Analysis of blended atomistic/continuum hybrid methods

Xingjie Helen Li, Christoph Ortner, Alexander V. Shapeev, Brian Van Koten

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We present a comprehensive error analysis of two prototypical atomistic-to-continuum coupling methods of blending type: the energy-based and the force-based quasicontinuum methods. Our results are valid in two and three dimensions, for finite range many-body interactions (e.g., EAM type), and in the presence of lattice defects (we consider point defects and dislocations). The two key ingredients in the analysis are (1) new force and energy consistency error estimates; and (2) a new technique for proving energy norm stability of a/c couplings that requires only the assumption that the exact atomistic solution is a stable equilibrium.

Original languageEnglish
Pages (from-to)275-326
Number of pages52
JournalNumerische Mathematik
Volume134
Issue number2
DOIs
Publication statusPublished - 1 Oct 2016

Keywords

  • Atomistic models
  • Atomistic-to-continuum coupling
  • Blending
  • Coarse graining
  • Quasicontinuum method

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