New eigensolvers for large-scale nanoscience simulations

Abstract

We present results for applications to nanosystems of state-of-the-art iterative eigensolvers based on conjugate gradients and variants of Davidson in the context of semi-empirical plane wave electronic structure calculations. We are concerned with the computation of electronic and optical properties of nanosystems using the Energy SCAN method to compute interior eigenstates around the band gap that determine their properties. Numerically, this interior Hermitian eigenvalue problem poses several challenges, with respect to both accuracy and efficiency. All the iterative eigensolvers are seeking the minimal eigenvalues of the folded operator with reference shift in the band-gap. The tested methods include standard conjugate-gradient (CG)-based Rayleigh quotient minimization, Locally optimal block-preconditioned CG (LOBPCG) and two variants of the (Jacobi-)Davidson method: JDQMR and GD+1. Our experimental results indicated that Davidson-type methods are often the fastest.