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spectral derivation of aperiodic function

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Old   February 9, 2013, 12:56
Default spectral derivation of aperiodic function
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Christine Darcoux
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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?

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Old   February 9, 2013, 13:34
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Filippo Maria Denaro
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Originally Posted by bouloumag View Post
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
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Old   February 10, 2013, 14:26
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Christine Darcoux
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Originally Posted by FMDenaro View Post
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.
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Old   February 10, 2013, 20:40
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Originally Posted by bouloumag View Post
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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