A multi-mesh adaptive finite element method for solving the Gross-Pitaevskii equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915725929611264 |
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| author | Li, Mingzhe Kuang, Yang Hu, Zhicheng |
| author_facet | Li, Mingzhe Kuang, Yang Hu, Zhicheng |
| contents | It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh, even with adaptive refinement, can lead to excessive computational costs due to the need to accommodate the most oscillatory solution. To address this issue, we present a multi-mesh adaptive finite element method for solving the GPE. To this end, we first convert it into a time-dependent equation through the imaginary time propagation method. Then the equation is discretized by the backward Euler method temporally and the multi-mesh adaptive finite element method spatially. The proposed method is compared with the single-mesh adaptive method through a series of numerical experiments, which demonstrate that the multi-mesh adaptive method can achieve the same numerical accuracy with less computational consumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08299 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A multi-mesh adaptive finite element method for solving the Gross-Pitaevskii equation Li, Mingzhe Kuang, Yang Hu, Zhicheng Numerical Analysis Mathematical Physics It is found that the wave functions of the Gross-Pitaevskii equation (GPE) often vary significantly in different spatial regions, with some components exhibiting sharp variations while others remain smooth. Solving the GPE on a single mesh, even with adaptive refinement, can lead to excessive computational costs due to the need to accommodate the most oscillatory solution. To address this issue, we present a multi-mesh adaptive finite element method for solving the GPE. To this end, we first convert it into a time-dependent equation through the imaginary time propagation method. Then the equation is discretized by the backward Euler method temporally and the multi-mesh adaptive finite element method spatially. The proposed method is compared with the single-mesh adaptive method through a series of numerical experiments, which demonstrate that the multi-mesh adaptive method can achieve the same numerical accuracy with less computational consumption. |
| title | A multi-mesh adaptive finite element method for solving the Gross-Pitaevskii equation |
| topic | Numerical Analysis Mathematical Physics |
| url | https://arxiv.org/abs/2601.08299 |