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

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.Electrical Engineering, Mathematics and Computer Scienc