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Stability of a force-based hybrid method with planar sharp interface

Publication ,  Journal Article
Lu, J; Ming, P
Published in: SIAM Journal on Numerical Analysis
January 1, 2014

We study a force-based hybrid method that couples an atomistic model with a Cauchy-Born elasticity model with sharp transition interface. We identify stability conditions that guarantee the convergence of the hybrid scheme to the solution of the atomistic model with second order accuracy, as the ratio between lattice parameter and the characteristic length scale of the deformation tends to zero. Convergence is established for hybrid schemes with planar sharp interface for systems without defects, with general finite range atomistic potential and simple lattice structure. The key ingredients of the proof are regularity and stability analysis of elliptic systems of difference equations. We apply the results to atomistic-to-continuum scheme for a two-dimensional triangular lattice with planar interface.

Duke Scholars

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

January 1, 2014

Volume

52

Issue

4

Start / End Page

2005 / 2026

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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MLA
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Lu, J., & Ming, P. (2014). Stability of a force-based hybrid method with planar sharp interface. SIAM Journal on Numerical Analysis, 52(4), 2005–2026. https://doi.org/10.1137/130904843
Lu, J., and P. Ming. “Stability of a force-based hybrid method with planar sharp interface.” SIAM Journal on Numerical Analysis 52, no. 4 (January 1, 2014): 2005–26. https://doi.org/10.1137/130904843.
Lu J, Ming P. Stability of a force-based hybrid method with planar sharp interface. SIAM Journal on Numerical Analysis. 2014 Jan 1;52(4):2005–26.
Lu, J., and P. Ming. “Stability of a force-based hybrid method with planar sharp interface.” SIAM Journal on Numerical Analysis, vol. 52, no. 4, Jan. 2014, pp. 2005–26. Scopus, doi:10.1137/130904843.
Lu J, Ming P. Stability of a force-based hybrid method with planar sharp interface. SIAM Journal on Numerical Analysis. 2014 Jan 1;52(4):2005–2026.

Published In

SIAM Journal on Numerical Analysis

DOI

ISSN

0036-1429

Publication Date

January 1, 2014

Volume

52

Issue

4

Start / End Page

2005 / 2026

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics