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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.…
Development of an Optimization-Based Atomistic-to-Continuum Coupling Method
Derek Olson, Pavel Bochev, Mitchell Luskin +1
Atomistic-to-Continuum (AtC) coupling methods are a novel means of computing the properties of a discrete crystal structure, such as those containing defects, that combine the accu…
(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods
Christoph Ortner, Alexander Shapeev, Lei Zhang
We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c co…
Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
V. Ehrlacher, C. Ortner, A. V. Shapeev
Numerical simulations of crystal defects are necessarily restricted to finite computational domains, supplying artificial boundary conditions that emulate the effect of embedding t…