A Hybrid Multiscale Method for Coupling Atomistic and Continuum Models

In this paper we develop and test a hybrid multiscale method for coupling atomistic and continuum simulations. Our goal is to bridge the gap on both the time and space scales between the microscopic (atomistic) and macroscopic (continuum) models. A macroscale solver for diffusion equation, here the finite difference scheme, is used on a coarse grid, while Monte Carlo simulation for random walks of particles serves as the microscopic model and is used to supply the necessary data, e.g., the macroscale fluxes or the boundary condition, for the macroscopic model. Our approach depends strongly on the efficient and stable coupling between the microscale and macroscale solvers. Numerical results and error analysis for several examples demonstrate the efficacy of our method.