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Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
Alexander V. Shapeev
This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has…
Homogenization-based Analysis of Quasicontinuum Method for Complex Crystals
Assyr Abdulle, Ping Lin, Alexander V. Shapeev
Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method, introduced by Tadmor, Ortiz, and Phillips (1996), has attracted growing interest in…
The Spectrum of the Force-Based Quasicontinuum Operator for a Homogeneous Periodic Chain
Matthew Dobson, Christoph Ortner, Alexander V. Shapeev
We show under general conditions that the linearized force-based quasicontinuum (QCF) operator has a positive spectrum, which is identical to the spectrum of the quasinonlocal quas…