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A high-order accurate moving mesh finite element method for the radial Kohn--Sham equation

2024/11/07 by Zheming Luo, Yang Kuang, Luo, Zheming +1
Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics Simulations and Interactions #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2411.04701

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce a highly accurate and efficient numerical solver for the radial Kohn--Sham equation. The equation is discretized using a high-order finite element method, with its performance further improved by incorporating a parameter-free moving mesh technique. This approach greatly reduces the number of elements required to achieve the desired precision. In practice, the mesh redistribution involves no more than three steps, ensuring the algorithm remains computationally efficient. Remarkably, with a maximum of 13 elements, we successfully reproduce the NIST database results for elements with atomic numbers ranging from 1 to 92.

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