Force-Based Atomistic/Continuum Blending for Multilattices

TL;DR

This paper introduces a new force-based multiscale method for multilattices with point defects, providing rigorous error estimates and convergence rates, demonstrated through numerical experiments on graphene.

Contribution

The paper develops the first rigorous error analysis and convergence results for a force-based atomistic/continuum blending method applied to multilattices with defects.

Findings

Convergence rate established in terms of computational cost

Numerical validation with a Stone--Wales defect in graphene

Error estimates depend on approximation parameters

Abstract

We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene.