[QE-users] Meaning of three G vectors sets

[Stefano de Gironcoli]

A small addition to Lorenzo's explanation

On 24/04/25 10:46, Lorenzo Paulatto wrote:
>>
>> Parallelization info
>>
>> --------------------
>>
>> sticks: densesmooth PW G-vecs:dense smoothPW
>>
>> Min 287 287 819007990079 13189
>>
>> Max 288 288 829013090130 13206
>>
>> Sum25872587733 810915 810915118781
>>
>
> Hello Lorenzo,
>
> the G-vecs are the plane waves, the 3x3 table gives the maximum and 
> minimum number per CPU and the total number for the charge density 
> grid (ecutrho), the "smooth" (4xcutwfc) grid, and the plane-wave 
> (ecutwfc) grid.
>
the "dense" G-vecs number is the number of G-vectors inside the ecutrho 
sphere in the dense grid (which is the smallest grid that avoid aliasing 
errors for functions whose Fourier components vanish beyond ecutrho), 
used to expand density and potentials to the needed accuracy, "smooth" 
is the number of G-vecs inside the "4*ecutwfc" sphere in the smooth grid 
(which is the smallest grid that avoid aliasing errors for functions 
whose Fourier components vanish beyond 4*ecutwfc) , used to interpolate 
the potential on it so that V*psi can be computed exactly in real 
space,  PW number is the number of G-vecs inside the ecutwfc sphere in 
the smooth grid, used to inject psi on the fft grid when going from G->R 
and extract hpsi when going from R->G.  check the attached pdf, hope it 
may be useful (discard last slide which is not valid anymore).
>
> The sticks, are the subdivisions of the plane waves over which the 
> parallelization occurs, i.e. the charge is subdivided in 2587 sticks 
> and every CPU inside a pool gets 287 or 288 to do Fourier transforms 
> (they used to be called planes, I guess it now depends if you are 
> using "pencil decomposition" or not)
>
in reciprocal space G-vectors assigned to an mpi process are organized 
in sticks or pencils, in real space they are organized in planes.

sticks are assigned to different mpi processes trying to have a balanced 
distribution, because they are the number of 1d fft to be performed, and 
in term of contained G-vectors, because this is the leading dimension of 
many g-space arrays (npw), planes in real space are also distributed in 
the most balanced possible way, but this is trivial.

hence "dense" is the number of sticks that intersect the cutoff sphere 
in the dense grid assigned to a given mpi process, "smooth" the same for 
the "4*ecutwfc" sphere on the smooth grid, "PW" the same on the smooth 
grid but for the "ecutwfc" sphere.

HTH

stefano

>> Second, when printing the energies per k-point, a number of G vectors 
>> is given as if it were the number of planewaves ( e.g. "k = 0.0833 
>> 0.1443 0.0000 (101603PWs) bands (ev):" ). What does this number 
>> actually refer to?
>>
> It is in fact the number of plane waves used to expand the wvafunction 
> at that k-point.
>
> The condition to include a plane wave is that (G+k)^2 < ecutwfc/ħ, 
> which defines a sphere in reciprocal space, with G being a multiple of 
> the reciprocal axis vectors and k is smaller than any G. So the number 
> varies with the k-point. Then, in order to do FFT, all the G from all 
> the spheres are combined and padded with extra point to make a 
> parallelogram.
>
> You take a parallelogram of twice the side in order to fit |psi|^2, 
> and if a larger ecutrho has been defined this will determine a third 
> grid with |G|^2 < ecutrho/ħ
>
> hth
>
>> Last question: how all these sets are related to the values of 
>> ecutwfc and ecutrho ?
>>
> should be explained above.
>
>
>> Many thanks!
>>
>>
>> -- 
>> Dr. Lorenzo Sponza
>>
>> Chargé de Recherche au CNRS
>> Université Paris-Saclay, ONERA, CNRS Laboratoire d'étude des 
>> microstructures (LEM)
>> 29 Avenue de la division Leclerc, 92322 Châtillon
>> Tel: +33146734464
>>
>> ETSF Research Team Leader
>> European Theoretical Spectroscopy Facility
>> 17 Sart-Tilman B-4000 Liège, Belgium
>>
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> -- 
> Dr. Lorenzo Paulatto
> IdR @ IMPMC - CNRS UMR 7590 & Sorbonne Université
> phone: +33 (0)1 442 79822 / skype: paulatz
> http://people.impmc.fr/lpaulatto/ - https://anharmonic.github.io/
> 23-24/423 B115, 4 place Jussieu 75252 Paris CX 05
>
> _______________________________________________________________________________
> The Quantum ESPRESSO Foundation stands in solidarity with all civilians worldwide who are victims of terrorism, military aggression, and indiscriminate warfare.
> --------------------------------------------------------------------------------
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing listusers at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
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