Super-localised wave function approximation of Bose-Einstein condensates

  • This paper presents a novel spatial discretisation method for the reliable and efficient simulation of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the corresponding nonlinear eigenvector problem. The method combines the high-accuracy properties of numerical homogenisation methods with a novel super-localisation approach for the calculation of the basis functions. A rigorous numerical analysis demonstrates superconvergence of the approach compared to classical polynomial and multiscale finite element methods, even in low regularity regimes. Numerical tests reveal the method's competitiveness with spectral methods, particularly in capturing critical physical effects in extreme conditions, such as vortex lattice formation in fast-rotating potential traps. The method's potential is further highlighted through a dynamic simulation of a phase transition from Mott insulator to Bose-Einstein condensate, emphasising its capability for reliable exploration of physicalThis paper presents a novel spatial discretisation method for the reliable and efficient simulation of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the corresponding nonlinear eigenvector problem. The method combines the high-accuracy properties of numerical homogenisation methods with a novel super-localisation approach for the calculation of the basis functions. A rigorous numerical analysis demonstrates superconvergence of the approach compared to classical polynomial and multiscale finite element methods, even in low regularity regimes. Numerical tests reveal the method's competitiveness with spectral methods, particularly in capturing critical physical effects in extreme conditions, such as vortex lattice formation in fast-rotating potential traps. The method's potential is further highlighted through a dynamic simulation of a phase transition from Mott insulator to Bose-Einstein condensate, emphasising its capability for reliable exploration of physical phenomena.show moreshow less

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2026/05/13

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Metadaten
Author:Daniel PeterseimORCiDGND, Johan Wärnegård, Christoph Zimmer
URN:urn:nbn:de:bvb:384-opus4-1080598
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/108059
ISSN:1090-2716OPAC
ISSN:0021-9991OPAC
Parent Title (English):Journal of Computational Physics
Publisher:Elsevier
Place of publication:Amsterdam
Type:Article
Language:English
Year of first Publication:2024
Embargo Date:2026/05/13
Publishing Institution:Universität Augsburg
Release Date:2023/09/22
Volume:510
First Page:113097
DOI:https://doi.org/10.1016/j.jcp.2024.113097
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Fakultätsübergreifende Institute und Einrichtungen
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Fakultätsübergreifende Institute und Einrichtungen / Zentrum für Advanced Analytics and Predictive Sciences (CAAPS)
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik
Licence (German):CC-BY-NC-ND 4.0: Creative Commons: Namensnennung - Nicht kommerziell - Keine Bearbeitung (mit Print on Demand)