SCF preconditioning for mixed systems

Fortunately the general lockdown due to the Corona pandemic slowly starts to ease around Paris as well. While basically all seminars are only virtual it is good to see old procedures and habits to slowly return. From my end I gave the first talk after the forced break today in the EMC2 group meeting.

Since it was the first time discussing DFTK in the EMC2 synergy group I decided to talk about it taking the angle of tackling an actual research problem. After presenting briefly DFT methods and DFTK in the first half of the talk, I therefore focused on one of my ongoing projects with Antoine Levitt, namely constructing better preconditioners for the self-consistent field (SCF) iterations in mixed systems. What is meant by mixed systems are systems where locally differing dielectric properties are found, i.e. where some parts of the material are insulating, others may be metallic or semiconductors. Since the dielectric properties are closely related to the spectrum of the SCF fixed-point map, they therefore also control the convergence properties of SCF procedures. For metals and (to a minor extent) semiconductors simple SCF procedures, where one just applies the SCF cycle over and over require extremely small step sizes (i.e. small damping values). As a result the SCF converges only very slowly. The remedy is to precondition the spectrum of the SCF map itself by using so-called mixing techniques. In state-of-the-art approaches these are usually material-specific, i.e. different mixings are used for insulators, metals or semiconductors. This is fine for bulk materials, but fails in case of mixed systems, since one has to globally select a single approach. Our recent work has been to investigate the spectrum of the SCF map and to try and construct a preconditioner which locally adapts and as a result is able to properly treat mixed systems as well. The results I presented today are, however, not yet final and more investigations are to be underdone for our approach to work as reliable as we want.

SCF preconditioning for mixed systems: A DFTK case study (Slides)
A few DFTK examples (Jupyter notebook)
SCF preconditioners in 1D (Jupyter notebook)