Efficient atomistic/continuum coupling using lattice Green’s functions

Abstract

Coupled Atomistic/Continuum (A/C) simulation methods significantly reduce the number of degrees of freedom in the solution of a boundary value problem by using continuum elasticity in domains where defects interact elastically. A/C coupling involves two boundaries: (a) an inner boundary that connects the atomistic and continuum domain and (b) an outer boundary where displacement or force boundary conditions are applied. Here, the lattice Green’s function (LGF)–based flexible boundary condition method is combined with the LGF-based discrete boundary element method to satisfy coupling and boundary conditions at the inner and outer boundaries, respectively, of 3D domains. The coupling algorithms for Dirichlet boundary conditions are presented, with other cases being similar. The LGF is further replaced by a more efficient coarsened LGF method that coarsens the atomistic degrees of freedom at the outer boundary. The scaling of memory and computation versus 3D size and degree of coarsening are discussed. The method and its accuracy are demonstrated using a large 2D problem involving applied forces inside the atomistic domain.