There has been an increasing interest in developing concurrent simulation technique based on coupled atomistic/continuum representations. An important challenge in implementing this technique in studying the nanoscale material systems is the incompatibility between the continuum and atomistic descriptions at the interface, which sometimes leads to artificial reflections and numerical errors. In this work, we present a space/time enrichment approach in which the enrichment scales are introduced on top of the continuum approximation. Using the partition-of-unity concept, we establish multiscale approximation based on the fine-scale physics that are associated with the particular application. Following this, a coupled solution scheme is developed and the coupled continuum/atomistic simulation method is derived within the framework of space/time discontinuous Galerkin method. A unique advantage of the developed methodology is that it allows one to directly address multiscale phenomena that are coupled in space and time. After an outline of the basic formulation, we illustrate the robustness of the method by focusing on finite temperature material systems. We show that the wave transmitting boundary conditions can be achieved simultaneously with energy conservation.

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