Riemannian Newton methods for energy minimization problems of Kohn-Sham type
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929400841240576 |
|---|---|
| author | Altmann, R. Peterseim, D. Stykel, T. |
| author_facet | Altmann, R. Peterseim, D. Stykel, T. |
| contents | This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross-Pitaevskii and Kohn-Sham models. In particular, we introduce the Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates its supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13820 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Riemannian Newton methods for energy minimization problems of Kohn-Sham type Altmann, R. Peterseim, D. Stykel, T. Numerical Analysis Optimization and Control 65K10, 65N25, 81Q10 This paper is devoted to the numerical solution of constrained energy minimization problems arising in computational physics and chemistry such as the Gross-Pitaevskii and Kohn-Sham models. In particular, we introduce the Riemannian Newton methods on the infinite-dimensional Stiefel and Grassmann manifolds. We study the geometry of these two manifolds, its impact on the Newton algorithms, and present expressions of the Riemannian Hessians in the infinite-dimensional setting, which are suitable for variational spatial discretizations. A series of numerical experiments illustrates the performance of the methods and demonstrates its supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes. |
| title | Riemannian Newton methods for energy minimization problems of Kohn-Sham type |
| topic | Numerical Analysis Optimization and Control 65K10, 65N25, 81Q10 |
| url | https://arxiv.org/abs/2307.13820 |