讲座内容介绍: |
We consider molecular dynamics (MD) model as a microscopic description of mechanical properties of a solid system. It is written as a Hamiltonian system for the position and momentum of the atoms. Many complicated material processes can in principle be understood at the atomic level using MD. However, a realist system often consists of a huge number of atoms, and the computation is too large for numerical simulations.
This talk will present a method to reduce the dimension, i.e., the number of atomic degrees of freedom, associated with the MD model. The method is motivated by traditional Galerkin projection for linear and nonlinear wave equations. Then we generalize this approach by introducing a set of auxiliary variables to extend the approximation to a larger subspace. The latter approach is similar to moment closure methods for kinetic equations. In addition to the numerical methods, we will present some error analysis along with some numerical experiments on the simulation of material defects. |