Comparative%20Visualization%20for%20Wave-based%20and%20Geometric%20Acoustics

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Comparative Visualization for Wave-based and
Geometric Acoustics

• Eduard Deines1, Martin Bertram3, Jan Mohring4,
  Jevgenij Jegorovs4, Frank Michel1, Hans Hagen2,
  and Gregory M. Nielson5

1IRTG Kaiserslautern 2University of
Kaiserslautern 3DFKI Kaiserslautern
4ITWM Kaiserslautern 5Arizona State University
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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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Motivation

• Shortcomings of geometric and wave-based methods
• Combination of both approaches
• Numerical and visual comparison

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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)

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Previous Work
Scattered data
Surfaces
Single particle
Listener based
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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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Modified Phonon Tracing

• Tracing pressure rather then energy
• gt better comparison with FEM

• Modeling linear pressure attenuation by Gaussian
  basis functions dilated proportional with
  traversed distance
• gt approximates partition of unity for the basis
  functions

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Phonon Emission

• For each phonon
• Pressure spectrum
• Virtual source
• Phonons current position

• One emmission, multiple collection passes for
  different listeners

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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

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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

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Phonon Collection

• Scaling depends on
• Reference pressure at 1m from source
• Gaussian weighting function
• split unit pulse into frequency bands

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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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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 gt reduction
  needed

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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 gt transformation of
  the continuous state-space model into a discrete
  one

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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 gt only for
  low-frequency bands

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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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Test Scenario
Simulation scenario
Geometry
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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

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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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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

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Interference Pattern (k6 / f328.5 Hz)
Phonon Tracing
FEM
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Interference Pattern (k12 / f657 Hz)
Phonon Tracing
FEM
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Interference Pattern
k6
k6
Phonon Tracing
FEM
k12
k12
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Overview

• Motivation
• Acoustic Simulation
• Modified Phonon Tracing
• FEM-based solver
• Comparison approach
• Interference pattern visualization
• Gain visualization

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Gain Visualization

• Acoustic metric influence of the room
• Error

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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

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Gain - Error
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Gain (k3 / f164.25 Hz)
Error
FEM
Phonon Tracing
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Gain (k6 / f328.5 Hz)
Error
FEM
Phonon Tracing
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Gain (k12 / f657 Hz)
Error
FEM
Phonon Tracing
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Acknowledgments

• Stiftung Rheinland-Pfalz fuer Innovation
• Kaiserslautern Excellence Cluster Dependable
  Adaptive Systems and Mathematical Modeling
• US Army Research Office

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Thank you for attention!