A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914126808219648 |
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| author | Chu, Tianyang Dai, Xiaoying Wu, Jing Zhou, Aihui |
| author_facet | Chu, Tianyang Dai, Xiaoying Wu, Jing Zhou, Aihui |
| contents | This paper concerns the mathematical and numerical analysis of the $L^2$ normalized gradient flow model for the Gross--Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the ground state of the Bose--Einstein condensate. We first provide the mathematical analysis for the model, including the well-posedness and the asymptotic behavior of the solution. Then we propose a normalized implicit-explicit fully discrete numerical scheme for the gradient flow model, and give some numerical analysis for the scheme, including the well-posedness and optimal convergence of the approximation. Some numerical experiments are provided to validate the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_27235 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis Chu, Tianyang Dai, Xiaoying Wu, Jing Zhou, Aihui Numerical Analysis This paper concerns the mathematical and numerical analysis of the $L^2$ normalized gradient flow model for the Gross--Pitaevskii eigenvalue problem, which has been widely used to design the numerical schemes for the computation of the ground state of the Bose--Einstein condensate. We first provide the mathematical analysis for the model, including the well-posedness and the asymptotic behavior of the solution. Then we propose a normalized implicit-explicit fully discrete numerical scheme for the gradient flow model, and give some numerical analysis for the scheme, including the well-posedness and optimal convergence of the approximation. Some numerical experiments are provided to validate the theory. |
| title | A gradient flow model for the Gross--Pitaevskii problem: Mathematical and numerical analysis |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2510.27235 |