Comparison of the Conjugate Gradient of NAS benchmark and of the multisplitting algorithm with the Jace environment

The aim of this paper is to study the behaviors of the well known conjugate gradient (CG) algorithm and the multisplitting algorithm in a grid context. We focus on the CG implementation used in the NAS benchmark and on the multisplitting approach which produces similar results (from a numerical point of view). By grid context we mean an architecture composed of several heterogeneous clusters geographically distributed and the use of a software environment able to tackle the heterogeneity of the nodes. Under these hypothesis, we performed a set of experiments on the Grid'5000 platform using the pure Java Jace V2 environment. We show that, by drastically reducing global synchronizations, the asynchronous multi-splitting method outperforms the NAS CG implementation, with distant sites, whatever the communication protocol used.