Arlequin framework for multi-model, multi-time scale and heterogeneous time integrators for structural transient dynamics

This paper presents a general framework for performing spatio-temporal multi-scale/multi-model coupling. Based on displacement continuity, this approach guarantees a global energy balance of the system in the context of the Arlequin method. It introduces specific interpolation of the Lagrange multipliers and parameters of time integration operators in the overlapping zone. A dual Schur implementation is then used. To illustrate the efficiency and robustness of the method, convergence analysis with numerical experiments is performed. Finally, 1D–1D and 2D–1D coupling applications are presented in which each subdomain is integrated in time, using different time steps and different schemes. This approach gives the user more ways of controlling computational behaviour via Newmark parameters, time steps and sizing the overlapping zones.