Analysis of blended atomistic/continuum hybrid methods

作者：Li Xingjie Helen; Ortner Christoph; Shapeev Alexander V^*; Van Koten Brian

来源：Numerische Mathematik, 2016, 134(2): 275-326.

DOI：10.1007/s00211-015-0772-z

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

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.

• 出版日期2016-10