Non-reflecting boundary conditions for atomistic, continuum and coupled atomistic/continuum simulations

We present a method to numerically calculate a non-reflecting boundary condition which is applicable to atomistic, continuum and coupled multiscale atomistic/continuum simulations. The method is based on the assumption that the forces near the domain boundary can be well represented as a linear function of the displacements, and utilizes standard Laplace and Fourier transform techniques to eliminate the unnecessary degrees of freedom. The eliminated degrees of freedom are accounted for in a time-history kernel that can be calculated for arbitrary crystal lattices and interatomic potentials, or regular finite element meshes using an automated numerical procedure. The new theoretical developments presented in this work allow the application of the method to non-nearest neighbour atomic interactions; it is also demonstrated that the identical procedure can be used for finite element and mesh-free simulations. We illustrate the effectiveness of the method on a one-dimensional model problem, and calculate the time-history kernel for FCC gold using the embedded atom method (EAM).