Abstract
A windowed Fourier method is proposed for approximation of non-periodic functions on equispaced nodes. Spectral convergence is obtained in most of the domain, except near the boundaries, where polynomial least-squares is used to correct the approximation. Because the method can be implemented using partition of unit and domain decomposition, it is suitable for adaptive and parallel implementations and large scale computations. Computations can be carried out using fast Fourier transforms. Comparisons with Fourier extension, rational interpolation and least-squares methods are presented.
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Acknowledgements
This work was supported in part by AFOSR FA9550-12-1-0393.
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Platte, R.B. (2015). A Windowed Fourier Method for Approximation of Non-periodic Functions on Equispaced Nodes. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_37
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DOI: https://doi.org/10.1007/978-3-319-19800-2_37
Publisher Name: Springer, Cham
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