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.

翻译：根据Kohn-Sham等式[G.Hu, X. X. Xie, F. Xu, J. Comput. Phys., 355 (2018), 436-449.]中提议的数值方法,本文件通过i)进一步提高了效率。 设计了一种数字方法,其战略是分别处理非线性Hartree潜力和交换-关系潜力,和ii) 。用一种双基因方法对算法进行平行。对两种方法的可行性进行了详细分析,并完整地描述了新的算法。与以往的结果相比,从大量的数字实验中可以观察到数字效率的显著提高,这使得新的方法更适合实际问题。