Rapid Prolate Pseudospectral Differentiation and Interpolation with the Fast Multipole Method

Authors:
Narayan Kovvali;Wenbin Lin;Zhiqin Zhao;Luise Couchman;Lawrence Carin
Affiliations:
-;-;-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2006

Citing 0
Cited 2

The EPS method: A new method for constructing pseudospectral derivative operators

Journal of Computational Physics
The Nonconvergence of $$h$$h-Refinement in Prolate Elements

Journal of Scientific Computing

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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.