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
N2 - 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.
AB - 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.
U2 - 10.1016/S0168-9274(01)00030-7
DO - 10.1016/S0168-9274(01)00030-7
M3 - Article
SN - 0168-9274
VL - 38
SP - 377
EP - 401
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 4
ER -