Energy-based ghost force removing techniques for the quasicontinuum method

This paper studies numerical methods for accurate treatment of the interface between the local and the nonlocal region in a QC approximation of atomistic materials. Only the energy-based methods are considered. Particularly, a quasicontinuum projection (QCP) method based on the idea of finite elements is shown to be accurate and efficient for this problem. We analyse the QCP method and study its relation to the existing methods, such as the quasinonlocal quasicontinuum method and the geometrically consistent reconstruction-based method. The analysis and the results of numerical tests confirm that the projection-based QC method successfully removes the ghost force with the same computational cost as the other methods. In all computed examples the error of QCP is either the same or lower as the error of the other methods. The performance of these methods in treating interfaces of elements in the local region is also examined.