Experiments and Recommendations for Partitioning Systems of Equations

Partitioning the systems of equations is a very important process when solving it on a parallel computer. This paper presents some criteria which leads to more efficient parallelization, that must be taken into consideration. New criteria added to preconditioning process by reducing average bandwidth are pro- posed in this paper. These new criteria lead to a combination between preconditioning and partitioning of systems equations, so no need two distinct algorithms/processes. In our proposed methods - where the preconditioning is done by reducing the average bandwidth- two directions were followed in terms of partitioning: for a given preconditioned system determining the best partitioning (or one as close) and the second consist in achieving an adequate preconditioning, depending on a given/desired partitioning. A mixed method it is also proposed. Experimental results, conclusions and recommendations, obtained after parallel implementation of conjugate gradient on IBM BlueGene /P supercomputer- based on a synchronous model of parallelization- are also presented in this paper.