HCFFT

HCFFT is a software package to efficiently treat high-dimensional multivariate functions. The implementation is based on the fast Fourier transform for arbitrary hyperbolic cross / sparse grid spaces. 

It is actually developed by the Virtual Materials Design department of the Fraunhofer Institute for Algorithms and Scientific Computing SCAI.

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, H¹_mix, 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

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]