An atomistic-based boundary element method for the reduction of molecular statics models

We propose a new reduced computational model, called atomistic-based boundary element model (ABEM), derived from a full atomistic model for a crystalline solid system. The procedure is based on a domain decomposition method, which allows the separation of the atoms near crystal defects from the surrounding region, in which the displacement of the atoms is smooth. A reduction method, which is similar to the boundary integral method for continuum models, is developed to eliminate the atoms in the surrounding region. The reduction procedure gives rise to a system of equations only involving the atoms at the remote boundary and at the boundaries of the atomistic regions containing local defects. In this paper, we will discuss the derivation of the model, the implementation, and further reduction methods. We also present applications to some test problems.