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

Ray tracing is an established method for computing the late-time part of room impulse responses. But it has the drawback that only very crude Monte Carlo models of boundary scattering and diffraction are possible to include without losing its attractive computational cost scaling. This happens because higher-resolution models of these processes output multiple child rays for every parent ray received, making the number of rays grow with reflection order. An emerging solution is so-called 'Surface-Based' Geometrical Acoustics. Here the distribution of rays arriving at a boundary is mapped onto a predefined set of spatial elements and angular interpolation functions, producing a vector of coefficients. Re-radiation of subsequent reflections is then a matrix multiplication, with the steady state solution being solvable via a Neumann series. Since rays only every propagate one reflection order before being collected, diffraction and scattering process that cause them to multiply can be included without issue. Here we present a new formulation based on a Galerkin Boundary Element Method (BEM). A unique feature is its ability to readily change interpolation functions, so their effect on accuracy and convergence can be assessed. In this preliminary work, it is verified against an Image Source Model for a rectangular room.

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“…[16]. The similarity of surface-based GA to BEM is discussed further in this papers sister paper, #1005 in these proceedings [17].…”

Section: Surface-based Gamentioning

confidence: 91%

Raytracing in Galerkin Boundary Integral form

McGee

Hargreaves

2023

inter noise

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“…Room acoustic simulation using physically motivated sound propagation models is typically separated into two approaches: (i) wave-based methods and (ii) geometric methods, along with hybrids between the two [1][2][3][4][5][6]. In wave-based methods, the intention is to solve the wave equation with boundary conditions, which has resulted in several numerical algorithms such as the boundary element method (BEM) [7], finite element method FEM [8], and the finite difference time-domain method (FDTD) [9].…”

Section: Introductionmentioning

confidence: 99%

Relating wave-based and geometric acoustics using a stationary phase approximation approximation of the boundary integral equation

Ali,

Dietzen,

Scerbo

et al. 2024

Proceedings of the 10th Convention of the European Acoustics Association Forum Acusticum 2023

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Room acoustic simulation using physically motivated sound propagation models are typically separated into wave-based methods and geometric methods. While each of these methods has been extensively studied, the question on when to transition from a wave-based to a geometric method still remains somewhat unclear. Towards building greater understanding of the links between wave-based and geometric methods, this paper investigates the transition question by using the method of stationary phase. As a starting point, we consider an elementary scenario with a geometrically interpretable analytic solution, namely that of an infinite rigid boundary mirroring a single monopole sound source, and apply the stationary phase approximation (SPA) to the wave-based boundary integral equation (BIE). The results of the analysis demonstrate how net boundary contributions give rise to the geometric interpretation offered by the SPA and provide the conditions when the SPA is asymptotically equal to the analytical solution in this elementary scenario. Although the results are unsurprising and intuitive, the insights gained from this analysis pave the way for investigating relations between wave-based and geometric methods in more complicated room acoustics scenarios.

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

Cited by 2 publications

References 23 publications

Raytracing in Galerkin Boundary Integral form

Raytracing in Galerkin Boundary Integral form

Relating wave-based and geometric acoustics using a stationary phase approximation approximation of the boundary integral equation

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