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Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation.

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Title: Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation.
Authors: Heid, Pascal1 (AUTHOR) pascal.heid@maths.ox.ac.uk, Stamm, Benjamin2 (AUTHOR) best@acom.rwth-aachen.de, Wihler, Thomas P.3 (AUTHOR) thomas.wihler@math.unibe.ch
Source: Journal of Computational Physics. Jul2021, Vol. 436, pN.PAG-N.PAG. 1p.
Subjects: Gross-Pitaevskii equations, Degrees of freedom, Elliptic operators
Abstract: • Numerical approximation of the ground state of the Gross-Pitaevskii equation. • Introduction of a novel mesh refinement technique based on local energy reductions. • Adaptive interplay of a gradient ow iteration and the novel mesh refinemen method. • Optimal convergence rate with respect to the degrees of freedom in the test problems. We present an effective adaptive procedure for the numerical approximation of the steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of a novel adaptive finite element mesh refinement technique, which does not rely on any a posteriori error estimates, and a recently proposed new gradient flow. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of degrees of freedom. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 150082315
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  Data: Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation.
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  Data: <searchLink fieldCode="AR" term="%22Heid%2C+Pascal%22">Heid, Pascal</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> pascal.heid@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Stamm%2C+Benjamin%22">Stamm, Benjamin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> best@acom.rwth-aachen.de</i><br /><searchLink fieldCode="AR" term="%22Wihler%2C+Thomas+P%2E%22">Wihler, Thomas P.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> thomas.wihler@math.unibe.ch</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Jul2021, Vol. 436, pN.PAG-N.PAG. 1p.
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  Data: <searchLink fieldCode="DE" term="%22Gross-Pitaevskii+equations%22">Gross-Pitaevskii equations</searchLink><br /><searchLink fieldCode="DE" term="%22Degrees+of+freedom%22">Degrees of freedom</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+operators%22">Elliptic operators</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: • Numerical approximation of the ground state of the Gross-Pitaevskii equation. • Introduction of a novel mesh refinement technique based on local energy reductions. • Adaptive interplay of a gradient ow iteration and the novel mesh refinemen method. • Optimal convergence rate with respect to the degrees of freedom in the test problems. We present an effective adaptive procedure for the numerical approximation of the steady-state Gross–Pitaevskii equation. Our approach is solely based on energy minimization, and consists of a combination of a novel adaptive finite element mesh refinement technique, which does not rely on any a posteriori error estimates, and a recently proposed new gradient flow. Numerical tests show that this strategy is able to provide highly accurate results, with optimal convergence rates with respect to the number of degrees of freedom. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.jcp.2021.110165
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      – Code: eng
        Text: English
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        PageCount: 1
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    Subjects:
      – SubjectFull: Gross-Pitaevskii equations
        Type: general
      – SubjectFull: Degrees of freedom
        Type: general
      – SubjectFull: Elliptic operators
        Type: general
    Titles:
      – TitleFull: Gradient flow finite element discretizations with energy-based adaptivity for the Gross-Pitaevskii equation.
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            NameFull: Heid, Pascal
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            NameFull: Stamm, Benjamin
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            – D: 01
              M: 07
              Text: Jul2021
              Type: published
              Y: 2021
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              Value: 436
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            – TitleFull: Journal of Computational Physics
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