Efficient non-reflecting boundary condition constructed via optimization of damped layers
RE Jones and CJ Kimmer, PHYSICAL REVIEW B, 81, 094301 (2010).
In this work we use analytic and numerical techniques to construct optimal, nearly reflectionless boundary layers for lattice dynamics by tuning the mass, stiffness, and damping of those layers. Using a one- dimensional nearest-neighbor chain as a model system, we obtain analytical results for the low and high-frequency behavior of such boundary conditions, as well as a continued fraction solution for the reflection coefficient of multiple layers. In addition, we obtain optimal parameters for the one-dimensional system and a three- dimensional system using wave packets with normal incidence and compare the results to an implementation of the exact boundary condition in one dimension and optimal versions of the commonly used ramped damping in three dimensions.
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