A novel time-marching formulation for wave propagation analysis: The adaptive hybrid explicit method

Abstract

This paper proposes an adaptive hybrid approach to explicitly analyse hyperbolic models. The new methodology considers the combination of simple and enhanced explicit time-marching procedures, which are both based on adaptive time integrators. By applying this combined approach, the hybrid formulation allows avoiding solver routines (explicit analysis), enables considering larger time-step values (higher stability limits are provided by the method) and permits reduced computational efforts, per time step, to be obtained. Thus, the novel technique may be considered very efficient. In addition, the proposed hybrid approach is entirely automated, providing automatic distributions of regular and enhanced subdomains along the discretized model, demanding no expertise and/or effort from the user. The time integrators of the method are adaptively evaluated, taking into account the local properties of the discretized domain and the behaviour of the computed responses, enabling a very versatile solution methodology. In this context, a link between the temporal and the spatial discretizations may be established, as well as optimized algorithmic dissipation can be introduced into the analyses, providing enhanced accuracy. Numerical results are presented at the end of the manuscript, illustrating the excellent performance of the proposed adaptive hybrid explicit method.