Ten-million-atom electronic structure calculations on the K computer with a massively parallel order-N theory

TL;DR

This paper introduces a massively parallel order-N electronic structure calculation method capable of handling ten-million-atom systems on the K computer, demonstrating high efficiency and novel analysis tools for large-scale data.

Contribution

It presents a new linear algebraic algorithm for large-scale electronic structure calculations and a post-processing analysis method suitable for distributed data.

Findings

Achieved 98,304 processor core efficiency on ten-million-atom systems.

Developed the pi-COHP analysis method for large electronic structure data.

Demonstrated visualization of nano-composite carbon systems.

Abstract

A massively parallel order-N electronic structure theory was constructed by an interdisciplinary research between physics, applied mathematics and computer science. (1) A high parallel efficiency with ten-million-atom nanomaterials was realized on the K computer with upto 98,304 processor cores. The mathematical foundation is a novel linear algebraic algorithm for the generalized shifted linear equation. The calculation was carried out by our code ' ELSES ' (www.elses.jp) with modelled (tight-binding-form) systems based on ab initio calculations. (2) A post-calculation analysis method, called pi-orbital crystalline orbital Hamiltonian population (pi-COHP) method, is presented, since the method is ideal for huge electronic structure data distributed among massive nodes. The analysis method is demonstrated in an sp2-sp3 nano-composite carbon solid, with an original visualization software 'VisBAR'. The present research indicates general aspects of computational physics with current or next-generation supercomputers.