Novel linear algebraic theory and one-hundred-million-atom electronic structure calculation on the K computer

TL;DR

This paper introduces a new linear algebra algorithm, the multiple Arnoldi method, enabling large-scale electronic structure calculations for 100-million-atom systems on the K computer, advancing computational physics and applied mathematics.

Contribution

The paper presents a novel Krylov-subspace solver algorithm and its implementation for large-scale electronic structure calculations, including a new eigenstate calculation method.

Findings

Achieved electronic state calculations for 100-million-atom systems.

Developed the multiple Arnoldi method for generalized shifted linear equations.

Implemented the algorithm in the order-N code ELSES.

Abstract

A novel linear-algebraic algorithm, multiple Arnoldi method, was developed in an interdisciplinary study between physics and applied mathematics and realized one-hundred-million-atom (100-nm-scale) electronic state calculations on the K computer. The algorithms are Krylov-subspace solvers for generalized shifted linear equations and were implemented in our order-N calculation code ELSES (http://www.elses.jp/). Moreover, a method for calculating eigen states is presented as a theoretical extension.