An order-N electronic structure theory with generalized eigenvalue equations and its application to a ten-million-atom system

Abstract

A linear algebraic theory called the multiple Arnoldi method is presented and realizes large-scale (order-N) electronic structure calculations with generalized eigenvalue equations. A set of linear equations, in the form of (zSH)x=b, are solved simultaneously with multiple Krylov subspaces. The method is implemented in a simulation package ELSES (www.elses.jp) with tight-binding-form Hamiltonians. A finite-temperature molecular dynamics simulation is carried out for metallic and insulating materials. A calculation with 10 7 atoms was realized by a workstation. The parallel efficiency is shown up to 1024 CPU cores. © 2012 IOP Publishing Ltd.