مقایسهٔ روش‌ها

	روش المان مرزی (BEM)	ردیابی پرتو صوتی
حوزه	صوت‌شناسی	صوت‌شناسی
خانواده	Process / pipeline	Process / pipeline
سال پیدایش	1971	1979
پدیدآور	Carlos Brebbia, Robert Butterfield	James Allen, David Berkley
نوع	Computational simulation for acoustics	Computational room acoustics method
منبع بنیادین	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.	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.
نام‌های دیگر	BEM, boundary element method, indirect BEM, direct BEM	ray tracing, geometric acoustics, image source method, sound ray propagation
مرتبط	5	5
خلاصه	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.	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.