Preliminary progamme

The DFTK school will run from Mo 29th August until We 31st August with lectures in the morning and hands-on practical session in the afternoon. Both lectures and practical sessions will take place at the Jussieu campus of Sorbonne Université. The preliminary schedule is as follows.

Mo 29 August

Morning lectures: Introduction and physical background

• Time: 9:00 - 12:30

• Location: LJLL seminar room, 15-16-309 (3rd floor corridor between towers 15 and 16)

• Topics Emmanuel Fromager:

  • Slides

  • Introduction to DFT

  • Exact DFT and Levy's constrained search

  • DFT approximations

  • DFT functional approximations

• Topics Fabien Bruneval:

  • Slides

  • Periodic problems and lattices

  • Bloch theorem

  • Plane-wave basis sets

  • Pseudopotentials

  • SCF cycles

Poster session and buffet lunch

• Time: 12:30 - 14:00

• Location: Patio under buildings 24-25

• Lunch will be provided by us during the poster session (included in the workshop)

Afternoon practical: Numerical modelling of periodic problems

• Time: 14:00 - 17:00

• Location: LJLL seminar room, 15-16-309 (3rd floor corridor between towers 15 and 16)

• Topics:

  • Introduction to Julia programming: Jupyter notebooks

  • Jupyter notebooks on workshop git repository:

    • Contrast of discretisation techniques

    • Simple tight-binding models for atomic chains

  • DFTK tutorial introducing periodic problems

Tu 30 August

Morning lectures: Numerical techniques for DFT

• Time: 9:00 - 12:30

• Location: LJLL seminar room, 15-16-309 (3rd floor corridor between towers 15 and 16)

• Topics Eric Cancès:

  • Slides

  • Fourier series and Fourier analysis for periodic functions

  • Bloch theorem for supercells

  • Brillouin zone discretisations for metals

• Topics Michael Herbst:

  • Lecture notes

  • Analysis of SCF convergence

  • Mixing and preconditioning techniques

  • Direct minimisation

Lunch break

• Time: 12:30 - 14:00

Afternoon practicals: Study of DFT algorithms

• Time: 14:00 - 17:00

• Location: 24-25-101 and 24-25-103 (1st floor corridor between towers 24 and 25)

• Topics:

  • Tutorial introduction and DFTK examples

  • Jupyter notebooks on the workshop git repository:

    • Standard DFT setups (insulators, metals, isolated systems)

    • SCF algorithms

    • Analysis of SCF convergence

    • Comparison of SCF and direct minimisation

We 31 August

Morning lectures: Advanced topics

• Time: 9:00 - 12:30

• Location: LJLL seminar room, 15-16-309 (3rd floor corridor between towers 15 and 16)

• Topics Marc Torrent:

  • Slides

  • Hardware and programming models in HPC

  • Benefits and prospects of HPC for DFT calculations

  • DFT diagonalisations: Algorithms and their range of applicability

• Topics Geneviève Dusson:

  • Slides

  • A posteriori error estimation of the discretisation error in DFT

  • Error estimation of quantities of interest (forces etc.)

• Topics Antoine Levitt:

  • General methodology of algorithmic differentiation

  • Implementation of algorithmic differentiation in Julia

  • Application to DFT: Phonons and response properties

Lunch

• Time: 12:30 - 14:00

Afternoon practicals: Hands-on study of advanced topics

• Time: 14:00 - 17:00

• Location: 24-25-101 and 24-25-103 (1st floor corridor between towers 24 and 25)

• Miniprojects on AD / response:

  • Use AD in functional minimisation problem

  • Three ways to do response: Finite differences, forward-mode AD and analytic

• Miniprojects on HPC:

  • Performance benchmarking of DFTK

  • Code your own eigensolver and engineer its performance

  • Implement and parallelise a 1D band-structure computation

• Miniproject on error control:

  • Estimating discretisation errors on forces

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