Stable absorbing boundary conditions for molecular dynamics in general domains

TL;DR

This paper introduces a novel absorbing boundary condition for molecular dynamics that uses a dynamic Dirichlet-to-Neumann map, applicable to general geometries, with rational function approximations ensuring stability and effectiveness.

Contribution

It develops a general geometric absorbing boundary condition for molecular dynamics based on a dynamic DtN map with rational approximations, ensuring stability.

Findings

The boundary condition accurately absorbs waves in molecular dynamics simulations.

The method is stable for various approximations.

Numerical tests confirm effectiveness in different scenarios.

Abstract

A new type of absorbing boundary conditions for molecular dynamics simulations are presented. The exact boundary conditions for crystalline solids with harmonic approximation are expressed as a dynamic Dirichlet- to-Neumann (DtN) map. It connects the displacement of the atoms at the boundary to the traction on these atoms. The DtN map is valid for a domain with general geometry. To avoid evaluating the time convo- lution of the dynamic DtN map, we approximate the associated kernel function by rational functions in the Laplace domain. The parameters in the approximations are determined by interpolations. The explicit forms of the zeroth, first, and second order approximations will be presented. The stability of the molecular dynamics model, supplemented with these absorbing boundary conditions is established. Two numerical simulations are performed to demonstrate the effectiveness of the methods.