1. Minimizing synchronization in IDR ( s).
- Author
-
Collignon, Tijmen P. and van Gijzen, Martin B.
- Subjects
SYNCHRONIZATION ,ALGORITHMS ,ITERATIVE methods (Mathematics) ,MATHEMATICAL symmetry ,LINEAR systems ,GRID computing ,BOTTLENECKS (Manufacturing) ,CLUSTER analysis (Statistics) ,NUMERICAL analysis - Abstract
IDR ( s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are investigated for alleviating this bottleneck. First, a recently proposed IDR ( s) algorithm that is highly efficient and stable is reformulated in such a way that it has a single global synchronization point per iteration step. Second, the so-called test matrix is chosen so that the work, communication, and storage involving this matrix is minimized in multi-cluster environments. Finally, a methodology is presented for a-priori estimation of the optimal value of s using only problem and machine-based parameters. Numerical experiments applied to a 3D convection-diffusion problem are performed on the DAS-3 Grid computer, demonstrating the effectiveness of our approach. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF