A Dynamical Concurrent Multiscale Method Employing a Transmitting Boundary to Minimize Wave Reflections at the Domain Interface

Abstract

In this work, we present a reformulation of a concurrent multi-scale computation method, previously developed and demonstrated in a static setting at zero temperature, to extend the method for dynamic cases. Additionally, within the context of dynamics, a well-known problem faced in multi-scale simulations pertains to the spurious wave reflections that occur at the artificially introduced interface between the atomistic domain and the coarse scale domain. To address this computational issue, we derive and demonstrate from first principles a simple yet effective solution to mitigate the manifestation of such nonphysical wave reflections at the surface of an artificially truncated domain. We obtain an explicit relationship between the displacement and the velocity terms of the terminal atom and the additional force that needs to be applied on this atom in order to absorb any incident wave. We present how the proposed transmitting boundary can be implemented within the multi-scale formulation for dynamic cases and include numerical examples to verify the efficacy of the methods.