Fast transform from an adaptive multi-wavelet representation to a partial Fourier representation

Authors:
Jun Jia;Robert Harrison;George Fann
Affiliations:
Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, USA;Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, USA;Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367, USA
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We present a fast algorithm to compute the partial transformation of a function represented in an adaptive pseudo-spectral multi-wavelet representation to a partial Fourier representation. Such fast transformations are useful in many contexts in physics and engineering, where changes of representation from a piece wise polynomial basis to a Fourier basis. The algorithm is demonstrated for a Gaussian in one and in three dimensions. For 2D, we apply this approach to a Gaussian in a periodic domain. The accuracy and the performance of this method is compared with direct summation.