Collective Behavior: Macroscopic versus Kinetic Descriptions

Coupling particle, kinetic and fluid models by HMM

Bjorn Engquist

The University of Texas at Austin

The heterogeneous multi-scale method (HMM) is a framework for developing and analyzing numerical methods that couple computations from very different scales. Local micro-scale simulations on small domains supply missing data to a macro-scale simulation on the full domain. An example could be local molecular dynamics computations that produce data to kinetic or fluid macro-scale models. The goal is to gain computational efficiency by restricting the micro-scale computations to small subsets but to keep most of the fidelity of the more detailed models. We will discuss this framework with respect to analysis and applications.