An adaptive time integration procedure for automated extended-explicit/implicit hybrid analyses

Abstract

This paper introduces a new explicit-implicit time-marching formulation, presenting a novel hybrid approach for wave propagation analysis. The proposed solution algorithm employs a set of simple, single-step, single-solver, truly self-starting recurrence relationships, which incorporate three time-integration parameters. These parameters are adaptively evaluated for each element of the adopted spatial discretization, taking into account the local characteristics of the model and a user defined parameter. They enable automated extended-explicit/implicit and non-dissipative/dissipative elements to be established, allowing enhanced hybrid analyses to be straightforwardly performed. The proposed formulation is highly accurate, efficient, and very simple to implement and to apply, avoiding complex coupling procedures and interface treatments that are typically considered for mixed explicit/implicit analyses. The new technique is also very versatile, allowing the user to locally control the numerical properties of the adopted time-integration procedure and, consequently, to elaborate very sophisticated solution strategies. Numerical results are presented at the end of the paper, illustrating the good performance and the effectiveness of the proposed novel approach, which combines the best features (such as stability, reduced solver efforts etc.) of both implicit and explicit formulations.