The simulation of discrete systems often leads to large scale problems, for instance if they result of a discretization technique, or a modeling at a small scale. A multiscale analysis may involve an homogenized macroscopic problem, as well as a coarse space mechanism to accelerate convergence of the numerical scheme. A multilevel domain decomposition technique is used herein as both a numerical strategy to simulate the behaviour of a non smooth discrete media, and to provide a macroscopic numerical behaviour of the same system. Several generic formulations for such systems are discussed in this article. A multilevel domain decomposition is tested and several choices of the embedded coarse space are discussed, in particular with respect of the emergence of weak interfaces, characteristics of the discrete media substructuration. The application problem is the quasi-static simulation of a large scale tensegrity grid.