Multiscale Methods in Computational Mechanics
ENG ME 711
This course will cover the state-of-the-art in analytical and (especially) computational techniques for solving problems with multiple spatial and temporal scales. Such problems are now at the forefront of computational mechanics with applications ranging from turbulence and its modeling to the coupling of atomistic and continuum scales in solid mechanics. We will begin with the more traditional methods including multi-scale perturbation techniques and renormalization group theory. Thereafter we will focus on more recent developments with distinct computational focus including: the Optimal Prediction Method of Chorin et al., the Equation Free Method of Kevrekidis et al, the Variational Multiscale Method of Hughes et al. and the Heterogeneous Multiscale Method of Weinan et al. We will also cover an approach to determine unknown parameters in the models derived from these methods. The differences and similarities between these methods will also be discussed and highlighted.