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 …
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 …
Sharp estimation of convergence rate for self-consistent field iteration to solve eigenvector-dependent nonlinear eigenvalue problems
We present a comprehensive convergence analysis for the self-consistent field (SCF)
iteration to solve a class of nonlinear eigenvalue problems with eigenvector dependency …
iteration to solve a class of nonlinear eigenvalue problems with eigenvector dependency …
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 …
The self-consistent field iteration for p-spectral clustering
The self-consistent field (SCF) iteration, combined with its variants, is one of the most widely
used algorithms in quantum chemistry. We propose a procedure to adapt the SCF iteration …
used algorithms in quantum chemistry. We propose a procedure to adapt the SCF iteration …
The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem
P Henning - Mathematical Models and Methods in Applied …, 2023 - World Scientific
In this paper, we consider the generalized inverse iteration for computing ground states of
the Gross–Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear …
the Gross–Pitaevskii eigenvector (GPE) problem. For that we prove explicit linear …
A two level approach for simulating Bose–Einstein condensates by localized orthogonal decomposition
In this work, we consider the numerical computation of ground states and dynamics of single-
component Bose–Einstein condensates (BECs). The corresponding models are spatially …
component Bose–Einstein condensates (BECs). The corresponding models are spatially …