We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation is derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical ``ghost'' forces that occur in the atomistic to continuum interface.
We prove that the force-based quasicontinuum equations have a unique solution under suitable restrictions on the loads. For Lennard-Jones next-nearest-neighbor interactions, we show that unique solutions exist for loads in a symmetric region extending nearly to the tensile limit.
We give an analysis of the convergence of the ghost force iteration method to solve the equilibrium equations for the force-based quasicontinuum approximation. We show that the ghost force iteration is a contraction and give an analysis for its convergence rate.
On the effect of ghost force in the quasicontinuum method: dynamic problems in one dimension
the Pennsylvania State University（宾夕法尼亚州立大学）；Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）
Ghost Force Influence of a Quasicontinuum Method in Two Dimension
Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）
A study on the quasiconinuum approximations of a one-dimensional fracture model
the Pennsylvania State University（宾夕法尼亚州立大学）；Institute of Computational Mathematics and Scientific/Engineering Computing, AMSS, Chinese Academy of Sciences（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）
