Keywords: multisplitting algorithm, grid computing, asynchronous iteration model.

This chapter proposes a synthesis of multisplitting algorithms executed with JACE (Java asynchronous computing environment). The class of multisplitting algorithms allows us to solve iteratively sparse linear and non-linear systems in parallel by decomposing a large problem into simpler ones. In parallel, some multisplitting algorithms may be executed with either the synchronous iteration model or with the asynchronous one. In the latter case, processors execute their iteration freely without any synchronization. From the programming point of view the design of an asynchronous iterative algorithm has two main differences with the design of a synchronous iterative one: the convergence detection and the management of communications. In order to underload the programmer from these constraints, JACE takes charge of those particularities and consequently offers a programming and execution environment that allows users to easily design synchronous and asynchronous iterative algorithms. Moreover, since this environment has been developed in Java, it is very easy to deploy an application in a grid environment context composed of many geographically distant clusters. In this chapter, we report experiments that highlight the fact that multisplitting algorithms are well suited to grid environments. Experiments also show that asynchronous multisplitting algorithms may perform faster than synchronous ones.

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