A high-order accurate moving mesh finite element method for the radial Kohn--Sham equation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910687821824000 |
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| author | Luo, Zheming Kuang, Yang |
| author_facet | Luo, Zheming Kuang, Yang |
| contents | 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 $92$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04701 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A high-order accurate moving mesh finite element method for the radial Kohn--Sham equation Luo, Zheming Kuang, Yang Numerical Analysis Computational Physics 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 $92$. |
| title | A high-order accurate moving mesh finite element method for the radial Kohn--Sham equation |
| topic | Numerical Analysis Computational Physics |
| url | https://arxiv.org/abs/2411.04701 |