A Dynamical Concurrent Multiscale Method Employing a Transmitting Boundary to Minimize Wave Reflections at the Domain Interface (Communications in Computational Physics, 2020)
In this work, we present a reformulation of a concurrent multi-scale computation method, previously developed and demonstrated in a static setting at zerotemperature, to extend the method for dynamic cases. Additionally, within the context of dynamics, a well-known problem faced in multi-scale simulations pertains tothe spurious wave reflections that occur at the artificially introduced interface betweenthe atomistic domain and the coarse scale domain. To address this computational issue, we derive and demonstrate from first principles a simple yet effective solution tomitigate the manifestation of such nonphysical wave reflections at the surface of anartificially truncated domain. We obtain an explicit relationship between the displacement and the velocity terms of the terminal atom and the additional force that needsto be applied on this atom in order to absorb any incident wave. We present how theproposed transmitting boundary can be implemented within the multi-scale formulation for dynamic cases and include numerical examples to verify the efficacy of themethods.