Code coupling involves very often non matching grids or different discretisations between the interacting domains. A first concern is the proper discretisation of the coupling terms in order to ensure well-posedness and good approximation properties via a numerical analysis. A well known approach is the mortar method. It has the advantage to be optimal in terms of approximation error often involves a master-slave coupling where an interface enforces its Dirichlet values (the master) to the other interface. In Japhet et al., a different approach is introduced via the use of Robin interface conditions which are symmetrically imposed by every interface to its neighbor. Then, the next step is to solve the linear system resulting from the chosen coupling. In Japhet et al., in addition to a numerical analysis, the convergence of a fixed point method based on concurrent exact local solves is shown. In our work, we introduce more efficiency and parallelism by - replacing the fixed point method by a Krylov solver - using approximate local two-level DD preconditioners in the domains either used a fixed number of times or a fixed tolerance. - introducing a two-level domain decomposition method based on a coarse space for the coupled problem obtained by using local coarse spaces glued together the method defined in Japhet et al. but with a GenEO type coarse space discretization in each subdomain. One of the implementation challenge is the handling of the interface non matching grids in a parallel environment. Going ahead we also plan on extending this work by considering immersed boundaries to model fluid-structure interactions. We will present numerical results.