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math.NA2011★ 37 cited
Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
Alexander V. Shapeev
Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in const…
math.NA2011★ 9 cited
Numerical Methods for Multilattices
Assyr Abdulle, Ping Lin, Alexander V. Shapeev
Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed fo…
math.NA2011★ 28 cited
Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
Christoph Ortner, Alexander V. Shapeev
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pa…