Eigenproblems and Eigensolvers in Density Functional Theory

In DFT based simulations each SCF cycle comprises dozens of large generalized eigenproblems. In a recent study, it has been proposed to consider simulations as made of dozens of sequences of eigenvalue problems, where each sequence groups together eigenproblems with equal k-vector and increasing iteration index i. It was then demonstrated that successive eigenproblems in a sequence are strongly correlated to one another. In particular, by tracking the evolution over iterations of the angle between eigenvectors of adjacent iterations, it was shown the angles decrease noticeably after the first few iterations and become close to collinear. This last result suggests we could use the eigenvectors solution of a problem in a sequence as an educated guess for the eigenvectors of the successive problem. In this talk we present preliminary results that would eventually open the way to a widespread use of iterative solvers in ab initio electronic structure codes. We provide numerical examples where opportunely selected iterative solvers benefit from the reuse of eigenvectors when applied to sequences of eigenproblems extracted from simulations of real-world materials