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  • 1.
    Brandén, Henrik
    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.
    Convergence Acceleration for Flow Problems2001Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Convergence acceleration techniques for the iterative solution of system of equations arising in the discretisations of compressible flow problems governed by the steady state Euler or Navier-Stokes equations is considered. The system of PDE is discretised using a finite difference or finite volume method yielding a large sparse system of equations. A solution is computed by integrating the corresponding time dependent problem in time until steady state is reached.

    A convergence acceleration technique based on semicirculant approximations is applied. For scalar model problems, it is proved that the preconditioned coefficient matrix has a bounded spectrum well separated from the origin. A very simple time marching scheme such as the forward Euler method can be used, and the time step is not limited by a CFL-type criterion. Instead, the time step can asymptotically be chosen as a constant, independent of the number of grid points and the Reynolds number. Numerical experiments show that grid and parameter independent convergence is achieved also in more complicated problem settings. A comparison with a multigrid method shows that the semicirculant convergence acceleration technique is more efficient in terms of arithmetic complexity.

    Another convergence acceleration technique based on fundamental solutions is proposed. An algorithm based on Fourier technique is provided for the fast application. Scalar model problems are considered and a theory, where the preconditioner is represented as an integral operator is derived. Theory and numerical experiments show that for first order partial differential equations, grid independent convergence is achieved.

    List of papers
    1. Convergence acceleration for hyperbolic systems using semicirculant approximations
    Open this publication in new window or tab >>Convergence acceleration for hyperbolic systems using semicirculant approximations
    1999 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 14, p. 357-393Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-68358 (URN)10.1023/A:1023256615895 (DOI)
    Available from: 2006-05-20 Created: 2006-05-20 Last updated: 2018-01-10Bibliographically approved
    2. Convergence acceleration for the linearized Navier-Stokes equations using semicirculant approximations
    Open this publication in new window or tab >>Convergence acceleration for the linearized Navier-Stokes equations using semicirculant approximations
    2000 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 21, p. 1524-1550Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-36510 (URN)10.1137/S1064827597317983 (DOI)
    Available from: 2006-05-20 Created: 2006-05-20 Last updated: 2018-01-11Bibliographically approved
    3. Convergence acceleration for the steady-state Euler equations
    Open this publication in new window or tab >>Convergence acceleration for the steady-state Euler equations
    2003 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 32, p. 1075-1092Article in journal (Refereed) Published
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-47163 (URN)10.1016/S0045-7930(02)00088-9 (DOI)
    Available from: 2006-05-20 Created: 2006-05-20 Last updated: 2018-01-11Bibliographically approved
    4. Preconditioners Based on Fundamental Solutions
    Open this publication in new window or tab >>Preconditioners Based on Fundamental Solutions
    2005 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2005-001
    National Category
    Computational Mathematics Computer Sciences
    Identifiers
    urn:nbn:se:uu:diva-68487 (URN)
    Available from: 2007-02-01 Created: 2007-02-01 Last updated: 2018-01-10Bibliographically approved
    5. Numerical boundary conditions for ODE
    Open this publication in new window or tab >>Numerical boundary conditions for ODE
    2000 (English)Report (Other academic)
    Series
    Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2000-026
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:uu:diva-78982 (URN)
    Available from: 2007-02-15 Created: 2007-02-15 Last updated: 2011-11-17Bibliographically approved
  • 2.
    Brandén, Henrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Scientific Computing. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Numerical Analysis.
    Convergence acceleration for flow problems using semicirculant approximations1999Licentiate thesis, comprehensive summary (Other academic)
  • 3.
    Brandén, Henrik
    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.
    Numerical boundary conditions for ODE2000Report (Other academic)
  • 4.
    Brandén, Henrik
    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.
    Holmgren, Sverker
    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.
    Convergence acceleration for hyperbolic systems using semicirculant approximations1999In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 14, p. 357-393Article in journal (Refereed)
  • 5.
    Brandén, Henrik
    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.
    Holmgren, Sverker
    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.
    Convergence acceleration for the steady state Euler equations2000Report (Other academic)
  • 6.
    Brandén, Henrik
    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.
    Holmgren, Sverker
    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.
    Convergence acceleration for the steady-state Euler equations2003In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 32, p. 1075-1092Article in journal (Refereed)
  • 7.
    Brandén, Henrik
    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.
    Holmgren, Sverker
    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.
    Sundqvist, 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.
    Discrete Fundamental Solution Preconditioning for Hyperbolic Systems of PDE2003Report (Other academic)
  • 8.
    Brandén, Henrik
    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.
    Holmgren, Sverker
    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.
    Sundqvist, 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.
    Discrete fundamental solution preconditioning for hyperbolic systems of PDE2007In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 30, p. 35-60Article in journal (Refereed)
  • 9.
    Brandén, Henrik
    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.
    Sundqvist, 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.
    An algorithm for computing fundamental solutions of difference operators2004In: Numerical Algorithms, ISSN 1017-1398, E-ISSN 1572-9265, Vol. 36, p. 331-343Article in journal (Refereed)
  • 10.
    Brandén, Henrik
    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.
    Sundqvist, 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.
    An Algorithm for Computing Fundamental Solutions of Difference Operators2003Report (Other academic)
  • 11.
    Brandén, Henrik
    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.
    Sundqvist, 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.
    Preconditioners Based on Fundamental Solutions2005Report (Other academic)
  • 12.
    Brandén, Henrik
    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.
    Sundqvist, 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.
    Preconditioners based on fundamental solutions2005In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 45, p. 481-494Article in journal (Refereed)
  • 13.
    Holmgren, Sverker
    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.
    Brandén, Henrik
    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.
    Sterner, 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.
    Convergence acceleration for the linearized Navier-Stokes equations using semicirculant approximations2000In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 21, p. 1524-1550Article in journal (Refereed)
  • 14. Jonsson, Jacob C.
    et al.
    Brandén, Henrik
    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.
    Obtaining the bidirectional transmittance distribution function of isotropically scattering materials using an integrating sphere2007In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 277, p. 228-236Article in journal (Refereed)
1 - 14 of 14
CiteExportLink to result list
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  • apa
  • ieee
  • modern-language-association
  • vancouver
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
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  • text
  • asciidoc
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