Multiscale Modeling and Simulations
In many areas of science and engineering, we face the problem that we are interested in analyzing the macroscale behavior of a given system, but we do not have an explicit and accurate macroscopic model for the macroscale quantities that we are interested in. On the other hand, we have a microscopic model with satisfactory accuracy (e.g. a molecular dynamics model)- the difficulty being that solving the full microscopic model is far too inefficient. Therefore it is desirable to develop hybrid numerical methods that are based on a combination of the two formulations in order to take an advantage of both the efficiency of the macroscale model and the accuracy of the microscale model.
Coupled atomistic-continuum methods.  My work in this area includes: (1) the development of coupled atomistic-continuum methods for fluids (including problems with unknown constitutive equation and/or unknown boundary conditions) in the framework of the heterogeneous multiscale method (HMM); (2) the stability analysis of domain-decomposition type of multiscale methods, and (3) the development of a general scheme for designing seamless multiscale methods. See the following references for more details.
WEIQING REN Last modified: Mon Dec 3 20:55:34 EST 2007