The realization of interactive, immersive virtual worlds requires the ability to present a realistic audio experience that convincingly compliments their visual rendering. Physical simulation is a natural way to achieve such realism, enabling deeply immersive virtual worlds. However, physically-based sound simulation is very computationally expensive owing to the high-frequency, transient oscillations underlying audible sounds. The increasing computational power of desktop computers has served to reduce the gap between required and available computation, and it has become possible to bridge this gap further by using a combination of algorithmic improvements that exploit the physical, as well as perceptual properties of audible sounds. My thesis is a step in this direction. My dissertation concentrates on developing real-time techniques for both sub-problems of sound simulation: synthesis and propagation. Sound synthesis is concerned with generating the sounds produced by objects due to elastic surface vibrations upon interaction with the environment, such as collisions. I present novel techniques that exploit human auditory perception to simulate scenes with hundreds of sounding objects undergoing impact and rolling in real time. Sound propagation is the complementary problem of modeling the high-order scattering and diffraction of sound in an environment as it travels from source to listener. I discuss my work on a novel numerical acoustic simulator (ARD) that is hundred times faster and consumes ten times less memory than a high-accuracy finite-difference technique, allowing acoustic simulations on previously intractable spaces, such as a cathedral, on a desktop computer. Lastly, I present my work on interactive sound propagation that leverages my ARD simulator to render the acoustics of arbitrary static scenes for multiple moving sources and listener in real time, while accounting for scene-dependent effects such as low-pass filtering and smooth attenuation behind obstructions, reverberation, scattering from complex geometry and sound focusing. This is enabled by a novel compact representation that takes a thousand times less memory than a direct scheme, thus reducing memory footprints to within available main memory. To the best of my knowledge, this is the only technique and system in existence to demonstrate auralization of physical wave-based effects in real-time on large, complex 3D scenes
