We study the performance of several widely used preconditioners for 2D elliptic partial differential equations (SSOR, ILU, MILU and polynomial preconditioners) with the natural and red-black orderings implemented on the Connection Machine (CM). Their performance is primarily influenced by two factors: the rate of convergence and the ease of parallelization. The convergence rate is analyzed by Fourier analysis and confirmed with experimental results. Although the naturally ordered SSOR and MILU preconditioners have convergence rates one order faster than the other preconditioners, the experiments show that the red-black ordered SSOR, ILU, MILU, polynomial preconditioners takes less execution time than their naturally ordered counterparts. This is partially due to the fact that the red-blavk ordering provides more parallelism than the natural ordering.
Bibliographical noteFunding Information:
* This work was supported in part by the Department of Energy under contract DE-F003-87ER25037, the National Science Foundation under contracts NSF-DMS87-14612 and BBS 87 14206, the Army Research Office under contract DAALO3-88-K-0085 and by the Research Institute for Ad-vanced Computer Science, NASA Ames.
ASJC Scopus subject areas
- Hardware and Architecture
- Physics and Astronomy(all)