Traditional largesparselinearsolvers are not suited in agrid computing environment as they require alarge amount of synchronization and communication penalizing the performance on this architecture. This paper presents some features of the solver designed during the current GREMLINS (GRid Efficient Method forLINear Systems) project. The GREMLINS solver limits the amount of communication as it is based on a coarse grained iterative method called multisplitting method. Moreover, the solver can be executed either in a synchronous or an asynchronous mode. In the latter case, iterations are desynchronized and there is no more synchronization at all. It may result in a faster execution time compared to the synchronous case. Some experiments presented in this paper with the GRID'5000 architecture, a nation wide experimental grid in France, allowed us to highlight interesting features of this solver.