Optimal choice of grid points in multidimensional pseudospectral fourier methods

R. H. Bisseling*, R. Kosloff

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The optimal choice of grid points for the multi-dimensional pseudospectral Fourier method is investigated. Optimal sampling is obtained by looking for the most isotropic sampling grid in momentum space. The points of this grid are found to be positioned at the center of densely packed hard spheres forming an oblique grid. It is found that by using this oblique grid the sampling efficiency can be enhanced, compared to a rectangular grid, by a factor ranging from 1.4 for three dimensions to 16 for eight dimensions. The method is checked in five dimensions by calculating the Laplacian in an oblique and in a Cartesian grid. The oblique grid was found to have superior accuracy using a factor of 2.5 less grid points. The method is also illustrated in six dimensions by a calculation of the ground and first excited states of two interacting triplet hydrogen atoms.

Original languageEnglish
Pages (from-to)243-262
Number of pages20
JournalJournal of Computational Physics
Volume76
Issue number2
DOIs
StatePublished - Jun 1988

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