70 citations · 380 across the 25 of their papers we have counts for
5 papers · 1 filter
Iterative Methods for the Force-based Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin, Christoph Ortner
Force-based atomistic-continuum hybrid methods are the only known pointwise consistent methods for coupling a general atomistic model to a finite element continuum model. For this…
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…
An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
Matthew Dobson, Mitchell Luskin
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the…