Numerical comparison of some explicit time integration schemes used in DEM, FEM/DEM and molecular dynamics

Discontinua simulations are becoming an important part of Computational Mechanics to the extent that Computational Mechanics of Discontinua is becoming a separate subdiscipline of Computational Mechanics. Among the most widely used methods of Computational Mechanics of Discontinua are Discrete Element Methods, Molecular Dynamics Methods, Combined Finite-Discrete Element Methods, DDA, Manifold Methods, etc. The common feature of all these methods is time discretization of the governing equations and the resulting mostly explicit time integration schemes. A wide range of time integration schemes is available in the literature. In this paper a comparative study of some of the most commonly used explicit time integration schemes is made in terms of accuracy, stability and CPU efficiency. The study has been performed using numerical experiments based on a one degree of freedom mass-spring system. The results are presented as charts that can be used when deciding which scheme to use for a particular discontinua problem