Speaker: Prof Xiantao Li  Department of Mathematics, Penn State

Time : 2013. 7.1,Monday, 4:00-5:00PM

Space: 数学楼二楼报告厅

Abstract：
 I will present a systematic approach to coarse-grain molecular dynamics models for solids. The coarse-grained models are derived by Galerkin projection to a sequence of Krylov subspaces. On the coarsest space, the model corresponds to a finite element discretization of the continuum elasto-dynamics model. On the other hand, the projection to the finest space yields the full molecular dynamics description. The models in between serve as a smooth transition between the two scales. Using this systematic approach, one can build a hierarchy of models with increasing accuracy, each of which is a well-posed model. At the top of the hierarchy is the continuum model, represented on a finite element mesh. Then, on the same mesh, we obtain higher order approximations of MD.   In the limit, the full MD description is recovered. This type of models are useful for problems where the full atomistic model is too expensive and the continuum model has limited accuracy.