TY - JOUR T1 - Stability of Atomic Simulations with Matching Boundary Conditions AU - Tang , Shaoqiang AU - Ji , Songsong JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 539 EP - 551 PY - 2014 DA - 2014/06 SN - 6 DO - http://doi.org/10.4208/aamm.2013.m360 UR - https://global-sci.org/intro/article_detail/aamm/34.html KW - Stability, matching boundary condition, atomic simulation. AB -

We explore the stability of matching boundary conditions in one space dimension, which was proposed recently for atomic simulations (Wang and Tang, Int. J. Numer. Mech. Eng., 93 (2013), pp. 1255-1285). For a finite segment of the linear harmonic chain, we construct explicit energy functionals that decay along with time. For a nonlinear atomic chain with its nonlinearity vanished around the boundaries, an energy functional is constructed for the first order matching boundary condition. Numerical verifications are also presented.