Positive-Definiteness of the Blended Force-Based Quasicontinuum Method
Numerical Analysis
2011-12-13 v1
Abstract
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasicontinuum (QCF) model remains an open problem. In 1D and 2D, we show that by blending atomistic and Cauchy--Born continuum forces (instead of a sharp transition as in the QCF method) one obtains positive-definite blended force-based quasicontinuum (B-QCF) models. We establish sharp conditions on the required blending width.
Keywords
Cite
@article{arxiv.1112.2528,
title = {Positive-Definiteness of the Blended Force-Based Quasicontinuum Method},
author = {Xingjie Helen Li and Mitchell Luskin and Christoph Ortner},
journal= {arXiv preprint arXiv:1112.2528},
year = {2011}
}