External coupling software based on the coupling algorithm proposed by Prakash and Hjelmstad (PH method) is compared to the previous external coupling software based on the GC (Gravouil and Combsecure) method. The salient features of multi-time-step partitioning methods are presented: they involve non-overlapping partitions and follow a dual Schur approach by enforcing the velocity continuity at the interface with Lagrange multipliers. The main difference between the two methods lies in the time scale at which the interface problem is solved: the micro-time scale for the GC algorithm and macro-time scale for the PH algorithm. During the multi-time-step co-computations involving two finite element codes (explicit and implicit FE codes), the tasks carried out by the coupling software PH-CPL, based on a variant of the PH algorithm, are illustrated and compared to the coupling software GC-CPL based on the GC algorithm. The advantage of the new coupling PH-CPL software is highlighted in terms of parallel capabilities. In addition, the PH-CPL coupling software alleviates the dissipative drawback of the GC method at the interface between the subdomains. Academic cases are investigated to check the energy features and the accuracy order for the GC and PH algorithms. Finally, explicit/implicit multi-time-step co-computations with CC-CPL and PH-CPL software are conducted for two engineering applications under the assumption of linear elastic materials: a reinforced concrete frame structure under blast loading striking its front face and a flat composite stiffened panel subjected to localised loads applied to its central frame. (C) 2014 Elsevier B.V. All rights reserved,