Numerical Sound Propagation using Adaptive Rectangular Decomposition Nikunj Raghuvanshi, Rahul Narain, Nico Galoppo, Ming C. Lin Department of Computer Science, UNC Chapel Hill

What is acoustics? The study of propagation of sound The study of propagation of sound Diverse applications – Diverse applications – – Earth Science (Seismic waves) – Engineering (Vibration and noise control) – Arts (Musical Acoustics) – Architecture (Architectural Acoustics) Games and Virtual Environments Games and Virtual Environments

Interference The resultant pressure at P due to two waves is simply their sum The resultant pressure at P due to two waves is simply their sum Phase is crucial Phase is crucial signal A signal B A + B in phase: addout of phase: cancel A B P

Diffraction A wave bends around obstacles of size approx. its wavelength, i.e. when ~ s A wave bends around obstacles of size approx. its wavelength, i.e. when ~ s P will have appreciable reception only if there is a good amount of diffraction P will have appreciable reception only if there is a good amount of diffraction This is the reason sound gets everywhere This is the reason sound gets everywhere s P s

ChallengesChallenges Multiple reflections are audible: Full time domain solution required, unlike light simulation Multiple reflections are audible: Full time domain solution required, unlike light simulation Interference is important. For example, Dead spots in auditoria Interference is important. For example, Dead spots in auditoria Diffraction is observable for sound and must be captured properly Diffraction is observable for sound and must be captured properly

Numerical Approaches Solve the Wave Equation: Solve the Wave Equation: is the laplacian operator in 3D is the laplacian operator in 3D = 340m/s is the speed of sound in air = 340m/s is the speed of sound in air is the pressure field to solve is the pressure field to solve The RHS is the forcing term, corresponding to sound sources in the scene The RHS is the forcing term, corresponding to sound sources in the scene

The Wave Equation can be solved analytically on a rectangular domain: High accuracy The Wave Equation can be solved analytically on a rectangular domain: High accuracy Solutions are expressible in terms of Discrete Cosine Transforms (DCT) Solutions are expressible in terms of Discrete Cosine Transforms (DCT) DCT can be performed efficiently with FFT on GPUs DCT can be performed efficiently with FFT on GPUs Result: Efficient, high-accuracy simulation Result: Efficient, high-accuracy simulation Main Idea

Overview of Technique

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Performance & Accuracy: Corridor

Performance & Accuracy: House

Time-Domain Numerical Acoustics that is nearly 100x faster than a high-order finite difference simulation with similar accuracy Time-Domain Numerical Acoustics that is nearly 100x faster than a high-order finite difference simulation with similar accuracy Capable of capturing high-order reflections and diffraction effects efficiently Capable of capturing high-order reflections and diffraction effects efficiently Conclusion

Army Research Office Army Research Office Carolina Development Foundation Carolina Development Foundation Intel Corporation Intel Corporation National Science Foundation National Science Foundation RDECOM RDECOM Acknowledgements