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The Sparse-Grid Combination Technique Applied to Time-Dependent Advection Problems

  • Boris Lastdrager
  • Barry Koren
  • Jan Verwer
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 14)

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.

Keywords

advection problems sparse grids combination techniques error analysis 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Boris Lastdrager
    • 1
  • Barry Koren
    • 1
  • Jan Verwer
    • 1
  1. 1.Center for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands

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