On accelerating a multilevel correction adaptive finite element method for Kohn-Sham equation

TL;DR

This paper enhances the efficiency of a multilevel correction adaptive finite element method for the Kohn-Sham equation by separately handling potentials and parallelizing the algorithm, resulting in significant practical improvements.

Contribution

It introduces a novel approach that separately manages nonlinear potentials and employs parallelization, significantly improving computational efficiency for the Kohn-Sham equation.

Findings

Significant reduction in computational time.

Enhanced suitability for practical problems.

Validation through extensive numerical experiments.

Abstract

Based on the numerical method proposed in [G. Hu, X. Xie, F. Xu, J. Comput. Phys., 355 (2018), 436-449.] for Kohn-Sham equation, further improvement on the efficiency is obtained in this paper by i). designing a numerical method with the strategy of separately handling the nonlinear Hartree potential and exchange-correlation potential, and ii).parallelizing the algorithm in an eigenpairwise approach. The feasibility of two approaches are analyzed in detail, and the new algorithm is described completely. Compared with previous results, a significant improvement of numerical efficiency can be observed from plenty of numerical experiments, which make the new method more suitable for the practical problems.