The Heterogeneous Multi-Scale Method

The heterogeneous multi-scale method (HMM) is a general strategy for dealing with problems involving multi-scales, with multi-physics, using multi-grids. It not only unifies several existing multi-scale methods, but also provide a methodology for designing new algorithms for new applications. In this paper, we review the history of multi-scale modeling and simulation that led to the development of HMM, the methodology itself together with some applications, and the mathematical theory of stability and accuracy.