A Space-time Approach to Coupled Atomistic/continuum Simulation

A space-time finite element method employing discontinuous Galerkin approach, for dynamic molecular simulations is proposed. In our approach, a small region of the domain is simulated using fine scale space-time FEM and it is coupled with a coarse scale simulation which employs enriched space-time FEM. The developed approach is motivated by the needs to understand the mechanics and physics that are governed by mechanisms that take place over multiple spatial and temporal scales.The space-time weak form is first developed for atomistic system in which a coarse-grained material model is introduced. In terms of the numerical approximation, the regular space-time shape function basis is augmented with enrichment function based on the problem physics by exploiting the concept of partition of unity. With the proper selection of the enrichment function, fine scale physics can be represented in the much coarser continuum simulation in both the spatial and temporal scales. The proposed method is demonstrated in example problems, in which we show that our method results in a reflectionless at the continuum/atomistic interface without the need to impose numerical dissipation.