An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.
Abstract-During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.
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