Multiple time scale algorithm for multiscale material modeling

This paper presents a novel multiple time scale algorithm integrated with the concurrent atomic/atom-based continuum modeling, which involves molecular dynamic (MD) simulation and coarse-grained molecular dynamic (CG-MD) simulation. To capture the key features of the solution region while still considering the computational efficiency, we decompose it into two sub-regions in space and utilize the central difference method with different time steps for different subregions to march on in time. Usually, the solution region contains a critical field and a non-critical far field. For the critical field (named atomic region) modeled by MD simulation, a relatively small time step is used to update the solutions; for the far field (named atom-based continuum region) modeled by CG-MD simulation, we adopt a relatively large time step to reduce the computational efforts and thereby it leads to an acceleration of such simulations. Here, we solve a wave propagation problem to demonstrate the capability and feasibility of this algorithm. The results show that the wave can propagate across the interface between atomic region and atom-based continuum region smoothly without inducing any spurious wave reflection. Also, the effects of nonlocality and nonlinearity, introduced unintentionally by the interatomic potential, will be discussed.