Riemannian Newton methods for energy minimization problems of Kohn-Sham type
- 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.
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| Author: | Robert AltmannORCiDGND, Daniel PeterseimORCiDGND, Tatjana StykelORCiDGND |
|---|---|
| URN: | urn:nbn:de:bvb:384-opus4-1073044 |
| Frontdoor URL | https://opus.bibliothek.uni-augsburg.de/opus4/107304 |
| ISSN: | 0885-7474OPAC |
| Parent Title (English): | Journal of Scientific Computing |
| Publisher: | Springer |
| Place of publication: | Berlin |
| Type: | Article |
| Language: | English |
| Year of first Publication: | 2024 |
| Publishing Institution: | Universität Augsburg |
| Release Date: | 2023/08/31 |
| Volume: | 101 |
| First Page: | 6 |
| DOI: | https://doi.org/10.1007/s10915-024-02612-3 |
| Institutes: | Mathematisch-Naturwissenschaftlich-Technische Fakultät |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik | |
| Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik | |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| Licence (German): |  CC-BY 4.0: Creative Commons: Namensnennung (mit Print on Demand) |
