Modeling sound scattering using a combination of the edge source integral equation and the boundary element method

Abstract

A hybrid method for sound scattering calculations is presented in this paper. The boundary element method (BEM) is combined with a recently developed edge source integral equation (ESIE) [J. Acoust. Soc. Am. 133, 3681-3691 (2013)]. Although the ESIE provides accurate results for convex, rigid polyhedra, it has several numerical challenges, one of which applies to certain radiation directions. The proposed method, denoted ESIEBEM, overcomes this problem with certain radiation directions by applying a similar approach as BEM. First, the sound pressure is calculated on the surface of the scattering object using the ESIE, and then second, the scattered sound is obtained at the receiver point using the Kirchhoff-Helmholtz boundary integral equation, as BEM does. The three methods have been compared for the scattering by a rigid cube. Based on results from several discretizations, ESIE and ESIEBEM results are typically (90% quartile) within 3-4 · 10 for a kL-value of 1.83 and 2 · 10 for kL = 9.15, L being the cube length, of reference results computed with the BEM. The computational cost of ESIEBEM appears to be lower than BEM.

Machine-learning-based estimation and rendering of scattering in virtual reality

“…This was a practical choice, as the simulation of such objects is computationally relatively efficient, taking approximately in the order of 5-30 s per source-object-receiver setup in a modern laptop computer, using the simulation methods described further in Sec. II C. The model has been found to correspond well to reference calculations for the scattering from a rigid cube (Martin et al, 2018). The simulation of arbitrary surfaces would have required more computational resources to model.…”

Diffraction modeling for scattering objects with non-rigid surfaces

“…2 (a). As shown in [2], the so-called ESIEBEM approach could be used to overcome these challenges but it was not implemented here. Since these known challenging positions cause very large errors, median and quantiles for the errors are presented in Fig.…”

“…For a special set of scattering objects -convex-shaped objects with rigid surfaces, the so-called edge-source integral equation (ESIE) has been shown to give very accurate results compared to analytical solutions [1] and results computed with the BEM [2]. The edge-source integral equation can not handle non-rigid surfaces directly, so the aim of this paper is to present a method to handle small impedance patches in otherwise rigid objects, based on the ESIE formulation.…”

Compressed sensing of impulse responses in rooms of unknown properties and contents

“…Besides compromising their validity below Schroeder's limit, classical geometrical methods are inaccurate in the presence of diffraction and scattering phenomena [8], caused by objects present in the room for instance. In such cases, closer approximations may result with integral diffraction formulations [11], wave-based models [12,13], and hybrid methods [14,15]. As anticipated earlier, however, accurate computer predictions rely on accurate modelling -that is, accurate knowledge-of the room properties and contents [16].…”