Parallel GMRES implementation for solving sparse linear systems on GPU clusters

In this paper, we propose an efficient parallel implementation of the GMRES method for GPU clusters. This implementation requires us to parallelize the GMRES algorithm between CPUs of the cluster. Hence, all parallel and intensive computations on local data are performed on GPUs and reduction operations to compute global results are carried out by CPUs. The performances of our parallel GMRES solver are evaluated on test matrices of sizes exceeding 10 7 rows. They show that solving large and sparse linear systems on a GPU cluster is faster than that performed on its CPU counterpart. It is noticed that a cluster of 12 GPUs is about 8 times faster than a cluster of 12 CPUs and about 5 times faster than a cluster of 24 CPUs.