711 citations · 2.4k across the 77 of their papers we have counts for
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A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
Brian Van Koten, Xingjie Helen Li, Mitchell Luskin +1
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the sta…
An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model
Xingjie Helen Li, Mitchell Luskin
The quasi-nonlocal quasicontinuum method (QNL) is a consistent hybrid coupling method for atomistic and continuum models. Embedded atom models are empirical many-body potentials th…
Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane
Pavel Belik, Mitchell Luskin
We give an analysis of the stability and displacement error for linear and circular atomistic chains in the plane when the atomistic energy is approximated by the Cauchy-Born conti…
Analysis of Energy-Based Blended Quasicontinuum Approximations
Brian Van Koten, Mitchell Luskin
The development of patch test consistent quasicontinuum energies for multi-dimensional crystalline solids modeled by many-body potentials remains a challenge. The original quasicon…
A Generalized Quasi-Nonlocal Atomistic-to-Continuum Coupling Method with Finite Range Interaction
Xingjie Helen Li, Mitchell Luskin
The accurate and efficient computation of the deformation of crystalline solids requires the coupling of atomistic models near lattice defects such as cracks and dislocations with…