Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method

TL;DR

This paper introduces a theory-informed blending approach for atomistic-to-continuum coupling, demonstrating through numerical experiments that it outperforms energy-based schemes in accuracy and stability.

Contribution

It presents a novel blending mechanism for force-based quasicontinuum methods, supported by theoretical analysis and extensive numerical validation.

Findings

B-QCF achieves higher accuracy than energy-based schemes

The method exhibits improved stability properties

Numerical results confirm theoretical predictions

Abstract

We formulate an atomistic-to-continuum coupling method based on blending atomistic and continuum forces. Our precise choice of blending mechanism is informed by theoretical predictions. We present a range of numerical experiments studying the accuracy of the scheme, focusing in particular on its stability. These experiments confirm and extend the theoretical predictions, and demonstrate a superior accuracy of B-QCF over energy-based blending schemes.