Gradient Flow Finite Element Discretisations with Energy-Based Adaptivity for Excited States of Schrödinger's Equation
Year: 2023
Author: Pascal Heid
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 933–955
Abstract
The purpose of this paper is to verify that the computational scheme from [Heid et al., Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation, J. Comput. Phys. 436 (2021)] for the numerical approximation of the ground state of the Gross-Pitaevskii equation can equally be applied for the effective approximation of excited states of Schrödinger's equation. That procedure employs an adaptive interplay of a Sobolev gradient flow iteration and a novel local mesh refinement strategy, and yields a guaranteed energy decay in each step of the algorithm. The computational tests in the present work highlight that this strategy is indeed able to approximate excited states, with (almost) optimal convergence rate with respect to the number of degrees of freedom.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2207-m2020-0302
Journal of Computational Mathematics, Vol. 41 (2023), Iss. 5 : pp. 933–955
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Schrödinger's equation Excited states Gradient flows Adaptive finite element methods.