Analysis of an optimization-based atomistic-to-continuum coupling method for point defects

TL;DR

This paper develops and analyzes an optimization-based atomistic-to-continuum coupling method for accurately simulating point defects, combining atomistic and continuum models with proven well-posedness and error bounds.

Contribution

It introduces a novel optimization-based framework for coupling atomistic and continuum models specifically for point defects, with rigorous analysis.

Findings

The method is mathematically well-posed.

Error estimates are established for the coupling approach.

The approach effectively combines atomistic accuracy with continuum efficiency.

Abstract

We formulate and analyze an optimization-based Atomistic-to-Continuum (AtC) coupling method for problems with point defects. Near the defect core the method employs a potential-based atomistic model, which enables accurate simulation of the defect. Away from the core, where site energies become nearly independent of the lattice position, the method switches to a more efficient continuum model. The two models are merged by minimizing the mismatch of their states on an overlap region, subject to the atomistic and continuum force balance equations acting independently in their domains. We prove that the optimization problem is well-posed and establish error estimates.