Large Scale Linear System Global Computing Resolution with GMRES Method

Grid computing attains high throughput computing by making use of a very large amount of unexploited computing resources. We present a typical parallel method GMRES to solve large sparse linear systems by the use of a lightweight GRID system XtremWeb. This global computing platform, just as many popular GRID systems, is mainly devoted to multi-parameters generic applications. We have implemented this important algorithm GMRES which is one of the key methods to resolve large, non-symmetric, linear problems. We discuss as well the performances of this implementation deployed on two XtremWeb networks: a local network with 128 nondedicated PCs in Polytech-Lille of University of Lille I in France, a remote network with 3 clusters of SCGN Grid that includes 91 CPUs totally in the High Performance Center for Computational Science of University of Tsukuba in Japan. We do the tests as well on the platform of supercomputer IBM SP4 and in a LAN MPI computing environment LAMMPI. We compare these performances. We present the advantages and drawbacks of our implementations on the three computing systems.