Iterations for the Airfoil Mesh. Multiplicative Schwarz

Overlap Level of Regular Dual graph (no. elements) coarse grid coarsening coarsening 0 None 56 56 0 4 21 22 0 3 15 12 1 None 16 16 1 4 10 10 1 3 7 7 2 None 14 14 2 4 8 8 2 3 5 5 Table 2 Multigrid iterations for the Airfoil mesh Regular coarsening Dual graph coarsening MG Levels Nodes Dir. B. Overlapping schwarz methods on unstructured meshes using non-matching coarse grids. Domain decomposition and multigrid methods for elliptic problems on unstructured meshes. domain decomposition methods for elliptic problems on unstructured meshes. 9 Fig. 2. The coarser Airfoil meshs Fig. 3. The Airfoil mesh: 16 subdomains computed by RSB 4.2. Multigrid results. In Table 2 we give the convergence results for standard V-cycle multigrid. We have used 2 pre and 2 post smoothing steps of symmetric pointwise Gauss-Seidel on each level. These results are comparable to those obtained on a uniformly reened mesh. REFERENCES 1] In H. Deconinck and Tim Barth, editors, Special course on unstructured grid methods for advection dominated ows, March 1992. AGARD REPORT 787, Special course at the VKI, Belgium. 2] S.T. Barnard and H.D. Simon. A fast multilevel implementation of recursive spectral bisection. Convergence estimates for product iterative methods with applications to domain decomposition. A non-nested coarse space for Schwarz type domain decomposition methods.