Improved explicit co-simulation methods incorporating relaxation techniques

Explicit co-simulation is an increasingly popular technique for solver coupling of multidisciplinary systems in a distributed environment. Compared to implicit approaches, explicit coupling schemes are simpler to implement, since explicit methods allow the synchronization of different subdomains at user-defined discrete communication points without a reinitialization of the subsystem solvers. However, a typical disadvantage of explicit schemes is the reduced stability behavior, which is introduced by errors resulting from the approximation of the coupling variables. In the manuscript at hand, improved explicit co-simulation methods incorporating relaxation techniques are considered for the case that the coupling of the subsystems is realized by constitutive laws. We discuss three decomposition techniques, namely force/force coupling, force/displacement coupling and displacement/displacement coupling. Two novel explicit coupling approaches are analyzed. Within the first approach, classical co-simulation methods based on Lagrange polynomials for extrapolating the coupling variables are modified by incorporating a straightforward relaxation approach using only the current and previous coupling variables. Applying the second approach, predicted coupling variables are generated by using a constant or linear acceleration approach for the coupling bodies. With the predicted, current and previous coupling variables, special approximation polynomials are generated also using a relaxation approach. The numerical stability and convergence characteristics will be analyzed for two explicit co-simulation approaches. It will be shown that stability and convergence can be notably improved by a proper choice of the relaxation parameters. The stabilized co-simulation techniques will be verified using several numerical examples.