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A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods

  • Brian Van Koten
  • Xingjie Helen Li
  • Mitchell Luskin
  • Christoph Ortner
Chapter
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 83)

Abstract

We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems – the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading. We find that our theoretical analysis of the accuracy near instabilities for one-dimensional model problems can successfully explain most of the computational results for these multi-dimensional benchmark problems. However, we also observe some clear discrepancies, which suggest the need for additional theoretical analysis and benchmark problems to more thoroughly understand the accuracy of quasicontinuum methods.

Keywords

Critical Strain Benchmark Test Atomistic Energy Continuum Region Atomistic Region 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

Acknowledgements

This work was supported in part by the National Science Foundation under DMS-0757355, DMS-0811039, the PIRE Grant OISE-0967140, the Institute for Mathematics and Its Applications, and the University of Minnesota Supercomputing Institute. This work was also supported by the Department of Energy under Award Number DE-SC0002085. CO was supported by the EPSRC grant EP/H003096/1 “Analysis of Atomistic-to-Continuum Coupling Methods.”

We wish to thank Ellad Tadmor for helpful discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Brian Van Koten
    • 1
  • Xingjie Helen Li
    • 1
  • Mitchell Luskin
    • 1
  • Christoph Ortner
    • 2
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Mathematical InstituteOxfordUK

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