Daubechies Wavelets in Electronic Structure Calculation: BigDFT Code Tutorial
- Luigi Genovese (Alternative Energies and Atomic Energy Commission (CEA), Grenoble, France)
- Thierry Deutsch (French Alternative Energies and Atomic Energy Commission (CEA), Grenoble, France)
- Stefan Goedecker (University of Basel, Switzerland)
- Damien Caliste (Alternative Energies and Atomic Energy Commission (CEA), France)
Daubechies wavelets have a number of interesting properties for a basis set being used for electronic structure calculations of complex systems.They form a systematic orthogonal and smooth basis, localized both in real and Fourier space and that allows for adaptivity.Since 2007 the BigDFT code uses this basis for Kohn-Sham Density Functional Theory. The performances of this code meet both the requirements of precision and localization found in many applications.This code may treat traditional and complex environment (e.g. charged systems, electric fields, different boundary conditions...) with a systematic treatment and a mathematically clean description.The formalism is also suitable for state-of-the art high performance computing architectures.The data repartition scheme of the BigDFT code allows to reach optimal efficiency on massively parallel runs.Moreover, in the recent years the Daubechies wavelets formalism has proven useful to benefit from material accelerators (GPU).this code has been the object of the 2009 French Bull-Fourier prize.A hybrid (CPU-GPU) version of the full BigDFT code is available and may benefit of these architectures without reducing the efficiency in parallel runs.
Exploring the benefits of the Daubechies wavelets formalism in the context of electronic structure calculation is thus of great importance either to push state-of-the art approaches to complex environments or to implement novel treatments which may take advantage from the peculiar properties of this basis set.
Main article explaining the wavelet formalism applied to BigDFT:
L. Genovese, A. Neelov, S. Goedecker, T. Deutsch, S. A. Ghasemi, A. Willand, D. Caliste, O. Zilberberg, M. Rayson, A. Bergman, R. Schneider
Daubechies wavelets as a basis set for density functional pseudopotential calculations
Journal of Chemical Physics, Vol. 129, p. 014109 (2008)
Application with large calculations using BigDFT in order to determine properly the binding energy of impurities (neutral and charged defects):
Y. M. Niquet, L. Genovese, C. Delerue, T. Deutsch
Ab initio calculation of the binding energy of impurities in semiconductors: Application to Si nanowires, Phys. Rev. B, Vol. 81, p. 161301(R) (2010)
Integration of BigDFT inside ABINIT:
X. Gonze et al.
ABINIT: first-principles approach to material and nanosystem properties.
Computer Physics Communications, Vol. 180, p. 2582-2615 (2009)
GPU development for BigDFT:
L. Genovese, M. Ospici, T. Deutsch, J.-F. Méhaut, A. Neelov, S. Goedecker
Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures
Journal of Chemical Physics, Vol. 131, p. 034103 (2009)
Poisson solver for polar surfaces:
L. Genovese, T. Deutsch, S. Goedecker
Efficient and accurate three-dimensional Poisson solver for surface problems
Journal of Chemical Physics, Vol. 127, p. 054704 (2007)
Poisson solver for isolated charged systems:
L. Genovese, T. Deutsch, A. Neelov, S. Goedecker, G. Beylkin
Efficient solution of Poisson's equation with free boundary conditions
Journal of Chemical Physics, Vol. 125, p. 074105 (2006)