Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation
Numerical Analysis
2007-08-02 v1 Mathematical Physics
math.MP
Abstract
We give a goal-oriented a posteriori error estimator for the atomistic-continuum modeling error in the quasicontinuum method, and we use this estimator to design an adaptive algorithm to compute a quantity of interest to a given tolerance by using a nearly minimal number of atomistic degrees of freedom. We present computational results that demonstrate the effectiveness of our algorithm for a periodic array of dislocations described by a Frenkel-Kontorova type model.
Cite
@article{arxiv.0708.0025,
title = {Goal-oriented Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation},
author = {Marcel Arndt and Mitchell Luskin},
journal= {arXiv preprint arXiv:0708.0025},
year = {2007}
}
Comments
9 pages, 2 figures