Free Access
Volume 43, Number 3, May-June 2009
Page(s) 591 - 604
Published online 08 April 2009
  1. M. Arndt and M. Luskin, Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation. Int. J. Mult. Comp. Eng. 5 (2007) 407–415. [CrossRef] [Google Scholar]
  2. M. Arndt and M. Luskin, Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model. Multiscale Model. Simul. 7 (2008) 147–170. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Arndt and M. Luskin, Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model. Comp. Meth. App. Mech. Eng. 197 (2008) 4298–4306. [CrossRef] [Google Scholar]
  4. S. Badia, M.L. Parks, P.B. Bochev, M. Gunzburger and R.B. Lehoucq, On atomistic-to-continuum (AtC) coupling by blending. Multiscale Model. Simul. 7 (2008) 381–406. [CrossRef] [MathSciNet] [Google Scholar]
  5. X. Blanc, C. Le Bris and F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. ESAIM: M2AN 39 (2005) 797–826. [Google Scholar]
  6. W. Curtin and R. Miller, Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sc. 11 (2003) R33–R68. [CrossRef] [Google Scholar]
  7. M. Dobson and M. Luskin, Analysis of a force-based quasicontinuum method. ESAIM: M2AN 42 (2008) 113–139. [CrossRef] [EDP Sciences] [Google Scholar]
  8. W. E and P. Ming. Analysis of the local quasicontinuum method, in Frontiers and Prospects of Contemporary Applied Mathematics, T. Li and P. Zhang Eds., Higher Education Press, World Scientific (2005) 18–32. [Google Scholar]
  9. W. E., J. Lu and J. Yang, Uniform accuracy of the quasicontinuum method. Phys. Rev. B 74 (2006) 214115. [CrossRef] [Google Scholar]
  10. J. Knap and M. Ortiz, An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49 (2001) 1899–1923. [CrossRef] [Google Scholar]
  11. P. Lin, Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model. Math. Comp. 72 (2003) 657–675 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Lin, Convergence analysis of a quasi-continuum approximation for a two-dimensional material. SIAM J. Numer. Anal. 45 (2007) 313–332. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Miller and E. Tadmor, The quasicontinuum method: Overview, applications and current directions. J. Comput. Aided Mater. Des. 9 (2002) 203–239. [Google Scholar]
  14. R. Miller, L. Shilkrot and W. Curtin. A coupled atomistic and discrete dislocation plasticity simulation of nano-indentation into single crystal thin films. Acta Mater. 52 (2003) 271–284. [CrossRef] [Google Scholar]
  15. P. Ming and J.Z. Yang, Analysis of a one-dimensional nonlocal quasicontinuum method. Preprint. [Google Scholar]
  16. J.T. Oden, S. Prudhomme, A. Romkes and P. Bauman, Multi-scale modeling of physical phenomena: Adaptive control of models. SIAM J. Sci. Comput. 28 (2006) 2359–2389. [Google Scholar]
  17. C. Ortner and E. Süli, A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension. Research Report NA-06/13, Oxford University Computing Laboratory (2006). [Google Scholar]
  18. C. Ortner and E. Süli, Analysis of a quasicontinuum method in one dimension. ESAIM: M2AN 42 (2008) 57–91. [Google Scholar]
  19. M.L. Parks, P.B. Bochev and R.B. Lehoucq, Connecting atomistic-to-continuum coupling and domain decomposition. Multiscale Model. Simul. 7 (2008) 362–380. [CrossRef] [MathSciNet] [Google Scholar]
  20. S. Prudhomme, P.T. Bauman and J.T. Oden, Error control for molecular statics problems. Int. J. Mult. Comp. Eng. 4 (2006) 647–662. [CrossRef] [Google Scholar]
  21. D. Rodney and R. Phillips, Structure and strength of dislocation junctions: An atomic level analysis. Phys. Rev. Lett. 82 (1999) 1704–1707. [CrossRef] [Google Scholar]
  22. V. Shenoy, R. Miller, E. Tadmor, D. Rodney, R. Phillips and M. Ortiz, An adaptive finite element approach to atomic-scale mechanics – the quasicontinuum method. J. Mech. Phys. Solids 47 (1999) 611–642. [CrossRef] [MathSciNet] [Google Scholar]
  23. T. Shimokawa, J. Mortensen, J. Schiotz and K. Jacobsen, Matching conditions in the quasicontinuum method: Removal of the error introduced at the interface between the coarse-grained and fully atomistic regions. Phys. Rev. B 69 (2004) 214104. [CrossRef] [Google Scholar]
  24. G. Strang and G. Fix, Analysis of the Finite Elements Method. Prentice Hall (1973). [Google Scholar]
  25. E. Tadmor, M. Ortiz and R. Phillips, Quasicontinuum analysis of defects in solids. Phil. Mag. A 73 (1996) 1529–1563. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you