Adaptive basis refinement

[gkemlin]

Hi,

we would like with @ra-lainezr to implement in DFTK the error bounds we developed in this paper , so this post is not really an issue but rather a way to start brainstorming on how to do it. We have two main questions :

1. We are able to track (approximate) discretization and SCF errors along the SCF iterations. How would you like it to be implemented ? Should it be by computed by default or if a flag is activated ?

2. We would like to use it for basis refinement in terms of Ecut. At the moment, we just rebuild new basis, but this is not the most efficient way to do it. Is there already a function to build a basis with Ecut_large from a basis with Ecut_small < Ecut_large ? I could not find one, so maybe we should implement one.

PS: That's not urgent, just to start thinking about it 😄

[antoine-levitt]

1 Behind a flag sounds good (at least at the beginning: if it's cheap and reasonable we can turn it on by default later). 2 I don't think so, but the cost of basis creation is not that huge anyway

[mfherbst]

Behind a flag sounds good

To me this is something where a marker struct could make sense. But perhaps a good way to think about it is also as a "macro-iteration" around a standard SCF ? Just thinking this may make it easier to also employ such things in direct minimisation or related algorithm.

cost of basis creation is not that huge anyway

Well depends on your problem. One can feel it for larger-ish systems.