522 citations · 2.1k across the 73 of their papers we have counts for
6 papers · 2 filters
Positive-Definiteness of the Blended Force-Based Quasicontinuum Method
Xingjie Helen Li, Mitchell Luskin, Christoph Ortner
The development of consistent and stable quasicontinuum models for multi-dimensional crystalline solids remains a challenge. For example, proving stability of the force-based quasi…
Atomistic-to-Continuum Coupling Approximation of a One-Dimensional Toy Model for Density Functional Theory
B. Langwallner, C. Ortner, E. Süli
We consider an atomistic model defined through an interaction field satisfying a variational principle, and can therefore be considered a toy model of (orbital free) density functi…
Formulation and optimization of the energy-based blended quasicontinuum method
M. Luskin, C. Ortner, B. Van Koten
We formulate an energy-based atomistic-to-continuum coupling method based on blending the quasicontinuum method for the simulation of crystal defects. We utilize theoretical result…
Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem
Christoph Ortner, Lei Zhang
We present a new variant of the geometry reconstruction approach for the formulation of atomistic/continuum coupling methods (a/c methods). For multi-body nearest-neighbour interac…
Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
Mitchell Luskin, Christoph Ortner
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementin…
The role of the patch test in 2D atomistic-to-continuum coupling methods
Christoph Ortner
For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy--Born nonlinear elastic…