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Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method

Publication ,  Journal Article
Kovvali, N; Wenbin, L; Zhiqin, Z; Couchman, L; Carin, L
Published in: SIAM Journal on Scientific Computing
January 1, 2006

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.

Duke Scholars

Published In

SIAM Journal on Scientific Computing

DOI

ISSN

1064-8275

Publication Date

January 1, 2006

Volume

28

Issue

2

Start / End Page

485 / 497

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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ICMJE
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Kovvali, N., Wenbin, L., Zhiqin, Z., Couchman, L., & Carin, L. (2006). Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method. SIAM Journal on Scientific Computing, 28(2), 485–497. https://doi.org/10.1137/050635961
Kovvali, N., L. Wenbin, Z. Zhiqin, L. Couchman, and L. Carin. “Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method.” SIAM Journal on Scientific Computing 28, no. 2 (January 1, 2006): 485–97. https://doi.org/10.1137/050635961.
Kovvali N, Wenbin L, Zhiqin Z, Couchman L, Carin L. Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method. SIAM Journal on Scientific Computing. 2006 Jan 1;28(2):485–97.
Kovvali, N., et al. “Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method.” SIAM Journal on Scientific Computing, vol. 28, no. 2, Jan. 2006, pp. 485–97. Scopus, doi:10.1137/050635961.
Kovvali N, Wenbin L, Zhiqin Z, Couchman L, Carin L. Rapid prolate pseudospectral differentiation and interpolation with the fast multipole method. SIAM Journal on Scientific Computing. 2006 Jan 1;28(2):485–497.

Published In

SIAM Journal on Scientific Computing

DOI

ISSN

1064-8275

Publication Date

January 1, 2006

Volume

28

Issue

2

Start / End Page

485 / 497

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics