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  • 1.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Computational Ice Sheet Dynamics: Error control and efficiency2016Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Ice sheets, such as the Greenland Ice Sheet or Antarctic Ice Sheet, have a fundamental impact on landscape formation, the global climate system, and on sea level rise. The slow, creeping flow of ice can be represented by a non-linear version of the Stokes equations, which treat ice as a non-Newtonian, viscous fluid. Large spatial domains combined with long time spans and complexities such as a non-linear rheology, make ice sheet simulations computationally challenging. The topic of this thesis is the efficiency and error control of large simulations, both in the sense of mathematical modelling and numerical algorithms. In the first part of the thesis, approximative models based on perturbation expansions are studied. Due to a thick boundary layer near the ice surface, some classical assumptions are inaccurate and the higher order model called the Second Order Shallow Ice Approximation (SOSIA) yields large errors. In the second part of the thesis, the Ice Sheet Coupled Approximation Level (ISCAL) method is developed and implemented into the finite element ice sheet model Elmer/Ice. The ISCAL method combines the Shallow Ice Approximation (SIA) and Shelfy Stream Approximation (SSA) with the full Stokes model, such that the Stokes equations are only solved in areas where both the SIA and SSA is inaccurate. Where and when the SIA and SSA is applicable is decided automatically and dynamically based on estimates of the modeling error. The ISCAL method provides a significant speed-up compared to the Stokes model. The third contribution of this thesis is the introduction of Radial Basis Function (RBF) methods in glaciology. Advantages of RBF methods in comparison to finite element methods or finite difference methods are demonstrated.

    List of papers
    1. A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    Open this publication in new window or tab >>A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling
    2013 (English)In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, p. 417-435Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-205727 (URN)10.1093/qjmam/hbt009 (DOI)000327457200001 ()
    Projects
    eSSENCE
    Available from: 2013-08-09 Created: 2013-08-22 Last updated: 2017-12-06Bibliographically approved
    2. Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    Open this publication in new window or tab >>Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results
    2013 (English)In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, p. 2135-2152Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-213571 (URN)10.5194/gmd-6-2135-2013 (DOI)000329050500017 ()
    Projects
    eSSENCE
    Available from: 2013-12-19 Created: 2013-12-28 Last updated: 2017-12-06Bibliographically approved
    3. Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    Open this publication in new window or tab >>Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method
    2016 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed) Published
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-269822 (URN)10.1016/j.jcp.2015.12.025 (DOI)000369086700001 ()
    Projects
    eSSENCE
    Available from: 2015-12-17 Created: 2015-12-18 Last updated: 2017-12-01Bibliographically approved
    4. The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    Open this publication in new window or tab >>The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation
    2016 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-006
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-283438 (URN)
    Projects
    eSSENCE
    Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved
    5. A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    Open this publication in new window or tab >>A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla
    2016 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2016-005
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-283437 (URN)
    Projects
    eSSENCE
    Available from: 2016-04-19 Created: 2016-04-13 Last updated: 2016-05-16Bibliographically approved
  • 2.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    The ISCAL method and the grounding line: Combining the Stokes equations with the Shallow Ice Approximation and Shelfy Stream Approximation2016Report (Other academic)
  • 3.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A numerical study of scaling relations for non-Newtonian thin-film flows with applications in ice sheet modelling2013In: Quarterly Journal of Mechanics and Applied Mathematics, ISSN 0033-5614, E-ISSN 1464-3855, Vol. 66, p. 417-435Article in journal (Refereed)
  • 4.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A numerical study of the validity of Shallow Ice Approximations2012Report (Other academic)
  • 5.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accuracy of the zeroth and second order shallow ice approximation: numerical and theoretical results2013In: Geoscientific Model Development Discussions, ISSN 1991-9611, E-ISSN 1991-962X, Vol. 6, p. 4281-4325Article in journal (Other academic)
  • 6.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Accuracy of the zeroth- and second-order shallow-ice approximation: numerical and theoretical results2013In: Geoscientific Model Development, ISSN 1991-959X, E-ISSN 1991-9603, Vol. 6, p. 2135-2152Article in journal (Refereed)
  • 7.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Kirchner, Nina
    Zwinger, Thomas
    Dynamically coupling the non-linear Stokes equations with the shallow ice approximation in glaciology: Description and first applications of the ISCAL method2016In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 308, p. 1-19Article in journal (Refereed)
  • 8.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Shcherbakov, Victor
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 330, p. 633-649Article in journal (Refereed)
  • 9.
    Ahlkrona, Josefin
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Shcherbakov, Victor
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    A meshfree approach to non-Newtonian free surface ice flow: Application to the Haut Glacier d'Arolla2016Report (Other academic)
  • 10.
    Fagerlund, Fritjof
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Holmgren, Hanna
    Nielsen, Kristin
    Yang, Zhibing
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
    Niemi, Auli
    Uppsala University, Disciplinary Domain of Science and Technology, Earth Sciences, Department of Earth Sciences, LUVAL.
    Kreiss, Gunilla
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Analysis of boundary conditions in numerical simulations of geological CO2 storage2011In: 8th EGU General Assembly, Göttingen, Germany: Copernicus Publications , 2011, p. EGU2011-7410-Conference paper (Other academic)
    Abstract
  • 11. Helanow, Christian
    et al.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Stabilized equal low-order finite elements in ice sheet modeling: accuracy and robustness2018In: Computational Geosciences, ISSN 1420-0597, E-ISSN 1573-1499, Vol. 22, p. 951-974Article in journal (Refereed)
  • 12. Kirchner, Nina
    et al.
    Ahlkrona, Josefin
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Gowan, Evan J.
    Lötstedt, Per
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Lea, James M.
    Noormets, Riko
    von Sydow, Lina
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Dowdeswell, Julian A.
    Benham, Toby
    Shallow ice approximation, second order shallow ice approximation, and full Stokes models: A discussion of their roles in palaeo-ice sheet modelling and development2016In: Quaternary Science Reviews, ISSN 0277-3791, E-ISSN 1873-457X, Vol. 135, p. 103-114Article, review/survey (Refereed)
1 - 12 of 12
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