Year: 2006
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 305–322
Abstract
In this paper we propose the well-known Fourier method on some non-tensor product domains in $\textrm{R}^d$, including simplex and so-called super-simplex which consists of $(d+1)!$ simplices. As two examples, in $2$-D and $3$-D case a super-simplex is shown as a parallel hexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm (FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT) and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a Laplacian-like operator over these domains is explored.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2006-JCM-8754
Journal of Computational Mathematics, Vol. 24 (2006), Iss. 3 : pp. 305–322
Published online: 2006-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Multivariate Fourier transform Simplex and super-simplex Multivariate sine and cosine functions Eigen-decomposition for Laplacian-like operator Multivariate fast Fourier transform.