The sparse-grid combination technique applied to time-dependent advection problems

B. Lastdrager, B. Koren, J.G. Verwer

    Research output: Contribution to journalArticleAcademicpeer-review

    4 Citations (Scopus)
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    Abstract

    In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp–Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp–Crowley test, standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.
    Original languageEnglish
    Pages (from-to)377-401
    JournalApplied Numerical Mathematics
    Volume38
    Issue number4
    DOIs
    Publication statusPublished - 2001

    Fingerprint

    Sparse Grids
    Advection
    Extrapolation
    Grid
    Richardson Extrapolation
    Asymptotic Convergence
    Time Stepping
    Numerical Techniques
    Variable Coefficients
    Parallelization
    Test Problems
    Error Estimates
    Numerical Examples
    Coefficient

    Cite this

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    abstract = "In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp–Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp–Crowley test, standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.",
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    The sparse-grid combination technique applied to time-dependent advection problems. / Lastdrager, B.; Koren, B.; Verwer, J.G.

    In: Applied Numerical Mathematics, Vol. 38, No. 4, 2001, p. 377-401.

    Research output: Contribution to journalArticleAcademicpeer-review

    TY - JOUR

    T1 - The sparse-grid combination technique applied to time-dependent advection problems

    AU - Lastdrager, B.

    AU - Koren, B.

    AU - Verwer, J.G.

    PY - 2001

    Y1 - 2001

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    JO - Applied Numerical Mathematics

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