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

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.

Numerical Studies of a Coarse-grained Approximation for Dynamics of an Atomic Chain

“…The limiting factors of large number of particles and even larger number of interactions prompted development of methods and methodologies that design coarse-grained models computationally. Several approaches have been proposed and intensively explored in recent years both in materials simulations and theoretical studies, most notably the quasicontinuum method, [34,23,17], the coarse-grained molecular dynamics, [29,27], the heterogeneous multi-scale method, [7,8], the bridging scale method, [35]. Related approaches have been proposed for simulations involving stochastic systems ( [5,16,15]) but in this paper we focus on deterministic, molecular dynamics simulations only.…”

“…Also its numerical analysis has been attempted in [20,3,8,21,9,12,24,25]. There are generalizations of the method to dynamical cases ( [10,22,29,27]) but careful numerical or mathematical studies are still in its infancy. In this paper we would like to provide a numerical study of a one-dimensional material.…”

“…Other coarse-grained molecular dynamics techniques are developed based on the average energy of the canonical ensemble on a constrained phase space near the thermal equilibrium (see, e.g., [29,16]) and/or finite temperature quasicontinuum method, e.g., [23]. In such methods the coarse-grained Hamiltonian would be usually in a similar format as (4).…”

An embedded statistical method for coupling molecular dynamics and finite element analyses

“…A generalized formulation of conventional FEM, which allows FEM nodes to be considered as coarse-grained MD "atoms" led to another computational scheme for atomistic-continuum coupling called Coarse Grained Molecular Dynamics (CGMD). A detailed discussion of CGMD is given by Rudd and Broughton [11,12]. In yet another coupling method, the Coupling of Length Scales (CLS) method [2], the nodes in a finite element model representing the continuum region are directly connected to the atoms in an atomistic region forming an interface of "pad" atoms.…”

“…Over the past decade, various methods have been developed to address different problems involving atomistically large material domains [1][2][3][4][5][6][7][8][9][10][11][12]. The most challenging problem in developing these coupled methods is the formulation of a seamless computational connection along an interface between different material representations.…”