computational scaling in QS
Nichols A. Romero
naro... at gmail.com
Wed Jun 6 14:55:02 UTC 2007
Hi,
I was hoping that I can get some clarification about the scaling in QS. I
read through
Comp. Phys. Comm. 167 (2005) 103. My background is PW methods.
There are two ways to obtain the KS ground state in QS:
1. SCF + traditional diagonalization (TD)
- The construction of the KS matrix is approximately O(N ln N) < O
(N^(1+epsilon))
- TD scales as M^3
N is the number of occupied orbitals ??
M is the number of basis functions
Fig. 4 on p. 110 of the article uses N only, instead of M and N. I guess one
parameter
indicative of system size was used instead of multiple parameters.
Also, could someone comment on the memory requirement using SCF + TD.
2. OT
- On p. 117, the text states that in the most optimal situation the method
scales as M*N^2 and M^2*N in the worst case (non-sparse) scenario.
- The memory scales as O(M*N) which I is also similar to a PW method
but with a localized basis M is substantiall smaller. I imagine the other
terms
that contribute to the memory scaling, e.g. potential, charge density, etc.
are negligible ??
--
Nichols A. Romero, Ph.D.
1613 Denise Dr. Apt. D
Forest Hill, MD 21050
443-567-8328 (C)
410-306-0709 (O)
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