Sparse-Grid Combination Technique Applied to Time-Dependent Advection Problems.211 Modelling, Analysis and Simulation

摘要

In the numerical technique considered in this paper, time-stepping is performed211u001eon a set of semi-coarsened space grids. At given time levels the solutions on the 211u001edifferent space grids are combined to obtain the asymptotic convergence of a 211u001esingle, fine uniform grid. We present error estimates for the two-dimensional 211u001espatially constant-coeffcient model problem and discuss numerical examples. A 211u001espatially variable-coeffcient problem (Molenkamp-Crowley test) is used to assess 211u001ethe practical merits of the technique. The combination technique is shown to be 211u001emore effcient than the single-grid approach, yet for the Molenkamp-Crowley test, 211u001estandard Richardson extrapolation is still more effcient than the combination 211u001etechnique. However, parallelization is expected to significantly improve the 211u001ecombination technique's performance.