Numerical Algorithms for Density Functional Theory

Monday, July 30, 2007 - 11:15am - 12:30pm
EE/CS 3-180
Yousef Saad (University of Minnesota, Twin Cities)
Density Functional Theory (DFT) is a successful technique used to
determine the electronic structure of matter which is based on a
number of approximations that convert the original n-particle
problem into an effective one-electron system. The end-problem is
essentially a non-linear eigenvalue problem which is solved
iteratively. The challenge comes from the large number of
eigenfunctions to be computed for realistic systems with, say,
hundreds or thousands of electrons. We will discuss techniques for
diagonalization, and for dealing with the nonlinearity. It is
important consider the problem as one of computing an invariant
subspace in the non-linear context of the Kohn-Sham equations. This
viewpoint leads to considerable savings as it de-emphasizes the
accurate computation of individual eigenvectors and focuses instead on
the subspace which they span. We will also discuss other algorithmic
issues encountered in DFT and will offer some thoughts on
diagonalization-free techniques.