Riemannian Newton Methods for Energy Minimization Problems of Kohn-Sham Type
© The Author(s) 2024.
| Veröffentlicht in: | Journal of scientific computing. - 1999. - 101(2024), 1 vom: 15., Seite 6 |
|---|---|
| 1. Verfasser: | |
| Weitere Verfasser: | , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2024
|
| Zugriff auf das übergeordnete Werk: | Journal of scientific computing |
| Schlagworte: | Journal Article Grassmann manifold Gross–Pitaevskii eigenvalue problem Kohn–Sham model Newton method Riemannian optimization Stiefel manifold |
| Zusammenfassung: | © The Author(s) 2024. 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 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 their supremacy compared to other well-established schemes such as the self-consistent field iteration and gradient descent schemes |
|---|---|
| Beschreibung: | Date Revised 24.09.2024 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0885-7474 |
| DOI: | 10.1007/s10915-024-02612-3 |