Efficient lattice Green's function method for bounded domain problems

Abstract

The lattice Green's function method (LGFM) is the discrete counterpart of the continuum boundary element method and is a natural approach for solving intrinsically discrete solid mechanics problems that arise in atomistic-continuum coupling methods. Here, the LGFM is extended to problems in a bounded domain with applied boundary conditions. An efficient controlled coarse-graining method is introduced to significantly reduce the number of atomistic degrees of freedom on the outer boundary, and thus the size of the dense Green's function matrices involved while preserving the high accuracy of the solution. The method is demonstrated on various example problems to show reductions in computational costs and errors versus reference solutions.