An analysis of the effect of ghost force oscillation on quasicontinuum error

Mathematical Modelling and Numerical Analysis

Volumn 43, Issue 3, 2009, Pages 591-604

  Dobson, Matthew ^a   Luskin, Mitchell ^a  

^a UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Atomistic to continuum; Ghost force; Quasicontinuum

Indexed keywords

EID: 67650249008     PISSN: 0764583X     EISSN: 12903841     Source Type: Journal    
DOI: 10.1051/m2an/2009007     Document Type: Article

References (25)

1. M. Arndt and M. Luskin, Goal-oriented atomistic-continuum adaptivity for the quasicontinuum approximation. Int. J. Mult. Comp. Eng. 5(2007) 407-415.
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.
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.
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.
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.
6. W. Curtin and R. Miller, Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sc. 11(2003) R33-R68.
7. M. Dobson and M. Luskin, Analysis of a force-based quasicontinuum method. ESAIM: M2AN 42(2008) 113-139.
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.
9. W. E., J. Lu and J. Yang, Uniform accuracy of the quasicontinuum method. Phys. Rev. B 74(2006) 214115.
10. J. Knap and M. Ortiz, An analysis of the quasicontinuum method. J. Mech. Phys. Solids 49(2001) 1899-1923.
11. P. Lin, Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model. Math. Comp.72(2003) 657-675 (electronic).
12. P. Lin, Convergence analysis of a quasi-continuum approximation for a two-dimensional material. SIAM J. Numer. Anal. 45(2007) 313-332.
13. R. Miller and E. Tadmor, The quasicontinuum method: Overview, applications and current directions. J. Comput. Aided Mater. Des. 9(2002) 203-239.
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.
15. P. Ming and J.Z. Yang, Analysis of a one-dimensional nonlocal quasicontinuum method.Preprint.
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.
17. C. Ortner and E. Siili, A-posteriori analysis and adaptive algorithms for the quasicontinuum method in one dimension. Research Report NA-06/13, Oxford University Computing Laboratory (2006).
18. C. Ortner and E. Suli, Analysis of a quasicontinuum method in one dimension. ESAIM: M2AN 42(2008) 57-91.
19. M.L. Parks, P.B. Bochev and R.B. Lehoucq, Connecting atomistic-to- continuum coupling and domain decomposition. Multi-scale Model. Simul. 7(2008) 362-380.
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.
21. D. Rodney and R. Phillips, Structure and strength of dislocation junctions: An atomic level analysis. Phys. Rev. Lett. 82(1999) 1704-1707.
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.
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.
24. G. Strang and G. Fix, Analysis of the Finite Elements Method. Prentice Hall (1973).
25. E. Tadmor, M. Ortiz and R. Phillips, Quasicontinuum analysis of defects in solids. Phil. Mag. A 73(1996) 1529-1563.