Solving large nonlinear generalized eigenvalue problems
from Density Functional Theory calculations in parallel
by Claus Bendtsen,
Ole H. Nielsen,
and Lars B. Hansen.
Center for Atomic-scale Materials Physics (CAMP), Dept. of Physics,
Technical University of Denmark, Bldg. 307, DK-2800 Lyngby, Denmark.
Published in Applied Numerical Mathematics Vol. 37 (1-2) (2001) pp. 189-199.
Online paper is
here.
Abstract
The quantum mechanical ground state of electrons is described by
Density Functional Theory, which leads to large minimization problems.
An efficient minimization method uses a selfconsistent field (SCF)
solution of large eigenvalue problems. The iterative Davidson
algorithm is often used, and we propose a new algorithm of this kind
which is well suited for the SCF method, since the accuracy of the
eigensolution is gradually improved along with the outer
SCF-iterations. Best efficiency is obtained for small-block-size
iterations, and the algorithm is highly memory efficient. The
implementation works well on both serial and parallel computers, and
good scalability of the algorithm is obtained.
PostScript file of the full paper,
73 kB.