comparative visualization for wave-based and geometric acoustics

Comparative Visualization for Wave-based and Geometric AcousticsEduard Deines1, Martin Bertram3, Jan Mohring4, Jevgenij Jegorovs4, Frank Michel1, Hans Hagen2, and Gregory M. Nielson5

1IRTG Kaiserslautern2University of Kaiserslautern3DFKI Kaiserslautern

4ITWM Kaiserslautern5Arizona State University

Comparative Visualization for Wave-based and Geometric Acoustics

2Overview

• Motivation

• Acoustic Simulation• Modified Phonon Tracing• FEM-based solver

• Comparison approach• Interference pattern visualization• Gain visualization


3Motivation

• Shortcomings of geometric and wave-based methods

• Combination of both approaches

• Numerical and visual comparison


4Previous 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)


5Previous Work

Scattered data

Listener based

SurfacesSingle particle


6Overview

• Motivation




7Modified Phonon Tracing

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

• Tracing pressure rather then energy => better comparison with FEM


8Phonon Emission

• For each phonon:• Pressure spectrum• Virtual source• Phonon’s current

position

• One emmission, multiple collection passes for different listeners


9Phonon Emission

• Reflection at scene elements• Update virtual source• Multiply pressure by

• Re-use path by next phonons• Record phonons on scene

elements

• Emission according to source distribution


10Phonon 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


11Phonon Collection

• Scaling depends on:• Reference pressure at 1m from

source• Gaussian weighting function

• split unit pulse into frequency bands


12Overview

• Motivation




13Finite 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



• 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



• 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


16Overview

• Motivation




17Test Scenario

Geometry Simulation scenario


18Simulation

• 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


19Overview

• Motivation




20Interference 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


21Interference Pattern (k=6 / f=328.5 Hz)

FEM

Phonon Tracing


22Interference Pattern (k=12 / f=657 Hz)

FEM

Phonon Tracing


23Interference Pattern

k=6 k=6

k=12 k=12

FEM

Phonon Tracing


24Overview

• Motivation




25Gain Visualization

• Acoustic metric: influence of the room

• Error:


26Gain 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


27Gain - Error


28Gain (k=3 / f=164.25 Hz)

FEM Phonon Tracing Error


29Gain (k=6 / f=328.5 Hz)



30Gain (k=12 / f=657 Hz)



31Acknowledgments

• Stiftung Rheinland-Pfalz fuer Innovation

• Kaiserslautern Excellence Cluster Dependable Adaptive Systems and Mathematical Modeling

• US Army Research Office


32

Thank you for attention!

comparative visualization for wave-based and geometric acoustics

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