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Wavelet PDE Matlab Sought

Started by Unknown December 11, 2004

What MatLab Packages are there for solving PDEs using WaveLets?


This problem has been solved with Collocation up to now, 

but I need the inputs and outputs to be in WaveLet 
form for upstream and downstream analysis.



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vjp2.at@at.BioStrategist.dot.dot.com wrote:
> What MatLab Packages are there for solving PDEs using WaveLets?
Probably none.
> This problem has been solved with Collocation up to now, > > but I need the inputs and outputs to be in WaveLet > form for upstream and downstream analysis.
Then you need to convert between wavelet domain and the domains of the input and outputs of your PDE software. There is no reason why there would be any advantage of using wavelets when working with PDEs. The solutions of PDEs are expressed in terms of normal modes (analytically) or certain eigenfunctions (numerically), but these are intimately connected with the way the problem was stated. There is no such link to wavelets, so there is no reason to expect that a wavelet-based PDE solver should be available. Rune
Rune Allnor wrote:
> vjp2.at@at.BioStrategist.dot.dot.com wrote: > >>What MatLab Packages are there for solving PDEs using WaveLets? > > > Probably none. > > >>This problem has been solved with Collocation up to now, >> >>but I need the inputs and outputs to be in WaveLet >>form for upstream and downstream analysis. > > > Then you need to convert between wavelet domain and the domains > of the input and outputs of your PDE software. > > There is no reason why there would be any advantage of using > wavelets when working with PDEs. The solutions of PDEs are > expressed in terms of normal modes (analytically) or certain > eigenfunctions (numerically), but these are intimately connected > with the way the problem was stated. There is no such link to > wavelets, so there is no reason to expect that a wavelet-based > PDE solver should be available. > > Rune >
I'm not sure about this Rune, I've seen PDE's mentioned in a number of introduction to wavelets. I would guess that they might be useful in time domain, non-Helmholtz equation, sort of situations.
Stan Pawlukiewicz wrote:
> Rune Allnor wrote: > > vjp2.at@at.BioStrategist.dot.dot.com wrote: > > > >>What MatLab Packages are there for solving PDEs using WaveLets? > > > > > > Probably none. > > > > > >>This problem has been solved with Collocation up to now, > >> > >>but I need the inputs and outputs to be in WaveLet > >>form for upstream and downstream analysis. > > > > > > Then you need to convert between wavelet domain and the domains > > of the input and outputs of your PDE software. > > > > There is no reason why there would be any advantage of using > > wavelets when working with PDEs. The solutions of PDEs are > > expressed in terms of normal modes (analytically) or certain > > eigenfunctions (numerically), but these are intimately connected > > with the way the problem was stated. There is no such link to > > wavelets, so there is no reason to expect that a wavelet-based > > PDE solver should be available. > > > > Rune > > > I'm not sure about this Rune, I've seen PDE's mentioned in a number
of
> introduction to wavelets. I would guess that they might be useful in
> time domain, non-Helmholtz equation, sort of situations.
I must confess that I have read more about PDEs than I have about wavelets. While the term "wavelet" is used in the PDE literature, it usually refers to some sort of time-domain general pulse shape (the pulse shapes emitted from the sources in either sonars or seismic experiments) and not the analysis tool we know from signal processing. If there is one thing I have learned during the past decade in various research institutions, it is that selling a point of view to an audience is far more important than substantiating the same point of view. Wavelets seem to me to be a reformulation and, at best, slight extension of well-know concepts (filter banks, the uncertainty principle). For some reason I tend to await justifications of any claim made of usefulness. I prefer to wait until the PDE people accept wavelets as a useful tool with PDEs. Rune
On 2004-12-14 07:13:42 +0100, "Rune Allnor" <allnor@tele.ntnu.no> said:

> If there is one thing I have learned during the past decade in > various research institutions, it is that selling a point of > view to an audience is far more important than substantiating > the same point of view. Wavelets seem to me to be a reformulation > and, at best, slight extension of well-know concepts (filter banks, > the uncertainty principle).
I partly second that. There are indeed researchers who try to combine different concepts that are "hip" at a given time to make their work appear cutting edge. I've seen it on more than one occasion that there are papers that just don't make *any* sense whatsoever, because their authors try to force different concepts to fit together that have no connection at all. -- Stephan M. Bernsee http://www.dspdimension.com
Stephan M. Bernsee wrote:
> On 2004-12-14 07:13:42 +0100, "Rune Allnor" <allnor@tele.ntnu.no> said: > >> If there is one thing I have learned during the past decade in >> various research institutions, it is that selling a point of >> view to an audience is far more important than substantiating >> the same point of view. Wavelets seem to me to be a reformulation >> and, at best, slight extension of well-know concepts (filter banks, >> the uncertainty principle). > > > I partly second that. There are indeed researchers who try to combine > different concepts that are "hip" at a given time to make their work > appear cutting edge. I've seen it on more than one occasion that there > are papers that just don't make *any* sense whatsoever, because their > authors try to force different concepts to fit together that have no > connection at all.
You may want to look at the Wavelet Digest. It is periodic e-newsletter. It often has preprints - I know some of the papers address using wavelets to solve PDE's. I don't know if the have any matlab code available or not. While I agree somewhat with Rune and Stephan - Wavelets have been around for quite some time in the Mathematics world, and only quite recent in the Engineering world. It was only once they drew the comparison between Filter Banks that they became popular in engineering. This relationship makes them easier to digest for those of us without a rigourous mathematical background. While the theory existed for Wavelets, their use in numerical methods required significant computational power which has only been commonly available, i.e. desktop vs Crays, in the last 10-20 years. We are still finding out the proper ways to use this new tool - yup sometimes it just becomes a buzz word. Cheers, David
On 2004-12-14 15:42:42 +0100, David Kirkland <spam@netscape.net> said:

> You may want to look at the Wavelet Digest.
Very good suggestion indeed. It's at http://www.wavelet.org , just to complement what David said. -- Stephan M. Bernsee http://www.dspdimension.com