Or the past few years, the clusters equipped with GPUs have become attractive tools for high performance computing. In this thesis, we have designed parallel iterative algorithms for solving large sparse linear and nonlinear systems on GPU clusters. First, we have focused on solving sparse linear systems using CG and GMRES iterative methods. The experiments have shown that a GPU cluster is more efficient that its pure CPU counterpart for solving large sparse systems of linear equations. Then, we have implemented the synchronous and asynchronous algorithms of the Richardson and the block relaxation iterative methods for solving sparse nonlinear systems. We have noticed that the best solutions developed for the CPUs are not necessarily well suited to GPUs. Indeed, the experiments performed on a GPU cluster have shown that the parallel algorithms of the Richardson method are far more efficient than those of the block relaxation method. In addition, they have shown that the computing power of GPUs allows to reduce the ratio between the time of the computation over that of the communication, which favors the use of the asynchronous iteration on GPU clusters. Finally, we are interested in geographically distant clusters for solving large sparse linear systems. In this context, we have used a multisplitting two-stage method using parallel GMRES method adapted to GPU clusters. It uses the synchronous iteration to solve locally the sub-linear systems and the asynchronous one to solve the global sparse linear system.
