llg-midpoint integrator

[Florian Slanovc]

Dear Vampire users,

I am currently investigating and comparing the stability behaviour of the llg-heun and llg-midpoint integrator, so my questions are:

-) Is there some (rough) documentation about the derivation of the midpoint-implementation, as it exists for the heun-method in the article "Atomistic spin model simulations of magnetic nanomaterials"?
-) Are there still any essential reasons not to use the midpoint-method? I am asking this because on the web page this integrator is still declared as "beta version", but its performance (essential with small damping constants and rough time steps) is nevertheless much better than the heun's one and therefore I would very much prefer it in future simulations!

Thanks in advance and a Happy New Year to everyone,
Florian

[Richard Evans]

Dear Florian,

The midpoint method in VAMPIRE was implemented  by Matt Ellis and briefly detailed in his thesis (Chapter 2):

http://etheses.whiterose.ac.uk/12215/10/MElliss_Thesis.pdf

I have not yet got round to comparing the performance of the different integrators. In principle the midpoint method should be better but Matt’s feeling was that for the tests he did it did not show any huge advantage. I would be very interested in seeing any analysis of this, particularly as a function of the damping.

All the best,

Richard

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[Florian Slanovc]

Dear Richard,

thank you very much for the reference - on the basis of the thesis I was able to understand the algorithm in the VAMPIRE-sourcecode very well!

My impressions with small damping constant are so far:
- For very small time steps, both methods (Heun and midpoint) lead to similar results.
- If the time step becomes larger, the midpoint-method reserves the magnetization curve quite well, whereas the heun-method yields completely unrealistic values very soon.

So if one tries to save as much computational effort as possible (as I do 24/7 :-) ) and simulates with critical time steps, I would personally choose the midpoint-method to be on the safer side!

Maybe we could pursue with further investigations about that - I have to discuss that with my advisor Prof. Dieter Suess!

Kind regards,
Florian