extremely similar. All wave propagation operations are represented by matrix multiplications.…”

Section: Algorithm Structurementioning

confidence: 84%

Section: Visibility and Shadow Regionsmentioning

confidence: 99%

“…These are included by allowing |𝜒| > 1, as is done in ref. [20], which makes the surfacenormal components of 𝐤 ̂− and 𝐤 ̂+ imaginary.…”

Section: Solution By Marching On In Reflection Ordermentioning

confidence: 99%

Section: Algorithm Structurementioning

confidence: 99%

“…[24] with the equivalent 2D versions derived in section 4.2.2 of ref. [20]. If that were done, then both algorithms would take the following structure:…”

Section: Algorithm Structurementioning

confidence: 99%

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