Low Communication Parallel Multigrid
The most common technique for the parallelization of multi- grid methods is grid partitioning. For such methods Brandt and Diskin have suggested the use of a variant of segmental refinement in order to re- duce the amount of inter-processor communication. A parallel multigrid method with this technique avoids all communication on the finest grid levels. This article will examine some features of this class of algorithms as compared to standard parallel multigrid methods. In particular, the communication pattern will be analyzed in detail.
Keywordselliptic pde parallel multigrid domain decomposition communication cost
Unable to display preview. Download preview PDF.
- 3.B. Diskin, Multigrid Solvers on Decomposed Domains, M. Sc. Thesis, Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science, 1993.Google Scholar
- 4.M. Griebel and G. Zumbusch, Parnass: Porting gigabit-LAN components to a workstation cluster, in: W. Rehm, ed., Proceedings des 1. Workshop Cluster-Computing, 6.-7. November 1997, in Chemnitz, (Chemnitzer Informatik Berichte, CSR-97-05) 101–124.Google Scholar
- 7.M. Mohr, Kommunikationsarme parallele Mehrgitteralgorithmen, Diplomarbeit, Institut für Mathematik, TU München, 1997.Google Scholar
- 8.M. Mohr, U. Rüde, Communication Reduced Parallel Multigrid: Analysis and Experiments, Technical Report No. 394, University of Augsburg, 1998.Google Scholar
- 9.D. Xie, L. Scott, The Parallel U—Cycle Multigrid Method, Virtual Proceedings ofthe 8th Copper Mountain Conference on Multigrid Methods, MGNET, 1997, (http://casper.cs.yale.edu/mgnet/www/mgnet.html).