*???????????标 ?????
*??座????????
Multiscale coupling methods such as atomistic/continuum (a/c methods) and quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations, when coarse scale models do not provide sufficient accuracy but fine scale models are computationally prohibitive. Adaptive coupling methods feature on-the-fly classification of the degrees of freedom during the simulation, allowing the fine scale and coarse scale subsystems to be updated as needed. We propose such adaptive coupling methods for material defect simulations based on residual based {\it a posteriori} error estimators, which provides upper bounds for the true error (lower bounds in some cases). We validate the analysis and illustrate the effectiveness of our schemes on numerical simulations for material defects.
*?????????
???????????????ё??????????????????????北???????(1999)??????????????????????????(2002)???????????????(2007)??Max-Planck????????????????????????????????????????????????????????????????????包?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????ぷ????????????????????????????(homogenization)?????(dimension reduction)???????????????????标????????(???????? ????????????????????????????????????????????????????????????????????????????????????????????-???????????????(atomistic-continuum coupling)????????作????????????????????????????????????????????????????????????????????????????????????????表??Comm. Pure. Appl. Math., SIAM J. Numer. Anal., SIAM MMS (Multiscale Modeling and Simulation)????????????????????1993???????????О????????2007??????????????????????????W.P. Carey Prize in applied mathematics)?? 2010-2012????????olfson?????????Research Fellow)??
