GREMLINS

The GREMLINS project is supported by the ANR (the French national research agency). This project features members of AND team (Distributed Numerical Algorithms) of LIFC (computer science labs of the university of Franche-Comté) and members of DCS team (Scientific Computation Department) of LIP6 (computer science lab. of university of Paris 6).

Sparse linear systems often appear in numerous scientific applications. There exist efficient libraries and tools to manage such systems on sequential machines or local clusters. Grid computing is an answer to the growing demand of computational power in many scientific domains (mechanic, biology,...) in order to solve such large linear systems. Unfortunately, the heterogeneity of the machines and the variability of the interconnection networks bring new algorithmic problems. The goal of this project is to define new algorithmic schemes to solve sparse linear systems on heterogeneous and distributed clusters. Those algorithms will be implemented in a library which will be freely available for the scientific community. The communications being penalizing on such distributed clusters, the new algorithms will have to be coarse grained in order to minimize the former. To achieve this goal, the multisplitting method which consists in decomposing the linear system into several sub-systems will be used. In this method, the resolution takes an iterative form by applying on each processor a sequential method (direct or iterative) to solve its sub-system until the global result becomes stable. This method can be used either in synchronous or in asynchronous mode. In the latter mode, processors work independently and use the last received data from their neighbours in their computations. However, this method is only applicable to some matrices with a particular spectral radius. To avoid this restriction, we aim at studying the influence of pre-processing techniques such as renumbering and pre-conditioning.