Extremely scalable algorithm for 10$^8$-atom quantum material simulation on the full system of the K computer

TL;DR

This paper introduces a highly scalable linear-algebraic algorithm for simulating quantum materials with 10^8 atoms, demonstrating excellent parallel performance on the K computer and enabling advanced material research.

Contribution

The paper presents a novel scalable algorithm based on shifted linear equations for large-scale quantum material simulation, applicable to other scientific fields.

Findings

Achieved strong scaling and fast solution times on the K computer.

Successfully simulated 10^8-atom quantum materials.

Enabled real material research for next-generation IoT devices.

Abstract

An extremely scalable linear-algebraic algorithm was developed for quantum material simulation (electronic state calculation) with 10$^8$ atoms or 100-nm-scale materials. The mathematical foundation is generalized shifted linear equations ((zB - A) x = b), instead of conventional generalized eigenvalue equations. The method has a highly parallelizable mathematical structure. The fundamental theory is mathematical and is applicable also to other scientific fields. The benchmark shows an extreme strong scaling and a qualified time-to-solution on the full system of the K computer. The method was demonstrated in a real material research for ultra-flexible (organic) devices, key devices of next-generation IoT products. The present paper shows that an innovative scalable algorithm for a real research can appear by the co-design among application, algorithm and architecture.