Coupling Atomistic, Elasticity and Boundary Element Models

TL;DR

This paper introduces a novel atomistic/continuum coupling method using boundary element techniques to improve boundary conditions, with proven error bounds in a 2D defect model.

Contribution

It develops a new a/c coupling scheme integrating BEM for better far-field boundary conditions and provides rigorous error analysis.

Findings

Established sharp error bounds for the coupling scheme.

Demonstrated effectiveness in a 2D point defect model.

Improved accuracy in boundary condition approximation.

Abstract

We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect embedded in a homogeneous crystal.