Riemannian Newton methods for energy minimization problems of Kohn-Sham type

R. Altmann; D. Peterseim; T. Stykel

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arXiv · 2307.13820

Riemannian Newton methods for energy minimization problems of Kohn-Sham type

R. Altmann·D. Peterseim·T. Stykel

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Abstract

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.

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BibTeX RIS

R. Altmann, D. Peterseim, T. Stykel. 2023-07-25. Riemannian Newton methods for energy minimization problems of Kohn-Sham type. https://arxiv.org/abs/2307.13820

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