Parallel solution of sparse linear systems arising in advection-diffusion problems

Flow problems permeate hydraulic engineering. In order to solve real--life problems, parallel solution must be engaged, for attaining large storage amounts and small wall--clock time. In this communication, we discuss valuable key points which allow for the efficient, parallel solution of our large, sparse linear systems, arising from the discretization of advection--diffusion flow problems. We show that data pre-fetching is an effective technique to improve the efficiency of the sparse matrix--vector product, a time consuming kernel of iterative solvers, which are the best choice for our problems. Preconditioning is another key topic for the efficient solution of large, sparse, ill--conditioned systems. Up to now, no extensive theory for choosing the best preconditioner is available, thus ad--hoc recipes and sound based experience is mandatory. We compare many preconditioners in order to show their efficiency and allowing a good choice when attacking problems like ours.