Coupling atomistic and continuum scales commonalities and differences

Jacob Fish

In this talk I will discuss how the state-of-the-art multiscale methods originated for bridging continuum scales can be extended to coupling atomistic and continuum scales. Formulations of mathematical homogenization, partition of unity, variational multiscale, domain-decomposition and multigrid methods will be discussed in the context of atomistic to continuum coupling. Critical issues of rigorous interfacing between discrete and continuum scales, the patch test for AtC? coupling, the interscale transfer operators, and the relation of various methods to statistical mechanics will be addressed.