Atomistic/Continuum Blending with Ghost Force Correction

Abstract

We combine the ideas of atomistic/continuum energy blending and ghost force correction to obtain an energy-based atomistic/continuum coupling scheme which has, for a range of benchmark problems, the same convergence rates as optimal force-based coupling schemes. We present the construction of this new scheme, numerical results exploring its accuracy in comparison with established schemes, as well as a rigorous error analysis for an instructive special case.

arXiv comment24 pages

References in corpus (10)

• Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
• Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
• Energy-Based Atomistic-to-Continuum Coupling Without Ghost Forces
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
• Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
• Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods
• Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem
• The role of the patch test in 2D atomistic-to-continuum coupling methods
• Analysis of Blended Atomistic/Continuum Hybrid Methods
• Development of an Optimization-Based Atomistic-to-Continuum Coupling Method

Cited by in corpus (8)

• Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
• A Posteriori Error Estimation and Adaptive Algorithm for the Atomistic/Continuum Coupling in 2D
• Blended Ghost Force Correction Method for 3D Crystalline Defects
• Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements
• Geometry Equilibration of Crystalline Defects in Quantum and Atomistic Descriptions
• A Priori Analysis of a Higher Order Nonlinear Elasticity Model for an Atomistic Chain with Periodic Boundary Condition
• QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned Interatomic Potentials
• A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions