Multidimensional pseudo-spectral methods on lattice grids

When multidimensional functions are approximated by a truncated Fourier series, the number of terms typically increases exponentially with the dimension s. However, for functions with more structure than just being L 2 -integrable, the contributions from many of the N s terms in the truncated Fourie...

Full description

Saved in:
Bibliographic Details
Published in:Applied numerical mathematics 2012-03, Vol.62 (3), p.155-165
Main Authors: Munthe-Kaas, Hans, Sørevik, Tor
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computational efficiency
Fourier analysis
Fourier series
Lattice rules
Lattices
Mathematical analysis
Mathematical models
Multidimensional Fourier expansion
Pseudo-spectral methods
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:When multidimensional functions are approximated by a truncated Fourier series, the number of terms typically increases exponentially with the dimension s. However, for functions with more structure than just being L 2 -integrable, the contributions from many of the N s terms in the truncated Fourier series may be insignificant. In this paper we suggest a way to reduce the number of terms by omitting the insignificant ones. We then show how lattice rules can be used for approximating the associated Fourier coefficients, allowing a similar reduction in grid points as in expansion terms. We also show that using a lattice grid permits the efficient computation of the Fourier coefficients by the FFT algorithm. Finally we assemble these ideas into a pseudo-spectral algorithm and demonstrate its efficiency on the Poisson equation.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2011.11.002