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Minimizing synchronization in IDR ( s )
Author(s) -
Collig Tijmen P.,
van Gijzen Martin B.
Publication year - 2011
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.764
Subject(s) - bottleneck , synchronization (alternating current) , grid , mathematics , a priori and a posteriori , algorithm , mathematical optimization , matrix multiplication , matrix (chemical analysis) , computer science , topology (electrical circuits) , philosophy , physics , geometry , materials science , epistemology , combinatorics , quantum mechanics , composite material , quantum , embedded system
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.