This paper deals with a non-overlapping domain decomposition method involving additional augmented terms along the interface between the sub-domains. The goal of these additional terms is to prevent the singularity of the sub-domain matrix problems, such as rigid body motion in mechanics or resonance frequencies in acoustics. If the definition of these augmented terms requires minor intrusion inside an existing computational code, the sub-domain matrices are however assembled in parallel and the sub-domain meshes are required for this purpose. To cope with these requirements, a small modification of the algorithm is proposed, which helps to partition automatically every global assembly matrix and helps in the development of the method as a 'black box' package. Details of the algorithms, implementation aspects and computational cost are clearly described in order to help the reader to implement this new algorithm. New numerical results performed on interior and exterior acoustics problems illustrate the performance and efficiency of the proposed methods. © 2016 IEEE.