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Comparative Visualization for Wave-based and Geometric Acoustics

Comparative Visualization for Wave-based and Geometric Acoustics. Eduard Deines 1 , Martin Bertram 3 , Jan Mohring 4 , Jevgenij Jegorovs 4 , Frank Michel 1 , Hans Hagen 2 , and Gregory M. Nielson 5. 4 ITWM Kaiserslautern 5 Arizona State University. 1 IRTG Kaiserslautern

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Comparative Visualization for Wave-based and Geometric Acoustics

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  1. Comparative Visualization for Wave-based and Geometric Acoustics Eduard Deines1, Martin Bertram3, Jan Mohring4, Jevgenij Jegorovs4, Frank Michel1, Hans Hagen2, and Gregory M. Nielson5 4ITWM Kaiserslautern 5Arizona State University 1IRTG Kaiserslautern 2University of Kaiserslautern 3DFKI Kaiserslautern

  2. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  3. Motivation • Shortcomings of geometric and wave-based methods • Combination of both approaches • Numerical and visual comparison Comparative Visualization for Wave-based and Geometric Acoustics

  4. Previous Work • Phonon tracing, based on sound particles • Computation of energy decomposition for each phonon (phonon emission) • Construction of response filters for each listener position (phonon collection) Comparative Visualization for Wave-based and Geometric Acoustics

  5. Previous Work Scattered data Single particle Surfaces Listener based Comparative Visualization for Wave-based and Geometric Acoustics

  6. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  7. Modified Phonon Tracing • Tracing pressure rather then energy • => better comparison with FEM • Modeling linear pressure attenuation by Gaussian basis functions dilated proportional with traversed distance • => approximates partition of unity for the basis functions Comparative Visualization for Wave-based and Geometric Acoustics

  8. Phonon Emission • For each phonon: • Pressure spectrum • Virtual source • Phonon’s current position • One emmission, multiple collection passes for different listeners Comparative Visualization for Wave-based and Geometric Acoustics

  9. Phonon Emission • Emission according to source distribution • Reflection at scene elements • Update virtual source • Multiply pressure by • Re-use path by next phonons • Record phonons on scene elements Comparative Visualization for Wave-based and Geometric Acoustics

  10. Phonon Collection • For each visible phonon: • Add unit pulse translated by distance • Scaling decreases with: • Accumulated length • Wall absorption • Scaling depends on: • Phonon outgoing direction • Direction from virtual source to listener position Comparative Visualization for Wave-based and Geometric Acoustics

  11. Phonon Collection • Scaling depends on: • Reference pressure at 1m from source • Gaussian weighting function • split unit pulse into frequency bands Comparative Visualization for Wave-based and Geometric Acoustics

  12. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  13. Finite Element Method (FEM) • Solving wave equation by FEM • FEM approximates the wave equation by a large system of ODEs • To many unknowns to solve the ODEs => reduction needed Comparative Visualization for Wave-based and Geometric Acoustics

  14. Finite Element Method (FEM) • Representation of the system dynamics by a superposition of eigenmodes • The coefficients of the eigenmodes are the unknowns of the reduced system • Samplewise constant input => transformation of the continuous state-space model into a discrete one Comparative Visualization for Wave-based and Geometric Acoustics

  15. Finite Element Method (FEM) • Typically few hundred unknowns rather than 10,000 degrees of freedom • Required number of unknowns increases as the third power of the frequency => only for low-frequency bands Comparative Visualization for Wave-based and Geometric Acoustics

  16. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  17. Test Scenario Simulation scenario Geometry Comparative Visualization for Wave-based and Geometric Acoustics

  18. Simulation • regular grid • wave number k = {3, 6, 9, 12, 15} • f = {164.25, 328.5, 492.7, 657, 821.2} Hz • Phonon Tracing: point source, 100000 phonons • FEM: small membrane Comparative Visualization for Wave-based and Geometric Acoustics

  19. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  20. Interference Pattern Visualization • Color mapping: • Positive pressure to red • Negative pressure to blue • Reduction of saturation, depending on the absolute pressure value • Mapping of pressure values below the hearing threshold to gray • Bilinear interpolation of color values for additional grid points Comparative Visualization for Wave-based and Geometric Acoustics

  21. Interference Pattern (k=6 / f=328.5 Hz) Phonon Tracing FEM Comparative Visualization for Wave-based and Geometric Acoustics

  22. Interference Pattern (k=12 / f=657 Hz) Phonon Tracing FEM Comparative Visualization for Wave-based and Geometric Acoustics

  23. Interference Pattern k=6 k=6 Phonon Tracing FEM k=12 k=12 Comparative Visualization for Wave-based and Geometric Acoustics

  24. Overview • Motivation • Acoustic Simulation • Modified Phonon Tracing • FEM-based solver • Comparison approach • Interference pattern visualization • Gain visualization Comparative Visualization for Wave-based and Geometric Acoustics

  25. Gain Visualization • Acoustic metric: influence of the room • Error: Comparative Visualization for Wave-based and Geometric Acoustics

  26. Gain Visualization • Color coding: • Use of HSV color space • Red for maximum value • Blue for minimum value • Same range for different simulations • Same range for all error plots Comparative Visualization for Wave-based and Geometric Acoustics

  27. Gain - Error Comparative Visualization for Wave-based and Geometric Acoustics

  28. Gain (k=3 / f=164.25 Hz) Error FEM Phonon Tracing Comparative Visualization for Wave-based and Geometric Acoustics

  29. Gain (k=6 / f=328.5 Hz) Error FEM Phonon Tracing Comparative Visualization for Wave-based and Geometric Acoustics

  30. Gain (k=12 / f=657 Hz) Error FEM Phonon Tracing Comparative Visualization for Wave-based and Geometric Acoustics

  31. Acknowledgments • Stiftung Rheinland-Pfalz fuer Innovation • Kaiserslautern Excellence Cluster Dependable Adaptive Systems and Mathematical Modeling • US Army Research Office Comparative Visualization for Wave-based and Geometric Acoustics

  32. Thank you for attention! Comparative Visualization for Wave-based and Geometric Acoustics

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