A hybrid self-adjustable explicit–explicit–implicit time marching formulation for wave propagation analyses

Abstract

In this paper, a novel hybrid explicit/implicit time marching procedure is proposed for wave propagation analyses. The new formulation considers local self-adjustable time integration parameters that are defined for each element of the adopted spatial discretization procedure, following the properties of the discretized model. Thus, the explicit/implicit subdomains of the analysis are established at an element level, taking into account automated computations. Two types of explicit approaches are considered here, allowing extended stability limits to be provided and more efficient analyses performed. Controllable numerical dissipation is also enabled following the locally defined adaptive time integrators of the method. In this sense, optimally designed time integration parameters are developed, providing null spectral radii for the highest sampling frequency of the elements, and close to one values for the important low-frequency response domain. Thus, the influence of spurious high-frequency modes is very effectively extinguished and reduced dissipative and dispersive errors are introduced into the analysis. At the end of the paper numerical results are provided, illustrating the excellent performance of the proposed new methodology.