Computerized room acoustics modeling has been practiced for almost 50 years up to date. These modeling techniques play an important role in room acoustic design nowadays, often including auralization, but can also help in the construction of virtual environments for such applications as computer games, cognitive research, and training. This overview describes the main principles, landmarks in the development, and state-of-the-art for techniques that are based on geometrical acoustics principles. A focus is given to their capabilities to model the different aspects of sound propagation: specular vs diffuse reflections, and diffraction.

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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.

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In room acoustics simulation and virtualization applications, accurate wall termination is a perceptually crucial feature. It is particularly important in the setting of wave-based modeling of 3D spaces, using methods such as the finite difference time domain method or finite volume time domain method. In this article, general locally reactive impedance boundary conditions are incorporated into a 3D finite volume time domain formulation, which may be specialized to the various types of finite difference time domain method under fitted boundary termination. Energy methods are used to determine stability conditions for general room geometries, under a large family of nontrivial wall impedances, for finite volume methods over unstructured grids. Simulation results are presented, highlighting in particular the need for unstructured or fitted cells at the room boundary in the case of the accurate simulation of frequencydependent room mode decay times.Index Terms-room acoustics, finite difference time domain method, finite volume methods.

An efficient algorithm for time-domain solution of the acoustic wave equation for the purpose of room acoustics is presented. It is based on adaptive rectangular decomposition of the scene and uses analytical solutions within the partitions that rely on spatially invariant speed of sound. This technique is suitable for auralizations and sound field visualizations, even on coarse meshes approaching the Nyquist limit. It is demonstrated that by carefully mapping all components of the algorithm to match the parallel processing capabilities of graphics processors (GPUs), significant improvement in performance is gained compared to the corresponding CPU-based solver, while maintaining the numerical accuracy. Substantial performance gain over a high-order finite-difference time-domain method is observed. Using this technique, a 1 second long simulation can be performed on scenes of air volume 7500 m 3 till 1650 Hz within 18 minutes compared to the corresponding CPU-based solver that takes around 5 hours and a high-order finite-difference time-domain solver that could take up to three weeks on a desktop computer. To the best of the authors' knowledge, this is the fastest time-domain solver for modeling the room acoustics of large, complex-shaped 3D scenes that generates accurate results for both auralization and visualization.

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