DOWNWIND GAUSS-SEIDEL SMOOTHING FOR CONVECTION DOMINATED PROBLEMS

In the case of convection dominated problems, multigrid methods requir e an appropriate smoothing to ensure robustness. As a first approach w e discuss a Gauss-Seidel smoothing with a correct numbering of the unk nowns and if necessary a special block partitioning. Numerical experim ents show that, in the case of general convection directions, the mult igrid algorithms obtained in this way have the same properties as in t he model situation. If the graph arising from the convection part is a cyclic, we describe a numbering algorithm which is valid for all spati al dimensions. Cycles give rise to special blocks for a blockwise Gaus s-Seidel smoothing. We describe an algorithm for the two-dimensional c ase. The proposed algorithm requires a computational work of optimal o rder (linear in the size of the problem). (C) 1997 by John Wiley & Son s, Ltd.