Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s)

Title

Author

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

IDR(s) is a family of fast algorithms for iteratively solving large nonsymmetric linear systems [14]. With cluster computing and in particular with Grid computing, the inner product is a bottleneck operation. In this paper, three techniques are combined in order to alleviate this bottleneck. Firstly, the efficient and stable IDR(s) algorithm from [16] is reformulated in such a way that it has a single global synchronisation point per iteration step. Secondly, the so–called test matrix is chosen so that the work, communication, and storage involving this matrix is minimised 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 these three techniques.

Subject

iterative methods
numerical linear algebra
nonsymmetric linear systems
IDR(s)
cluster and Grid computing
performance model

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Publisher

Delft University of Technology, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft Institute of Applied Mathematics

ISSN

1389-6520

Source

Reports of the Department of Applied Mathematical Analysis, 10-05

Part of collection

Institutional Repository