Linear stationary iterative methods for the force-based quasicontinuum approximation

Mitchell Luskin; Christoph Ortner

doi:10.1007/978-3-642-21943-6_14

Linear stationary iterative methods for the force-based quasicontinuum approximation

Mitchell Luskin, Christoph Ortner

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

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.

Original language	English (US)
Title of host publication	Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009
Editors	Olof Runborg, Bjorn Engquist, Yen-Hsi R. Tsai
Publisher	Springer Verlag
Pages	331-368
Number of pages	38
ISBN (Print)	9783642219429
DOIs	https://doi.org/10.1007/978-3-642-21943-6_14
State	Published - 2012
Event	Workshop on Numerical Analysis and Multiscale Computations, 2009 - Banff, Canada Duration: Dec 6 2009 → Dec 11 2009

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	82
ISSN (Print)	1439-7358

Other

Other	Workshop on Numerical Analysis and Multiscale Computations, 2009
Country/Territory	Canada
City	Banff
Period	12/6/09 → 12/11/09

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2012.

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Luskin, M., & Ortner, C. (2012). Linear stationary iterative methods for the force-based quasicontinuum approximation. In O. Runborg, B. Engquist, & Y.-H. R. Tsai (Eds.), Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009 (pp. 331-368). (Lecture Notes in Computational Science and Engineering; Vol. 82). Springer Verlag. https://doi.org/10.1007/978-3-642-21943-6_14

Linear stationary iterative methods for the force-based quasicontinuum approximation. / Luskin, Mitchell; Ortner, Christoph.
Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. ed. / Olof Runborg; Bjorn Engquist; Yen-Hsi R. Tsai. Springer Verlag, 2012. p. 331-368 (Lecture Notes in Computational Science and Engineering; Vol. 82).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Luskin, M & Ortner, C 2012, Linear stationary iterative methods for the force-based quasicontinuum approximation. in O Runborg, B Engquist & Y-HR Tsai (eds), Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. Lecture Notes in Computational Science and Engineering, vol. 82, Springer Verlag, pp. 331-368, Workshop on Numerical Analysis and Multiscale Computations, 2009, Banff, Canada, 12/6/09. https://doi.org/10.1007/978-3-642-21943-6_14

Luskin M, Ortner C. Linear stationary iterative methods for the force-based quasicontinuum approximation. In Runborg O, Engquist B, Tsai YHR, editors, Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. Springer Verlag. 2012. p. 331-368. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-642-21943-6_14

Luskin, Mitchell ; Ortner, Christoph. / Linear stationary iterative methods for the force-based quasicontinuum approximation. Numerical Analysis of Multiscale Computations - Proceedings of a Winter Workshop at the Banff International Research Station 2009. editor / Olof Runborg ; Bjorn Engquist ; Yen-Hsi R. Tsai. Springer Verlag, 2012. pp. 331-368 (Lecture Notes in Computational Science and Engineering).

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Linear stationary iterative methods for the force-based quasicontinuum approximation

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