Stability of Atomic Simulations with Matching Boundary Conditions (Advances in Applied Mathematics and Mechanics, 2014)
We explore the stability of matching boundary conditions in onespace 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, weconstruct explicit energy functionals that decay along with time.For a nonlinear atomic chain with its nonlinearity vanished aroundthe boundaries, an energy functional is constructed for the firstorder matching boundary condition. Numerical verifications are alsopresented.