A Note on Multi-Block Relaxation Schemes for Multigrid Solvers.
INSTITUTE FOR COMPUTER APPLICATIONS IN SCIENCE AND ENGINEERING HAMPTON VA
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Efficient and robust multigrid solvers for anisotropic problems typically use either semi-coarsened grids or implicit smoothers - line relaxation in 2D and plane relaxation in 3D. However, both of these may be difficult to implement in codes using multi-block structured grids where there may be no natural definition of a global line or plane. These multi-block structured grids are often used in fluid dynamic applications to capture complex geometries andor to facilitate parallel processing. In this paper, we investigate the performance of multigrid algorithms using implicit smoothers within the blocks of a such a grid. By looking at a model problem, the 2-D anisotropic diffusion equation, we show that true multigrid efficiency is achieved only when the block sizes are proportional to the strength of the anisotropy. Further, the blocks must overlap and the size of the overlap must again be proportional to the strength of the anisotropy.
- Operations Research