We discuss recent progress in hybrid atomistic-continuum methods with particular emphasis on developments in boundary condition imposition in molecular simulations, an essential ingredient of hybrid methods. Both Dirichlet (state variable) and flux boundary conditions are discussed. We also briefly review various coupling approaches and discuss the effects of compressibility and molecular fluctuations on the choice of coupling method. Common elements between hybrid methods and related multiscale simulation approaches are also briefly discussed.
The paper contains a description of a multiscale algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model. The atomic model uses empirical pair-wise potentials to describe interactions between atoms. The Newton-Raphson method is applied to solve a nanoscale model. The continuum domain is modelled by using BEM. The application of BEM reduces the total number of degrees of freedom in the multiscale model. Some numerical results of simulations
at the nanoscale are shown to examine the presented algorithm.