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

Abstract

Flow problems permeate hydraulic engineering. In order to solve real-life problems, parallel solutions 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 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. © Springer-Verlag Berlin Heidelberg 2005.