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  • 1. Flyer, Natasha
    et al.
    Lehto, Erik
    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.
    Rotational transport on a sphere: Local node refinement with radial basis functions2010In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, p. 1954-1969Article in journal (Refereed)
  • 2. Flyer, Natasha
    et al.
    Lehto, Erik
    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.
    Blaise, Sébastien
    Wright, Grady B.
    St-Cyr, Amik
    A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, p. 4078-4095Article in journal (Refereed)
  • 3. Flyer, Natasha
    et al.
    Lehto, Erik
    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.
    Blaise, Sébastien
    Wright, Grady B.
    St-Cyr, Amik
    RBF-generated finite differences for nonlinear transport on a sphere: Shallow water simulations2011Report (Other academic)
  • 4. Fornberg, Bengt
    et al.
    Lehto, Erik
    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.
    Stabilization of RBF-generated finite difference methods for convective PDEs2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 2270-2285Article in journal (Refereed)
  • 5. Fornberg, Bengt
    et al.
    Lehto, Erik
    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.
    Powell, Collin
    Stable calculation of Gaussian-based RBF-FD stencils2012Report (Other academic)
  • 6. Fornberg, Bengt
    et al.
    Lehto, Erik
    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.
    Powell, Collin
    Stable calculation of Gaussian-based RBF-FD stencils2013In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668, Vol. 65, p. 627-637Article in journal (Refereed)
  • 7.
    Larsson, Elisabeth
    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.
    Lehto, Erik
    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.
    Heryudono, Alfa
    Fornberg, Bengt
    Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions2012Report (Other academic)
  • 8.
    Larsson, Elisabeth
    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.
    Lehto, Erik
    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.
    Heryudono, Alfa
    Fornberg, Bengt
    Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions2013In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 35, p. A2096-A2119Article in journal (Refereed)
  • 9.
    Lehto, Erik
    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.
    High Order Local Radial Basis Function Methods for Atmospheric Flow Simulations2012Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Since the introduction of modern computers, numerical methods for atmospheric simulations have routinely been applied for weather prediction, and in the last fifty years, there has been a steady improvement in the accuracy of forecasts. Accurate numerical models of the atmosphere are also becoming more important as researchers rely on global climate simulations to assess and understand the impact of global warming.

    The choice of grid in a numerical model is an important design decision and no obvious optimal choice exists for computations in spherical geometry. Despite this disadvantage, grid-based methods are found in all current circulation models. A different approach to the issue of discretizing the surface of the sphere is given by meshless methods, of which radial basis function (RBF) methods are becoming prevalent.

    In this thesis, RBF methods for simulation of atmospheric flows are explored. Several techniques are introduced to increase the efficiency of the methods. By utilizing a novel algorithm for adaptively placing the node points, accuracy is shown to improve by over one order of magnitude for two relevant test problems. The computational cost can also be reduced by using a local finite difference-like RBF scheme. However, this requires a stabilization mechanism for the hyperbolic problems of interest here. A hyper-viscosity scheme is introduced to address this issue.

    Another stability issue arising from the ill-conditioning of the RBF basis for almost-flat basis functions is also discussed in the thesis, and two algorithms are proposed for dealing with this stability problem. The algorithms are specifically tailored for the task of creating finite difference weights using RBFs and are expected to overcome the issue of stationary error in local RBF collocation.

    List of papers
    1. Rotational transport on a sphere: Local node refinement with radial basis functions
    Open this publication in new window or tab >>Rotational transport on a sphere: Local node refinement with radial basis functions
    2010 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, p. 1954-1969Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-111275 (URN)10.1016/j.jcp.2009.11.016 (DOI)000275092000002 ()
    Available from: 2009-12-08 Created: 2009-12-08 Last updated: 2018-01-12Bibliographically approved
    2. Stabilization of RBF-generated finite difference methods for convective PDEs
    Open this publication in new window or tab >>Stabilization of RBF-generated finite difference methods for convective PDEs
    2011 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, p. 2270-2285Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-157123 (URN)10.1016/j.jcp.2010.12.014 (DOI)000287425400005 ()
    Available from: 2010-12-21 Created: 2011-08-16 Last updated: 2018-01-12Bibliographically approved
    3. A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere
    Open this publication in new window or tab >>A guide to RBF-generated finite differences for nonlinear transport: Shallow water simulations on a sphere
    Show others...
    2012 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, p. 4078-4095Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-173564 (URN)10.1016/j.jcp.2012.01.028 (DOI)000302933600004 ()
    Available from: 2012-02-16 Created: 2012-04-26 Last updated: 2018-01-12Bibliographically approved
    4. Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions
    Open this publication in new window or tab >>Stable computation of differentiation matrices and scattered node stencils based on Gaussian radial basis functions
    2012 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-020
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-179191 (URN)
    Available from: 2012-08-13 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved
    5. Stable calculation of Gaussian-based RBF-FD stencils
    Open this publication in new window or tab >>Stable calculation of Gaussian-based RBF-FD stencils
    2012 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2012-018
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-179192 (URN)
    Available from: 2012-08-09 Created: 2012-08-09 Last updated: 2012-09-12Bibliographically approved
  • 10.
    Tillenius, Martin
    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, Computational Science.
    Larsson, Elisabeth
    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.
    Lehto, Erik
    Flyer, Natasha
    A scalable RBF–FD method for atmospheric flow2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 298, p. 406-422Article in journal (Refereed)
  • 11.
    Tillenius, Martin
    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, Computational Science.
    Larsson, Elisabeth
    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, Computational Science.
    Lehto, Erik
    Flyer, Natasha
    A task parallel implementation of a scattered node stencil-based solver for the shallow water equations2013In: Proc. 6th Swedish Workshop on Multi-Core Computing, Halmstad, Sweden: Halmstad University , 2013, p. 33-36Conference paper (Other academic)
  • 12.
    Tillenius, Martin
    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, Computational Science.
    Larsson, Elisabeth
    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.
    Lehto, Erik
    Flyer, Natasha
    A task parallel implementation of an RBF-generated finite difference method for the shallow water equations on the sphere2014Report (Other academic)
  • 13.
    von Sydow, Lina
    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.
    Ghafari, Paria
    Lehto, Erik
    Wångersjö, Mats
    Pricing of basket options using dimension reduction and adaptive finite differences in space, and discontinuous Galerkin in time2016In: Numerical Mathematics and Advanced Applications: ENUMATH 2015, Springer, 2016, p. 607-615Conference paper (Refereed)
1 - 13 of 13
CiteExportLink to result list
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Cite
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  • apa
  • ieee
  • modern-language-association
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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