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Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
Derek Olson, Alexander V. Shapeev, Pavel Bochev +1
We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-bas…
Accuracy of computation of crystalline defects at finite temperature
Alexander V. Shapeev, Mitchell Luskin
The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions correspondi…
Analysis of Blended Atomistic/Continuum Hybrid Methods
Xingjie Helen Li, Christoph Ortner, Alexander V. Shapeev +1
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.…