An improved adaptive formulation for explicit analyses of wave propagation models considering locally-defined self-adjustable time-integration parameters

Abstract

In this paper, a novel explicit time-marching procedure is proposed for wave propagation analyses, considering an improved adaptive formulation. In this adaptive approach, different time-integration parameters are defined for each element of the adopted spatial discretization, allowing different stability limits (as well as other properties) to be locally applied. Thus, self-adjustable dissipative and non-dissipative parameters are automatically distributed along the discretized domain of the model, following the properties of its elements, and their use is triggered regarding the behaviour of the computed responses. In this context, the errors of the adopted spatial discretization method may be properly countervailed by the time-integration procedure, allowing substantially better accuracy to be provided. In addition, as is discussed along the manuscript, the novel time-marching formulation is very simple to implement and to apply, and it provides more efficient analyses than standard time integration techniques, enabling larger time-step values to be considered as well as reduced computational efforts to be attained per time step. At the end of the paper, numerical results are presented, illustrating the effectiveness and excellent performance of the proposed technique.