@inproceedings{1945ed99096a4eadbda9a7654177e7d2,
title = "Linear stationary iterative methods for the force-based quasicontinuum approximation",
abstract = "Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. However, the development of efficient and reliable iterative solution methods for the force-based approximation presents a challenge due to the non-symmetric and indefinite structure of the linearized force-based quasicontinuum approximation, as well as to its unusual stability properties. In this paper, we present rigorous numerical analysis and computational experiments to systematically study the stability and convergence rate for a variety of linear stationary iterative methods.",
author = "Mitchell Luskin and Christoph Ortner",
year = "2012",
doi = "10.1007/978-3-642-21943-6_14",
language = "English (US)",
isbn = "9783642219429",
series = "Lecture Notes in Computational Science and Engineering",
publisher = "Springer Verlag",
pages = "331--368",
editor = "Olof Runborg and Bjorn Engquist and Tsai, {Yen-Hsi R.}",
booktitle = "Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009",
note = "Workshop on Numerical Analysis and Multiscale Computations, 2009 ; Conference date: 06-12-2009 Through 11-12-2009",
}