Multi-scale methods and complex processes: A survey and look ahead

Abst r Ac t A comprehensive overview of numerical methodologies currently available for analyzing and building understanding of complex processes is presented. Both equation-free and equation-based methods are discussed. Many multi-scale techniques, including the use of reduced order models, lifting-restricting methods, averaging strategies such as molecular dynamics, Monte Carlo simulation and the mean value theorem, stochastic sampling methods like kriging, fitting and interpolation approaches such as surrogate solution maps and gap-tooth schemes, and others are described. The importance of and ways in which information is communicated between contents