This talk will discuss the spatial and temporal reduction of molecular simulation models and Schrodinger-type models by Dirichlet-to-Neumann (DtN) map. In the static atomistic model, the DtN map which can be formulated as the boundary element method serves as the boundary condition for the reduced model. In the molecular dynamics model and time-dependent Schrodinger-type equations, absorbing boundary conditions (ABCs) are obtained by approximating the DtN map. ABCs in molecular dynamics can be further extended to the finite temperature scenario.
The idea of model reduction is verified by several numerical experiments: fracture problems in atomistic model, phonons propagation in molecular dynamics, time-dependent Schrodinger equation, and time-dependent Hartree-Fock model. The stability of the system augmented by ABCs will be investigated. The application of finite temperature ABCs for the rare event phenomenon will be briefly discussed.