Thank your very much for your clarification.
Best Regards,
Jan
Zitat von Emilio Artacho <ea...@cam.ac.uk>:
On 19 Jul 2011, at 14:37, Jan Sommer wrote:
Dear all,
this may be a simple question but it confuses me somehow.
If I read papers about siesta they always describe the calculation
with an order-n method.
Does this method only apply by using "SolutionMethon ordern" and
"SolutionMethod Diagon" scales with N^3 or does it apply for both
variants and "ordern" is a special option?
of the two main components of a DFT calculation,
- the calculation of the H and S matrix elements, and
- the solution of the KS problem to get E, density and forces,
the first one is always done with an O(N) method, for which
there is no alternative. The actual scaling of that bit
is not linear for small systems, but it becomes O(N) when the
system dimensions are larger than the scale of orbital r_c's.
For the solution part, if diagon is used, that part scales as
N^3; it uses an O(N) method if using the ordern option for
the solver, and (again) it becomes linear scaling only if
the system size is larger than the radial cutoff for the
local solution wave-functions.
A practical fact is that the vast majority of users use
the O(N) character of the matrix-calculation bit, but use
diagon for the solution. This is due to:
- the vast majority of calculations would not benefit
from ordern (most of the calculations done are for
intermediate system sizes, for varied reasons e.g.
the long time scales needed in MD simulations for
growing system sizes).
- The ordern options are substantially more difficult to
use, and can be quite fragile for some systems.
An additional practicality is that because of both reasons
above, bugs creeping into ordern options as the code evolves
have been more resilient than in more popular bits of the code.
We are working now on cleaning and automatising ordern
options better, to try to get them more used and thus more
dynamic in their evolution and optimisation.
The relative importance of both parts of a calculation
depends very much on the kind of calculation. Mesh cutoff
affects only matrix-element calculation; orbital cutoff radii
affect matrix elements and the linear-scaling solver, but not
the diagonalisation; k-sampling affects the solvers only,
and the number of basis orbitals affects them all.
Bottomline, the siesta method allows running in O(N),
but the actual scaling of your calculations depends on
the system, its size, and your choices for method
and parameters. I hope this clarifies on fundamentals and
practicalities.
Best
Emilio
Best Regards,
Jan
--
Emilio Artacho
Department of Earth Sciences, University of Cambridge
Downing Street, Cambridge CB2 3EQ, UK
Tel. (+44/0) 1223 333480, Fax (+44/0) 1223 333450
emi...@esc.cam.ac.uk, http://www.esc.cam.ac.uk/~emilio
