On Optimal Convergence Rates for Discrete Minimizers of the Gross–Pitaevskii Energy in Localized Orthogonal Decomposition Spaces
P Henning, A Persson - Multiscale Modeling & Simulation, 2023 - SIAM
In this paper we revisit a two-level discretization based on localized orthogonal
decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D …
decomposition (LOD). It was originally proposed in [P. Henning, A. Målqvist, and D …
Convergence analysis of direct minimization and self-consistent iterations
This article is concerned with the numerical solution of subspace optimization problems,
consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed …
consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed …
An overview of a posteriori error estimation and post-processing methods for nonlinear eigenvalue problems
In this article, we present an overview of different a posteriori error analysis and post-
processing methods proposed in the context of nonlinear eigenvalue problems, eg arising in …
processing methods proposed in the context of nonlinear eigenvalue problems, eg arising in …
Sobolev gradient flow for the Gross--Pitaevskii eigenvalue problem: Global convergence and computational efficiency
P Henning, D Peterseim - SIAM Journal on Numerical Analysis, 2020 - SIAM
We propose a new normalized Sobolev gradient flow for the Gross--Pitaevskii eigenvalue
problem based on an energy inner product that depends on time through the density of the …
problem based on an energy inner product that depends on time through the density of the …
On the convergence of Sobolev gradient flow for the Gross–Pitaevskii eigenvalue problem
We study the convergences of three projected Sobolev gradient flows to the ground state of
the Gross–Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the …
the Gross–Pitaevskii eigenvalue problem. They are constructed as the gradient flows of the …
Energy-adaptive Riemannian optimization on the Stiefel manifold
This paper addresses the numerical solution of nonlinear eigenvector problems such as the
Gross–Pitaevskii and Kohn–Sham equation arising in computational physics and chemistry …
Gross–Pitaevskii and Kohn–Sham equation arising in computational physics and chemistry …
Second-order flows for computing the ground states of rotating Bose-Einstein condensates
Second-order flows in this paper refer to some artificial evolutionary differential equations
involving second-order time derivatives distinguished from gradient flows which are …
involving second-order time derivatives distinguished from gradient flows which are …
The J-method for the Gross–Pitaevskii eigenvalue problem
This paper studies the J-method of [E. Jarlebring, S. Kvaal, W. Michiels. SIAM J. Sci. Comput.
36-4: A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space …
36-4: A1978-A2001, 2014] for nonlinear eigenvector problems in a general Hilbert space …
On discrete ground states of rotating Bose–Einstein condensates
The ground states of Bose–Einstein condensates in a rotating frame can be described as
constrained minimizers of the Gross–Pitaevskii energy functional with an angular …
constrained minimizers of the Gross–Pitaevskii energy functional with an angular …
Mixed finite elements for the Gross–Pitaevskii eigenvalue problem: a priori error analysis and guaranteed lower energy bound
D Gallistl, M Hauck, Y Liang… - IMA Journal of Numerical …, 2024 - academic.oup.com
We establish an a priori error analysis for the lowest-order Raviart–Thomas finite element
discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence …
discretization of the nonlinear Gross-Pitaevskii eigenvalue problem. Optimal convergence …