Abstract
Atomic interactions in solid materials are described using network theory. The tools of network theory focus on understanding the properties of a system based upon the underlying interactions which govern their dynamics. While the full atomistic network is dense, we apply a spectral sparsification technique to construct a sparse interaction network model that reduces the computational complexity while preserving macroscopic conservation properties. This sparse network is compared to a reduced network created using a cut-off radius (threshold method) that is commonly used to speed-up computations while approximating interatomic forces. The approximations used to estimate the total forces on each atom are quantified to assess how local interatomic force errors propagate errors at the global or continuum scale by comparing spectral sparsification to thresholding. In particular, we quantify the performance of the spectral sparsification algorithm for the short-range Lennard-Jones potential and the long-range Coulomb potential. Spectral sparsification of the Lennard–Jones potential yields comparable results to thresholding while spectral sparsification yields improvements when considering a long-range Coulomb potential. The present network-theoretic formulation is implemented on two sample problems: relaxation of atoms near a surface and a tensile test of a solid with a circular hole.
Highlights
Molecular dynamics (MD) is a common simulation tool for modeling materials at the nano and micron length scales [1, 2]
In the framework of MD simulations, atoms are treated as point masses that are accelerated by an imbalance of interatomic forces from neighboring atoms
We briefly describe the fundamental concepts from network theory followed by its application to MD simulations and the spectral sparsification algorithm
Summary
Molecular dynamics (MD) is a common simulation tool for modeling materials at the nano and micron length scales [1, 2]. Sparsification is used to create computationally tractable representations of complex systems [27]. The use of sparsity to model continuum dynamics has recently emerged to describe nonlinear flow phenomena but there has been limited research in the field of atomistic scale computational materials science [28]. Spectral sparsification is applied and implemented to atomic networks using the Lennard– Jones and Coulomb potentials. Spectral sparsification conserves global network properties by reorganizing interatomic force distributions in order to achieve a sparse representation of the. The summation and calculation of F comprises the majority of the computational resources in MD simulations This is the one of the key aspects that motivates the use of a sparse force interaction network in this work. This paper uses the standard expression for the virial Cauchy stress
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