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?What is acoustics?What is acoustics?What is acoustics?

• The study of propagation of soundThe study of propagation of sound

• Diverse applications –Diverse applications –

– Earth Science (Seismic waves)Earth Science (Seismic waves)

– Engineering (Vibration and noise control)Engineering (Vibration and noise control)

– Arts (Musical Acoustics)Arts (Musical Acoustics)

– Architecture (Architectural Acoustics)Architecture (Architectural Acoustics)

• Games and Virtual EnvironmentsGames and Virtual Environments

InterferenceInterferenceInterferenceInterference

• The resultant pressure at P due to The resultant pressure at P due to two waves is simply their sumtwo waves is simply their sum

• Phase is crucialPhase is crucial

signal A

signal B

A + B

in phase: addout of phase: cancel

A

B

P

DiffractionDiffractionDiffractionDiffraction

• A wave bends around A wave bends around obstacles of size approx. obstacles of size approx. its wavelength, i.e. whenits wavelength, i.e. when

~ s ~ s

• P will have appreciable P will have appreciable reception only if there is a reception only if there is a good amount of diffractiongood amount of diffraction

• This is the reason sound This is the reason sound gets everywheregets everywhere

s

P

s

ChallengesChallengesChallengesChallenges

• Multiple reflections are audible: Full time domain Multiple reflections are audible: Full time domain solution required, unlike light simulationsolution required, unlike light simulation

• Interference is important. For example, Dead Interference is important. For example, Dead spots in auditoriaspots in auditoria

• Diffraction is observable for sound and must be Diffraction is observable for sound and must be captured properlycaptured properly

Numerical ApproachesNumerical ApproachesNumerical ApproachesNumerical Approaches

• Solve the Wave Equation:Solve the Wave Equation:

is the laplacian operator in 3Dis 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 solveis the pressure field to solve

• The RHS is the forcing term, corresponding to The RHS is the forcing term, corresponding to sound sources in the scenesound sources in the scene

• The Wave Equation can be solved The Wave Equation can be solved analyticallyanalytically on on a rectangular domain: High accuracya rectangular domain: High accuracy

• Solutions are expressible in terms of Discrete Solutions are expressible in terms of Discrete Cosine Transforms (DCT)Cosine Transforms (DCT)

• DCT can be performed efficiently with FFT on DCT can be performed efficiently with FFT on GPUsGPUs

• Result: Efficient, high-accuracy simulationResult: Efficient, high-accuracy simulation

Main IdeaMain IdeaMain IdeaMain Idea

Overview of TechniqueOverview of TechniqueOverview of TechniqueOverview of Technique

VideoVideoVideoVideo

Performance & Accuracy: CorridorPerformance & Accuracy: CorridorPerformance & Accuracy: CorridorPerformance & Accuracy: Corridor

Performance & Accuracy: HousePerformance & Accuracy: HousePerformance & Accuracy: HousePerformance & Accuracy: House

• Time-Domain Numerical Acoustics that is Time-Domain Numerical Acoustics that is nearly 100x faster than a high-order finite nearly 100x faster than a high-order finite difference simulation with similar accuracydifference simulation with similar accuracy

• Capable of capturing high-order reflections Capable of capturing high-order reflections and diffraction effects efficientlyand diffraction effects efficiently

ConclusionConclusionConclusionConclusion

• Army Research OfficeArmy Research Office

• Carolina Development FoundationCarolina Development Foundation

• Intel CorporationIntel Corporation

• National Science FoundationNational Science Foundation

• RDECOM RDECOM

AcknowledgementsAcknowledgementsAcknowledgementsAcknowledgements