手法を比較

	BEM Acoustics	音響ホログラフィ	音線追跡（Acoustic Ray Tracing）
分野	音響学	音響学	音響学
系統	Process / pipeline	Process / pipeline	Process / pipeline
提唱年	1971	1985	1979
提唱者	Carlos Brebbia, Robert Butterfield	James Maynard, Earl Williams, Yongjian Lee	James Allen, David Berkley
種類	Computational simulation for acoustics	Sound field reconstruction method	Computational room acoustics method
原典	Burton, A. J., & Miller, G. F. (1971). The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proceedings of the Royal Society A, 323(1553), 201–210.	Maynard, J. D., Williams, E. G., & Lee, Y. (1985). Near-field acoustic holography: I. Theory of generalized holography and the development of NAH. Journal of the Acoustical Society of America, 78(4), 1395–1413.	Allen, J. B., & Berkley, D. A. (1979). Image method for efficiently simulating small-room acoustics. Journal of the Acoustical Society of America, 65(4), 943–950.
別名	BEM, boundary element method, indirect BEM, direct BEM	NAH, near-field acoustics, sound field mapping, acoustic imaging	ray tracing, geometric acoustics, image source method, sound ray propagation
関連	5	5	5
概要	The Boundary Element Method (BEM) is a numerical technique for solving acoustic wave equations in complex geometries. Unlike finite element methods (FEM) that mesh entire volumes, BEM discretizes only the acoustic boundaries (surfaces), reducing computational cost and memory. First applied to acoustics by Burton and Miller in 1971, BEM is widely used for predicting room acoustics, exterior noise radiation, and acoustic scattering without the need for volumetric meshing.	Near-Field Acoustic Holography (NAH) is a technique for reconstructing 3D acoustic sound fields and visualizing sound radiation from sources by measuring pressure at a dense microphone array in the near field. Pioneered by Maynard, Williams, and Lee in 1985, NAH extends holographic principles from optics to acoustics, enabling detailed acoustic source characterization, noise source identification, and acoustic field visualization that is impossible with conventional single-point or line-array methods.	Acoustic ray tracing is a computational technique for predicting sound propagation in rooms by treating acoustic energy as rays that reflect specularly off surfaces. Formalized by Allen and Berkley in 1979 via the image source method, ray tracing is one of the most computationally efficient methods for room acoustic simulation, especially for early and mid-reflections. It is widely used in audio engineering, architectural acoustics, and interactive spatial audio for virtual environments.