The sparse-grid combination technique applied to time-dependent advection problems
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.
|Series expansions (e.g. Taylor, Lidstone series, but not Fourier series) (msc 41A58), Interpolation (msc 65D05), None of the above, but in MSC2010 section 65Gxx (msc 65G99), Multigrid methods; domain decomposition (msc 65M55)|
|Life Sciences (theme 5), Energy (theme 4)|
|Modelling, Analysis and Simulation [MAS]|
Lastdrager, B, Koren, B, & Verwer, J.G. (1999). The sparse-grid combination technique applied to time-dependent advection problems. Modelling, Analysis and Simulation [MAS]. CWI.