Downwind Gauß-Seidel Smoothing for Convection Dominated Problems

✍ Scribed by Wolfgang Hackbusch; Thomas Probst

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 151 KB
• Volume: 4
• Category: Article
• ISSN: 1070-5325
• DOI: 10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2

✦ Synopsis

In the case of convection dominated problems, multigrid methods require an appropriate smoothing to ensure robustness. As a first approach we discuss a Gauß-Seidel smoothing with a correct numbering of the unknowns and if necessary a special block partitioning. Numerical experiments show that, in the case of general convection directions, the multigrid algorithms obtained in this way have the same properties as in the model situation. If the graph arising from the convection part is acyclic, we describe a numbering algorithm which is valid for all spatial dimensions. Cycles give rise to special blocks for a blockwise Gauß-Seidel smoothing. We describe an algorithm for the two-dimensional case. The proposed algorithm requires a computational work of optimal order (linear in the size of the problem).