Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Numerical Analysis
2013-09-25 v1 Materials Science
Abstract
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accuracy of an atomistic (fully discrete) model with the efficiency of a continuum model. In this note we extend the optimization-based AtC, formulated in arXiv:1304.4976 for linear, one-dimensional problems to multi-dimensional settings and arbitrary interatomic potentials. We conjecture optimal error estimates for the multidimensional AtC, outline an implementation procedure, and provide numerical results to corroborate the conjecture for a 1D Lennard-Jones system with next-nearest neighbor interactions.
Cite
@article{arxiv.1309.5988,
title = {Development of an Optimization-Based Atomistic-to-Continuum Coupling Method},
author = {Derek Olson and Pavel Bochev and Mitchell Luskin and Alexander V. Shapeev},
journal= {arXiv preprint arXiv:1309.5988},
year = {2013}
}
Comments
12 pages, 3 figures