Wave2D: Wave Field Simulation in 2D
Within the EU shared cost project ALMA (ALgorithms for the Modeling of Acoustic interactions, IST-2001-33059), Stefan Petrausch and Rudolf Rabenstein have dealt with the work package "Object Modeling". In the scope of this work package they developed and implemented models of several vibrating structures (e.g. strings and membranes) for digital sound synthesis via physical modeling.
The modeling method applied was the so called Functional Transformation Method (FTM) [2003-29], which allows real-time sound synthesis of strings and membranes using models closely related to physics. In 2005, as an extension to this work, Stefan Petrausch developed highly efficient algorithms for the evaluation and visualization of the complete spatial domain (see [2005-18]).
The simulation tool "Wave2D" available on this site is a product of this development. This tool simulates an extended version of the so called wave equation in two spatial dimensions (2D) and visualizes this wave fields by 3D animations, realized with an OpenGL® interface. Detailed information and program download are available at
Description
The wave equation is a partial differential equation that constitutes the mathematical model of any type of wave propagation. It arises in many physical fields, like acoustics, electromagnetics, and fluid dynamics. A lot of different methods for the simulation of wave propagation are available. Most of them are based on the spatial discretization of the modeled geometry (e.g. the waveguide meshes and finite difference schemes). However, in doing so inaccuracy, so called numerical dispersion, is almost unavoidable. Here a different approach is demonstrated. Based on integral transformations (similar to the well known Laplace-transformation) the wave equation is solved analytically with the FTM. The analytical solution, a weighted sum of second order resonators (the harmonics of the model), is discretized in time and implemented in a computer. Details of this implementation can be found particularly in [2005-18]. Here just a few benefits of this approach are mentioned:
- simulations are totally free of numerical dispersion,
- algorithm equivalent in complexity with other methods, without visualization even faster,
- easy scalable in computational complexity: accuracy, temporal sampling, and spatial sampling are independent from each other,
- exact positioning of excitations and outputs, there is no spatial grid.
The major disadvantage of this approach is the restriction to simple geometries (see screenshots below). For high complex geometries it is not possible to find the harmonics of the system analytically, numerical methods would have to be used to find them. However, currently so called "block-based" modeling methods are under development, that circumvent this limitation by a minimal amount of spatial sampling or even by mixed paradigm modeling (see
[2005-19],[2005-37],[2005-43], and [2005-47]).
Features at a Glance
The FTM algorithms are embedded in a graphical user interface developed with the cross-platform Qt version 3.3 from Trolltech. The resulting program, called "Wave2D" so far, simulates 2D wave propagation (a 3D version is also running, see [2005-45]) and visualizes the outcoming wave field via a 3D OpenGL® interface. Typical simulation scenarios, for instance a 6x6m² room at a temporal sampling rate of 44100 samples per second, result in smooth animations (10-20 frames per second) on a Pentium IV at 2.8GHz. For the excitation it is possible to define several point sources, or even spatial distributed sources, with arbitrary temporal behavior. Besides the visual representation of the wave field, one can observe specific points, for an in-depth analysis or simply for sound output. All options and settings can be adjusted either via the graphical user interface by several dialog, or by editing XML-files. Here a list of the most important features:
- rectangular, circular, and triangular (alpha-stage) geometries,
- free adjustable physical parameters, including geometry parameters, speed of sound, dispersion, and damping constants,
- absorbing or reflecting boundary conditions,
- Export to Matlab feature,
- Screenshots and Movie Output supported,
- arbitrary number of excitations and observation points (=sound outputs),
- flexible visualization, both in color and viewing angle,
- all settings can be saved to XML-files.
Modeling Examples
Several modeling examples with appropriate screenshots are listed in an additional page. You can always have a look at the full-scale screenshot by clicking the scaled down versions. "Wave2D" has also already been applied for the simulation of wave field synthesis. The corresponding publication is [2005-27], details are also explained here. An extended version of "Wave2D", including the block-based feature mentioned above, has been published in [2006-1], see here for the corresponding web-site.
Recent Version
The current version of "Wave2D" is 0.1, this is the first version published online so it is in an early alpha stage. The program documentation is incomplete and under construction. A lot of minor bugs and typographic errors are likely to be present in this version, but the main functionality and the major features are all implemented. There is also a list of known bugs and/or limitations in the program's help system. You are welcome to report additional bugs or helpful suggestions to the author Stefan Petrausch. Principal feedback, how did you like the program, what is good or bad implemented, is welcome too.
It is also possible for you to contribute additional language support. In the German language support, there is a file with the name wave2d.de.ts. Simply copy this file (to wave2d.fr.ts for instance) and edit it with the Qt-Linguist tool. I would be happy to publish your contribution on this homepage.
Download
For download a Windows© version is currently available. To run "Wave2D" at least the executable wave2d.exe and the two dynamic-link-libraries qt-mt333.dll and libsndfile.dll are required. In addition German language support is provided by the zip-file german.zip, several example *.w2d-files are compiled in the zip-file examples.zip, and a beta-version of the help-system/documentation is zipped in the file doc.zip. For installation simply create a folder wave2d somewhere in your directory, copy and unzip all desired files to this folder (at least the executable and the two dynamic-link-libraries) and start the program by double-click on the file wave2d.exe. If you are using Windows XP©, there may be a warning that "Wave2D" is not certified. You can ignore this warning and proceed with the program.
Alternatively you can also download the all-in-one zip-file wave2d.zip, which creates a folder called wave2d that includes all files mentioned above.
* required
Related Publications
In the sequel several publications are listed, that are closely related to the scientific and technical background of the program "Wave2D". Some publications discussing "Wave2D" itself are also included. Most of them can be downloaded, available using either the Portable Document Format (pdf) or the PostScript (ps) format for direct printing.
| 2006-1 |
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S. Petrausch, R. Rabenstein |
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Wave Field Simulation with the Functional Transformation Method |
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submitted: Proc.
Int. Conf. on Acoustics, Speech & Signal Processing (ICASSP), IEEE,
Toulouse, France, May 2006 |
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| 2005-47 |
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S. Petrausch, R. Rabenstein
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Simulation of Room Acoustics via Block-Based Physical Modeling with the Functional Transformation Method |
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IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), pp. 195-198, New Paltz, New York, Oct. 2005 |
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| 2005-45 |
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S. Petrausch, R. Rabenstein |
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Efficient 3D Simulation of Wave Propagation with the Functional Transformation Method |
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18th
Symposium on Simulation Technique, Arbeitsgemeinschaft Simulation in
der Gesellschaft für Informatik (ASIM), pp. 323-330, Erlangen, Germany,
Sep. 2005 |
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| 2005-43 |
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S. Petrausch, R. Rabenstein
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Block-Based Physical Modeling for Digital Sound Synthesis of Membranes and Plates |
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International Computer Music Conference (ICMC 2005), Barcelona, Spain, Sep. 2005 |
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| 2005-37 |
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S. Petrausch, R. Rabenstein |
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Two-Dimensional Block Based Physical Modeling with the Functional Transformation Method |
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The Fourth International Workshop on Multidimensional Systems (NDS 2005), pp. 104-109, Wuppertal, Germany, Jul. 2005 |
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| 2005-27 |
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S. Petrausch, S. Spors, R. Rabenstein |
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Simulation and Visualization of Room Compensation for Wave Field Synthesis with the Functional Transformation Method |
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Audio Engineering Society (AES) 119th Convention, New York, Oct. 2005 |
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| 2005-19 |
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S. Petrausch, J. Escolano, R. Rabenstein |
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A General Approach to Block-Based Physical Modeling with Mixed Modeling Strategies for Digital Sound Synthesis |
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Proc.
Int. Conf. on Acoustics, Speech & Signal Processing (ICASSP), IEEE,
Vol. 3, pp. 21-24, Philadelphia, PA, USA, Mar. 2005 |
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| 2005-18 |
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S. Petrausch, R. Rabenstein |
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Highly Efficient Simulation and Visualization of Acoustic Wave Fields with the Functional Transformation Method |
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Simulation and Visualization, pp. 279-290, Otto von Guericke Univerität, Magdeburg, Mar. 2005 |
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| 2004-22 |
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S. Petrausch, R. Rabenstein |
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A Simplified Design of Multidimensional Transfer Function Models |
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International Workshop on Spectral Methods and Multirate Signal Processing (SMMSP2004), pp. 35-40, Vienna, Austria, Sep. 2004 |
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| 2003-34 |
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R. Rabenstein, L. Trautmann, S. Petrausch |
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Digitale Klangsynthese durch physikalische Modellierung |
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Mitteilungen
aus den Arbeitskreisen, Arbeitsgemeinschaft Simulation in der
Gesellschaft für Informatik (asim), Num. 87, Dr. Peter Schwarz (Hrsg.),
EAS Dresden, Mar. 2003 |
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| 2001-2 |
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L. Trautmann, S. Petrausch, R. Rabenstein |
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Physical Modeling of Drums by Transfer Function Methods |
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Proc. Int. Conf. on Acoustics, Speech & Signal Processing (ICASSP), IEEE, Salt Lake City, Utah, May 2001 |
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