Analysis of blended atomistic/continuum hybrid methods

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...

Full description

Saved in:
Bibliographic Details
Published in:Numerische Mathematik 2016-10, Vol.134 (2), p.275-326
Main Authors: Li, Xingjie Helen, Ortner, Christoph, Shapeev, Alexander V., Van Koten, Brian
Format: Article
Language:English
Subjects:
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Point defects
Simulation
Theoretical
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-015-0772-z