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240923s2024 xx |||||o 00| ||eng c |
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|a 10.1007/s10915-024-02612-3
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|a eng
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|a Altmann, R
|e verfasserin
|4 aut
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|a Riemannian Newton Methods for Energy Minimization Problems of Kohn-Sham Type
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|c 2024
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|a Text
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|a ƒaComputermedien
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|a ƒa Online-Ressource
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|a Date Revised 24.09.2024
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|a published: Print-Electronic
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|a Citation Status PubMed-not-MEDLINE
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|a © The Author(s) 2024.
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|a 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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|a Journal Article
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|a Grassmann manifold
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|a Gross–Pitaevskii eigenvalue problem
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|a Kohn–Sham model
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| 650 |
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|a Newton method
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| 650 |
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|a Riemannian optimization
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| 650 |
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|a Stiefel manifold
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1 |
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|a Peterseim, D
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Stykel, T
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t Journal of scientific computing
|d 1999
|g 101(2024), 1 vom: 15., Seite 6
|w (DE-627)NLM098177567
|x 0885-7474
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|g volume:101
|g year:2024
|g number:1
|g day:15
|g pages:6
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|u http://dx.doi.org/10.1007/s10915-024-02612-3
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