Accurate Boundary Conditions for Twin Boundary

Abstract

In this paper, we propose accurate numerical boundary conditions for atomic simulations of twin boundary. The heterogeneity of the lattice structure induces physical reflection across the twin boundary. When numerical boundary and the twin boundary coincide, the goal is to reproduce the correct amount of physical reflection. In particular, we consider waves periodic in the direction parallel to the twin boundary and reduce the problem into a complex-valued chain motion. Using Laplace transform, we design time history kernel (THK) treatment. We further design matching boundary conditions (MBC) by reproducing physical reflection at long wave limit and a specific wave number. Reflection analysis and numerical tests demonstrate the effectiveness of the proposed THK and MBC treatments.