Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
Numerical Analysis
2014-11-17 v1
Abstract
We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.
Cite
@article{arxiv.1411.4027,
title = {Analysis of an optimization-based atomistic-to-continuum coupling method for point defects},
author = {Derek Olson and Alexander V. Shapeev and Pavel Bochev and Mitchell Luskin},
journal= {arXiv preprint arXiv:1411.4027},
year = {2014}
}