Solving large nonlinear generalized eigenvalue problems from Density Functional Theory calculations in parallel

2000/11/07 by Claus Bendtsen, Ole H. Nielsen, Lars B. Hansen
Physics and Astronomy · #cond-mat.mtrl-sci

paper · pdf

published as Applied Numerical Mathematics, Vol. 37 (1-2) (2001) pp. 189-199 · 20 pages, 4 figures. Accepted for Applied Numerical Mathematics (Elsevier)

arxiv created 2000/11/07 · arxiv updated 2009/11/30

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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