Improving Coarsening and Interpolation for Algebraic Multigrid
This thesis looks at two modifications of the PMIS algorithm that aim to improve scalability. These include a greedy implementation of PMIS and restricting PMIS coarsening to finer grid levels while Cleary-Jones-Luby-Plassman coarsening (based on the standard Ruge-Stüben method) is performed on all other grids. It is shown that, for a variety of problems, the greedy PMIS algorithm does little to improve convergence, while the second modification can improve convergence. However, it is also shown that the second modification can result in increased memory usage that is unfavorable to scalability.
The PMIS based algorithm can be improved by redefining interpolation. As shown by De Sterck and Yang , PMIS coarsening combined with F-F interpolation dramatically improves convergence, but often has negative effects on computation time per iteration and memory usage that affect scalability. A third modification is proposed that aims to remedy this problem by altering F-F interpolation. The new algorithm is called F-F1 interpolation, and is shown to reduce computation time per iteration and memory usage compared to F-F interpolation, while maintaining fast convergence and good scalability, for a variety of problems.
School:University of Waterloo
School Location:Canada - Ontario
Source Type:Master's Thesis
Date of Publication:01/01/2006