# spectral derivation of aperiodic function

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 February 9, 2013, 12:56 spectral derivation of aperiodic function #1 New Member   Christine Darcoux Join Date: Jul 2011 Posts: 11 Rep Power: 7 I would like to calculate the spatial derivative of a variable defined on the points of a uniform grid. The domain is NOT periodic, so the FFT method is useless here. I wonder if there exist are other spectral methods to calculate the derivative on an aperiodic domain or if my only hope is to use the finite difference method? Last edited by bouloumag; February 9, 2013 at 13:31.

February 9, 2013, 13:34
#2
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Filippo Maria Denaro
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Quote:
 Originally Posted by bouloumag I would like to calculate the spatial derivative of a variable defined on the points of a uniform grid. The domain is NOT periodic, so the FFT method is useless here. I wonder if there exist are other spectral methods to calculate the derivative on an aperiodic domain or if my only hope is to use the finite difference method?

this is a recent article
http://arxiv.org/pdf/1209.4955.pdf

February 10, 2013, 14:26
#3
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Christine Darcoux
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Quote:
 Originally Posted by FMDenaro this is a recent article http://arxiv.org/pdf/1209.4955.pdf
This method looks promising, but it is not clear to me how to choose the parameter p for a specific problem.

February 10, 2013, 20:40
#4
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Quote:
 Originally Posted by bouloumag I would like to calculate the spatial derivative of a variable defined on the points of a uniform grid. The domain is NOT periodic, so the FFT method is useless here. I wonder if there exist are other spectral methods to calculate the derivative on an aperiodic domain or if my only hope is to use the finite difference method?
Discrete cosine transform (DCT) is a widely used transform for compression of digital images such as MPEG and JPEG. This is due to the capacity of the DCT to treat aperiodic fields while producing spectra where the variance is concentrated in the low-wavenumber components. It can also be used in spectral methods for PDE.

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