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Minimizing synchronization in IDR (s)

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.