A novel splitting strategy to accelerate solving generalized eigenvalue problem from Kohn--Sham density functional theory

TL;DR

This paper introduces a new eigenpair-splitting method inspired by divide-and-conquer strategies to efficiently solve generalized eigenvalue problems from Kohn-Sham density functional theory, improving computational speed and practical applicability.

Contribution

The paper presents a novel eigenpair-splitting approach that differs from traditional domain decomposition, integrating multi-mesh and soft-locking techniques for enhanced efficiency in electronic structure calculations.

Findings

Significantly improves simulation efficiency

Demonstrates effectiveness in HOMO-LUMO gap calculation

Provides insights into optimal eigenpair grouping strategies

Abstract

In this paper, we propose a novel eigenpair-splitting method, inspired by the divide-and-conquer strategy, for solving the generalized eigenvalue problem arising from the Kohn-Sham equation. Unlike the commonly used domain decomposition approach in divide-and-conquer, which solves the problem on a series of subdomains, our eigenpair-splitting method focuses on solving a series of subequations defined on the entire domain. This method is realized through the integration of two key techniques: a multi-mesh technique for generating approximate spaces for the subequations, and a soft-locking technique that allows for the independent solution of eigenpairs. Numerical experiments show that the proposed eigenpair-splitting method can dramatically enhance simulation efficiency, and its potential towards practical applications is also demonstrated well through an example of the HOMO-LUMO gap calculation. Furthermore, the optimal strategy for grouping eigenpairs is discussed, and the possible improvements to the proposed method are also outlined.