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.

  • A general strategy for designing seamless multiscale methods, W. E, W. Ren and E. Vanden-Eijnden, J. Comput. Phys. 228, 5437 (2009)  
  • Sequential multiscale modeling using sparse representation, C. Garcia-Cervera, W. Ren, J. Lu and W. E, Commun. Comput. Phys. 4, 1025 (2008)  
  • Seamless multiscale modeling of complex fluids using fiber bundle dynamics, W. Ren, Commun. Math. Sci. 5, 1027 (2007)  
  • Analytical and numerical study of coupled atomistic-continuum methods for fluids, W. Ren, J. Comput. Phys. 227, 1353 (2007)  
  • Heterogeneous multiscale methods: A review, W. E, B. Engquist, X. Li, W. Ren and E. Vanden-Eijnden, Commun. Comput. Phys. 2, 367 (2007) 
  • Heterogeneous multiscale method for the modeling of complex fluids and micro fluidics, W. Ren and W. E, J. Comput. Phys. 204, 1 (2005)  
  • A General framework for designing seamless multiscale methods , W. E, W. Ren and E. Vanden-Eijnden, preprint

Last modified: Mon Dec 3 20:55:34 EST 2007