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Theory-based benchmarking of the blended force-based quasicontinuum method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner and Alexander V. Shapeev Computer Methods in Applied Mechanics and Engineering 268 763 (2014) https://doi.org/10.1016/j.cma.2013.10.007
On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension
An Optimization-based Atomistic-to-Continuum Coupling Method
Derek Olson, Pavel B. Bochev, Mitchell Luskin and Alexander V. Shapeev SIAM Journal on Numerical Analysis 52(4) 2183 (2014) https://doi.org/10.1137/13091734X
An analysis of the boundary layer in the 1D surface Cauchy–Born model
Kavinda Jayawardana, Christelle Mordacq, Christoph Ortner and Harold S. Park ESAIM: Mathematical Modelling and Numerical Analysis 47(1) 109 (2013) https://doi.org/10.1051/m2an/2012021
Finite Element Analysis of Cauchy–Born Approximations to Atomistic Models
Positive Definiteness of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin and Christoph Ortner Multiscale Modeling & Simulation 10(3) 1023 (2012) https://doi.org/10.1137/110859270
Numerical Analysis of Multiscale Computations
Mitchell Luskin and Christoph Ortner Lecture Notes in Computational Science and Engineering, Numerical Analysis of Multiscale Computations 82 331 (2012) https://doi.org/10.1007/978-3-642-21943-6_14
A morphing strategy to couple non-local to local continuum mechanics
Gilles Lubineau, Yan Azdoud, Fei Han, Christian Rey and Abe Askari Journal of the Mechanics and Physics of Solids 60(6) 1088 (2012) https://doi.org/10.1016/j.jmps.2012.02.009
Iterative methods for the force-based quasicontinuum approximation: Analysis of a 1D model problem
Ghost forces and spurious effects in atomic‐to‐continuum coupling methods by the Arlequin approach
Ludovic Chamoin, Serge Prudhomme, H. Ben Dhia and Tinsley Oden International Journal for Numerical Methods in Engineering 83(8-9) 1081 (2010) https://doi.org/10.1002/nme.2879
Accuracy of quasicontinuum approximations near instabilities