(In-)stability and stabilization of QNL-type atomistic-to-continuum coupling methods

Christoph Rtner, Alexander V. Shapeev, Lei Zhang

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


We study the stability of ghost force-free energy-based atomistic-to-continuum (a/c) coupling methods. In one dimension we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilization mechanism for unstable coupling schemes. We then present a comprehensive study of a two-dimensional scalar planar interface setting, as a step towards a general two-dimensional/three-dimensional vectorial analysis. Our results point out various new challenges. For example, we find that none of the ghost force-free methods known to us is universally stable (i.e., stable under general interaction and general loads). We then explore to what extent our one-dimensional stabilization mechanism can be extended. & copy; 2014 Society for Industrial and Applied Mathematics

Original languageEnglish
Pages (from-to)1258-1293
Number of pages36
JournalMultiscale Modeling and Simulation
Issue number3
Publication statusPublished - 2014
Externally publishedYes


  • Atomistic-to-continuum coupling
  • Quasicontinuum
  • Stability


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