Review on multiscale modeling and computation

Multiscale problems and Multiscale methods are briefly reviewed in this paper. Some multiscale theories and their new achievements in modeling and computation of two typical categories multiscale problems are introduced. The advantages and disadvantages of different methods are also analyzed to evaluate their applicability. The limitations and existing problems are analyzed and the importance of further studies on multiscale methods is pointed out. Mainly, there are Non-local quasi-continuum method, MacroAtomistic ab-initio Dynamics (MAAD) method, Coarse Grained Molecular Dynamics (CGMD) method, Coarse-grained Monte Carlo (CGMC) method and Coupled continuum-MD model for isolated defects problems and local quasi-continuum method, Artificial compressibility method, Gas-kinetic scheme and HMM for constitutive modeling problems. Finally, some problems on this subject are explained.