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Computation of the complete acoustic field with Finite-Differences algorithms.
Adan GarrigaCarlos Spa
Vicente López
Forum Acusticum Budapest 31/08/2005
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Parc Barcelona Media
Summary:Summary:
• INTRODUCTION
• STATEMENT OF THE PROBLEM
• FINITE-DIFFERENCES ALGORITHMS: The MacCormack Method
• 2D AND 3D RESULTS: APPLICATIONS
• CONCLUSIONS AND FUTURE WORK
Contents
31/08/2005Forum Acusticum Budapest
Parc Barcelona Media
• Goal: Simulate the propagation of sound waves in 3D virtual environments. Physical renderization of sound fields.
Introduction
• Why?: New emerging multimedia technologies applications: digital cinema, video games, virtual reality, communications, music…
• Real Time: Many applications require renderization of the acoustic field in real time. Balance between accuracy and time of computation.
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Statement of the Problem
• Characterization of the acoustic field (4 quantities):
– Pressure of the fluid (air): P
– Three components of the air velocity: u
• Classical linear equations for the acoustic field:
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Parc Barcelona Media
Finite-Differences
Numerical Methods:Numerical Methods:
Numerical Methods can be divided in two groups:
• Geometrical-based methods. Decomposition of the sound field in elementary waves: Image Source , Ray-Tracing, Beam-Tracing…
• Physical-Based methods. Exact numerical solution of the differential equations: Boundary Elements (BE), Finite Elements (FE) and Finite Differences (FD).
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Why FD?Why FD?
• They give an accurate physical solution for the acoustic field
• For multimedia applications both the sound source and the
receiver can move around. Therefore, we need to compute
the sound field in the whole space at each time.
• Easy to implement in different geometries.
• Easy to parallelize.
Finite-Differences
31/08/2005Forum Acusticum Budapest
Numerical EquationsNumerical Equations
Finite-Differences
11
22
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Numerical Parameters:Numerical Parameters:
• Air density: 1,21 Kg/m
• The speed of sound: c = 330 m/s
• Space discretization: x = 0,01 m (valid for =100-1500 Hz)
• Time discretization: t = 0,00002 s
• Number of float operations per second for a square room of
2 X 2 meters: N=56 GFLOPS REAL TIME !
2D Results
3
31/08/2005Forum Acusticum Budapest
2D Results
31/08/2005Forum Acusticum Budapest
2D Results
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
3D Results:3D Results:
• For the same quality results, the number of floating point
operations per second (FLOPS) is: N = 16 TFLOPS.
• Only supercomputers work at this speed. NOT AT REAL TIME!
3D Results and Applications
Applications:Applications:
• 1D or 2D Real-Time rendering sound applications.
• 3D Non-Real-Time applications: digital cinema (RACINE)
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Conclusions:Conclusions:
• We have found upper bounds for high quality
rendering of acoustic fields.
• For 1D and 2D applications, the algorithm works at
Real-Time for frequencies = 100-1500 Hz.
Conclusions
31/08/2005Forum Acusticum Budapest
La UPF a Ca l’Aranyó
Future Work
Future Work:Future Work:
• For 3D applications we have to reduce the number
of FLOPS: we have to introduce approximations.
• We are developing new hybrid algorithms: using
geometric-based algorithms for high frequencies.
