Atomistic/Continuum Blending with Ghost Force Correction

TL;DR

This paper introduces a new atomistic/continuum coupling scheme that combines energy blending with ghost force correction, achieving optimal convergence rates and improved accuracy for benchmark problems.

Contribution

It presents a novel energy-based coupling scheme integrating ghost force correction, with theoretical analysis and numerical validation showing enhanced performance.

Findings

Achieves convergence rates comparable to optimal force-based schemes

Demonstrates improved accuracy over existing schemes in numerical tests

Provides rigorous error analysis for a specific case

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.