## Poster 54: Massively Parallel Eigensolvers Based on Unconstrained Energy Functionals Methods

**Authors:** Osni Marques (Lawrence Berkeley National Laboratory), Mauro Del Ben (Lawrence Berkeley National Laboratory), Andrew Canning (Lawrence Berkeley National Laboratory)

**Abstract:** This poster focuses on a preconditioned conjugate gradient based iterative eigensolver using an unconstrained energy functional minimization scheme. This scheme avoids an explicit reorthogonalization of the trial eigenvectors and becomes an attractive alternative for the solution of very large problems. The unconstrained formulation is implemented in the first-principles materials and chemistry CP2K code, which performs electronic structure calculations based on a density functional theory approximation to the solution of the many-body SchrÃ¶dinger equation. The systems we use in our studies have a number of atoms ranging from 2,247 to 12,288. We study the convergence of the unconstrained formulation and its scaling on a Cray XC40 (a partition with 9,688 Intel KNL nodes). We show that there is a trade-off between the preconditioner that leads to fast convergence and lower cost preconditioners that lead to best time to solution.

**Best Poster Finalist (BP):** yes

**Poster:** PDF

**Poster summary:** PDF

Back to Poster Archive Listing