An atomistic/continuum coupling method using enriched bases

TL;DR

This paper introduces an atomistic/continuum coupling method that reduces interface errors by enriching basis functions, leading to improved accuracy in multiscale modeling.

Contribution

It proposes a novel basis enrichment approach within a Galerkin framework to suppress interface errors in atomistic/continuum coupling methods.

Findings

Significant error reduction at the interface.

Enhanced overall accuracy demonstrated by examples.

Comparison shows advantages over existing quasicontinuum methods.

Abstract

A common observation from an atomistic to continuum coupling method is that the error is often generated and concentrated near the interface, where the two models are combined. In this paper, a new method is proposed to suppress the error at the interface, and as a consequence, the overall accuracy is improved. The method is motivated by formulating the molecular mechanics model as a two-stage minimization problem. In particular, it is demonstrated that the error at the interface can be considerably reduced when new basis functions are introduced in a Galerkin projection formalism. The improvement of the accuracy is illustrated by two examples. Further, the comparison to some quasicontinuum-type methods is provided.