HCFFT

Hyperbolic Cross Fast Fourier Transform

Features

Actual release v2.0

The actual release is free for non-commercial/academic purpose. If you are interested, please, just contact us. The main features are:

  • Hierarchical sparse grid interpolation based on:
    • Fourier Transform
    • Real Fourier TransformCosine Transform
    • Sine Transform
    • Chebyshev Transform
    • Legendre Transform
    • Generalized Hermite transform
    • Jacobi transform
    • Laguerre transform
  • Inverse transforms
  • Whenever possible, the fast versions of the transforms are used for the one-dimensional operations.
  • Support of several types of general sparse grids
    • Regular sparse grids
    • Generalized (Griebel-Knapek) sparse grids
    • Energy-norm type sparse grids
    • Finite-order sparse grids
  • Arbitrary admissible index sets can be handled and hence an extensionby user defined sparse grids is easy possible
  • Support of dimension-adaptive sparse grids
  • Computation of Laplace operator and gradients
  • Computation of norms, e.g. L2, H1, H1mix, and integrals
  • Long double support for high precision calculations
  • Support of arbitrary non-dyadic refined spaces, e.g. total degree sparse grids for analytic functions
  • Support to treat each dimension by a different hierarchical basis, e.g. mixed Fourier-Chebyshev grids

Documentation

[i] HCFFT Manual v2.0. [pdf]
[ii] M. Griebel and J. Hamaekers. Fast discrete Fourier transform on generalized sparse grids. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75-108. Springer, 2014. [bib]
[iii] K. Matuschke. Trigonometrische Interpolation auf verallgemeinerten dünnen Gittern mit beliebiger Levelstruktur. Diplomarbeit, Institut für Numerische Simulation, Universität Bonn, 2014. [bib]

Referencing HCFFT

If you use the software package HCFFT, please cite the following:

M. Griebel and J. Hamaekers. Fast discrete Fourier transform on generalized sparse grids. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75-108. Springer, 2014. [bib]

Selected references

[1] M. Griebel and J. Hamaekers. Fast discrete Fourier transform on generalized sparse grids. In Sparse grids and Applications, volume 97 of Lecture Notes in Computational Science and Engineering, pages 75-108. Springer, 2014. [bib]
[2] H.-J. Bungartz and M. Griebel. Sparse grids. Acta Numerica, 13:1-123, 2004.
[3] T. Gerstner and M. Griebel. Dimension-adaptive tensor-product quadrature. Computing, 71(1):65-87, 2003.
[4] M. Griebel and S. Knapek. Optimized tensor-product approximation spaces. Constructive Approximation, 16(4):525-540, 2000.
[5] K. Hallatschek. Fourier-transform on sparse grids with hierarchical bases. Numerische Mathematik, 63(1):83–97, 1992.
[6] K. Matuschke. Trigonometrische Interpolation auf verallgemeinerten dünnen Gittern mit beliebiger Levelstruktur. Diplomarbeit, Institut für Numerische Simulation, Universität Bonn, 2014. [bib]