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 ar