1202.0098 (T. Hoshi et al.)

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

T. Hoshi, S. Yamamoto, T. Fujiwara, T. Sogabe, S. -L. Zhang

A linear-algebraic theory called 'multiple Arnoldi method' is presented and
realizes large-scale (order-N) electronic structure calculation with
generalized eigen-value 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 (http://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 upto 1,024 CPU cores.

View original: http://arxiv.org/abs/1202.0098