An enhanced explicit–implicit time-marching formulation based on fully-adaptive time-integration parameters

In this paper, a new explicit–implicit time-marching formulation, which adapts to the properties of the model and to its computed responses, is proposed. In this novel mixed time-domain solution procedure, a group of three simple single-step recurrence relationships, which are formulated considering three time-integration parameters, is considered. These three time-integration parameters are here locally and adaptively computed and, as so, they are established for each element of the adopted spatial discretization procedure, considering optimized expressions that enable both enhanced numerically dissipative and non-dissipative analyses. Additionally, these self-adjustable parameters also define, taking into account entirely automated calculations, the explicit and implicit subdomains of the model, providing an explicit–implicit solution approach that is very easy to implement and to apply. At the end of the paper, numerical results are presented and compared to those of standard procedures, illustrating the excellent performance and effectiveness of the proposed new technique, which straightforwardly allows combining the best features (e.g., reduced solver efforts, guaranteed stability etc.) of both explicit and implicit formulations.