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arXiv · 2411.04661

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

Yang Kuang·Guanghui Hu
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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.

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Yang Kuang, Guanghui Hu. 2024-11-07. A novel splitting strategy to accelerate solving generalized eigenvalue problem from Kohn--Sham density functional theory. https://arxiv.org/abs/2411.04661

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