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Guest
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 Posted:
Sat Dec 11, 2004 2:55 pm Post subject:
Wavelet PDE Matlab Sought |
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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.
- = -
Vasos-Peter John Panagiotopoulos II, Columbia'81+, Bio$trategist
BachMozart ReaganQuayle EvrytanoKastorian
http://ourworld.compuserve.com/homepages/vjp2/vasos.htm
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Rune Allnor
Guest
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| Posted:
Sun Dec 12, 2004 2:27 pm Post subject:
Re: Wavelet PDE Matlab Sought |
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vjp2.at@at.BioStrategist.dot.dot.com wrote:
| Quote: | What MatLab Packages are there for solving PDEs using WaveLets?
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Probably none.
| Quote: | 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 |
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Stan Pawlukiewicz
Guest
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| Posted:
Mon Dec 13, 2004 7:54 pm Post subject:
Re: Wavelet PDE Matlab Sought |
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Rune Allnor wrote:
| Quote: | 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. |
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Rune Allnor
Guest
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| Posted:
Tue Dec 14, 2004 11:13 am Post subject:
Re: Wavelet PDE Matlab Sought |
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Stan Pawlukiewicz wrote:
| Quote: | 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.
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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 |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 11:56 am Post subject:
Re: Wavelet PDE Matlab Sought |
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On 2004-12-14 07:13:42 +0100, "Rune Allnor" <allnor@tele.ntnu.no> said:
| Quote: | 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 |
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David Kirkland
Guest
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| Posted:
Tue Dec 14, 2004 7:42 pm Post subject:
Re: Wavelet PDE Matlab Sought |
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Stephan M. Bernsee wrote:
| Quote: | 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.
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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 |
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Stephan M. Bernsee
Guest
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| Posted:
Tue Dec 14, 2004 10:26 pm Post subject:
Re: Wavelet PDE Matlab Sought |
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On 2004-12-14 15:42:42 +0100, David Kirkland <spam@netscape.net> said:
| Quote: | You may want to look at the Wavelet Digest.
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Very good suggestion indeed. It's at http://www.wavelet.org , just to
complement what David said.
--
Stephan M. Bernsee
http://www.dspdimension.com |
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