Absorbing Boundary Conditions for Molecular Dynamics

Abstract

With the goal of minimizing the domain size for Molecular dynamics (MD) simulations, we develop a new class of absorbing boundary conditions (MD-ABC's) that can mimic the phonon absorption of an unbounded exterior. The proposed MD-ABC's are extensions of perfectly matched discrete layers (PMDL), originally developed as an absorbing boundary condition for continuous wave propagation problems. Called MD-PMDL, this extension carefully targets the absorption of phonons, the high frequency waves, whose propagation properties are completely different from continuous waves.

This thesis presents the derivation of MD-PMDL for general lattice systems, followed by explicit application to one-dimensional and two-dimensional square lattice systems.The accuracy of MD-PMDL for phonon absorption is proven by analyzing reflection coefficients, and demonstrated through numerical experiments. Unlike existing ABC's that are effective for high frequency phonon absorption, MD-PMDL is local in both space and time and is thus more efficient. Based on their favorable properties, it is concluded that MD-PMDL could provide a more effective alternative to existing MD-ABC's.