title: 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 (zS - H)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.
authors.affiliation: Department of Applied Mathematics and Physics, Tottori University, Tottori, Japan. hoshi@damp.tottori-u.ac.jp
authors.forename: T
authors.initials: T
authors.lastname: Hoshi
authors.forename: S
authors.initials: S
authors.lastname: Yamamoto
authors.forename: T
authors.initials: T
authors.lastname: Fujiwara
authors.forename: T
authors.initials: T
authors.lastname: Sogabe
authors.forename: S-L
authors.initials: SL
authors.lastname: Zhang