Adaptive multiple time scales mapping in heterogeneous molecular simulation, a hierarchical domain decomposition approach

Heterogeneous molecular systems are mostly inspired by natural phenomena, such as, phase segregation, evaporation, among others. Those systems can be modeled by means of advanced molecular simulations methods, as it is done in multiscale concurrent and non-equilibrium simulations. Interestingly, the heterogeneity of the mentioned systems has a huge potential to map and span time and length scales beyond fully atomistic simulations, because a subdomain of the simulation box can be tackled with slowly diffusive regime, while other remains in a faster diffusive regime. From this description, a decisive question arises on how to map those heterogeneous time scales without losing the theoretical speedup planned from the method development perspective. Here, we introduce the heterogeneous time-spatial domain decomposition approach which is a combination of an heterogeneity sensitive spatial domain decomposition with a time evolution average of particles' diffusion domainwise estimated. Within this approach, the spatial domain decomposition is theoretically modeled and results in scaling-laws for the force calculation time, while timewise the subdomains with different diffusivity are adapted by means of the number of neighboring shells to a unique frequency of neighbors list updates.