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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2011.13173 |
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| _version_ | 1866908663563681792 |
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| author | Yin, Jianyuan Huang, Zhen Zhang, Lei |
| author_facet | Yin, Jianyuan Huang, Zhen Zhang, Lei |
| contents | We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-$k$ saddle points of an energy functional subject to equality constraints. With Riemannian manifold tools, the CHiSD is derived in a minimax framework, and its linear stability at an index-$k$ saddle point is proved. To ensure the manifold property, the CHiSD is numerically implemented using retractions and vector transport. Then we present a numerical approach by combining CHiSD with downward and upward search algorithms to construct the solution landscape in the presence of equality constraints. We apply the Thomson problem and the Bose-Einstein condensation as numerical examples to demonstrate the efficiency of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_13173 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Constrained high-index saddle dynamics for the solution landscape with equality constraints Yin, Jianyuan Huang, Zhen Zhang, Lei Numerical Analysis We propose a constrained high-index saddle dynamics (CHiSD) method to search for index-$k$ saddle points of an energy functional subject to equality constraints. With Riemannian manifold tools, the CHiSD is derived in a minimax framework, and its linear stability at an index-$k$ saddle point is proved. To ensure the manifold property, the CHiSD is numerically implemented using retractions and vector transport. Then we present a numerical approach by combining CHiSD with downward and upward search algorithms to construct the solution landscape in the presence of equality constraints. We apply the Thomson problem and the Bose-Einstein condensation as numerical examples to demonstrate the efficiency of the proposed method. |
| title | Constrained high-index saddle dynamics for the solution landscape with equality constraints |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2011.13173 |