522 citations · 2.1k across the 73 of their papers we have counts for
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A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D
C. Ortner
For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The…
Sharp Stability Estimates for the Force-based Quasicontinuum Method
Matthew Dobson, Mitchell Luskin, Christoph Ortner
A sharp stability analysis of atomistic-to-continuum coupling methods is essential for evaluating their capabilities for predicting the formation and motion of lattice defects. We…
Accuracy of Quasicontinuum Approximations Near Instabilities
Matthew Dobson, Mitchell Luskin, Christoph Ortner
The formation and motion of lattice defects such as cracks, dislocations, or grain boundaries, occurs when the lattice configuration loses stability, that is, when an eigenvalue of…
Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin, Christoph Ortner
Due to their algorithmic simplicity and high accuracy, force-based model coupling techniques are an exciting development in computational physics. For example, the force-based quas…