Experimentations and programming paradigms for matrix computing on peer to peer grid

In this paper we discuss the peer to peer solution for the deployment of large scale numerical applications on distributed resources. We use the XtremWeb P2P middleware for managing the computational resources. This global computing platform, such as much current grid deployments, is currently dedicated to multi-parameters applications. Our goal is to use it for executing numerical parallel applications that require communications between tasks. We discuss the performances of a block based matrix-vector product deployed for two XtremWeb networks; a local one with 128 non dedicated PCs, and for 261 PCs distributed on two geographic sites: University of Lille I and Paris XI University at Orsay. We give an investigation of the scheduling schemes well adapted for such systems and applications. We also present the performances of out-of-core products and discuss relationship between out-of-core and peer-to-peer computing for numerical applications.