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Volume 9, Issue 2
A Buffered Fourier Spectral Method for Non-periodic PDE

H. Fu & C. Liu

Int. J. Numer. Anal. Mod., 9 (2012), pp. 460-478.

Published online: 2012-09

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  • Abstract

Standard Fourier spectral method can be used to solve a lot of problems with periodic boundary conditions. However, for non-periodic boundary condition problems, standard Fourier spectral method is not efficient or even useless. This work has developed a new way to use Fourier spectral method for non-periodic boundary condition problems. First, the original function is normalized and then a smooth buffer polynomial is developed to extend the normalized function domain. The new function will be smooth and periodic with both function values and derivatives, which is easy to be treated by standard FFT for high resolution. This method has obtained high order accuracy and high resolution with a penalty of 25% over standard Fourier spectral method, as shown by our examples. The scheme demonstrates to be robust. The method will be further used for simulation of transitional and turbulent flow.

  • Keywords

Fourier spectral method, FFT, non-periodic PDE, buffer zone, high resolution.

  • AMS Subject Headings

35Q10, 65N30, 76D05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-9-460, author = {H. Fu and C. Liu}, title = {A Buffered Fourier Spectral Method for Non-periodic PDE}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2012}, volume = {9}, number = {2}, pages = {460--478}, abstract = {

Standard Fourier spectral method can be used to solve a lot of problems with periodic boundary conditions. However, for non-periodic boundary condition problems, standard Fourier spectral method is not efficient or even useless. This work has developed a new way to use Fourier spectral method for non-periodic boundary condition problems. First, the original function is normalized and then a smooth buffer polynomial is developed to extend the normalized function domain. The new function will be smooth and periodic with both function values and derivatives, which is easy to be treated by standard FFT for high resolution. This method has obtained high order accuracy and high resolution with a penalty of 25% over standard Fourier spectral method, as shown by our examples. The scheme demonstrates to be robust. The method will be further used for simulation of transitional and turbulent flow.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/642.html} }
TY - JOUR T1 - A Buffered Fourier Spectral Method for Non-periodic PDE AU - H. Fu & C. Liu JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 460 EP - 478 PY - 2012 DA - 2012/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/642.html KW - Fourier spectral method, FFT, non-periodic PDE, buffer zone, high resolution. AB -

Standard Fourier spectral method can be used to solve a lot of problems with periodic boundary conditions. However, for non-periodic boundary condition problems, standard Fourier spectral method is not efficient or even useless. This work has developed a new way to use Fourier spectral method for non-periodic boundary condition problems. First, the original function is normalized and then a smooth buffer polynomial is developed to extend the normalized function domain. The new function will be smooth and periodic with both function values and derivatives, which is easy to be treated by standard FFT for high resolution. This method has obtained high order accuracy and high resolution with a penalty of 25% over standard Fourier spectral method, as shown by our examples. The scheme demonstrates to be robust. The method will be further used for simulation of transitional and turbulent flow.

H. Fu and C. Liu. (2012). A Buffered Fourier Spectral Method for Non-periodic PDE. International Journal of Numerical Analysis and Modeling. 9 (2). 460-478. doi:
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