Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature

TL;DR

This paper develops and tests a coarse-grained molecular dynamics method that couples atomistic and continuum models, improving the simulation of elastic waves and finite temperature effects in solids.

Contribution

It introduces a CGMD formulation based on finite elements that is derived from MD without continuum parameters, enabling smooth coupling and error control at atomistic-continuum interfaces.

Findings

CGMD better describes elastic waves than FEM.

Elastic wave scattering is less severe in CGMD.

The rigid approximation simplifies CGMD with comparable accuracy.

Abstract

Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.