Print Email Facebook Twitter Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s) Title Fast solution of nonsymmetric linear systems on Grid computers using parallel variants of IDR(s) Author Collignon, T.P. Van Gijzen, M.B. 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 methodsnumerical linear algebranonsymmetric linear systemsIDR(s)cluster and Grid computingperformance model To reference this document use: http://resolver.tudelft.nl/uuid:fe60cf61-e824-4bd8-a8e3-9b70ec4a34c3 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 Document type report Rights (c)2010 Collignon, T.P., Van Gijzen, M.B. Files PDF 10.05.Colligny.pdf 261.9 KB Close viewer /islandora/object/uuid:fe60cf61-e824-4bd8-a8e3-9b70ec4a34c3/datastream/OBJ/view