Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method

Narayan Kovvali, Lin Wenbin, Zhao Zhiqin, Luise Couchman, Lawrence Carin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Pseudospectral methods utilizing prolate spheroidal wave functions as basis functions have been shown to possess advantages over the conventional pseudospectral methods based on trigonometric and orthogonal polynomials. However, the spectral differentiation and interpolation steps of the prolate pseudospectral method involve matrix-vector products, which, if evaluated directly, entail O(N2) memory requirement and computational complexity (where N is the number of unknowns utilized for discretization and interpolation). In this work we show that the fast multipole method (FMM) can be used to reduce the memory requirement and computational complexity of the prolate pseudospectral method to O(N). Example simulation results demonstrate the speed and accuracy of the resulting fast prolate pseudospectral solver. © 2006 Society for Industrial and Applied Mathematics.
Original languageEnglish (US)
Pages (from-to)485-497
Number of pages13
JournalSIAM Journal on Scientific Computing
Volume28
Issue number2
DOIs
StatePublished - Dec 1 2006
Externally publishedYes

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