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.
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