Formulation, analysis and computation of an optimization-based local-to-nonlocal coupling method

TL;DR

This paper introduces an optimization-based method to effectively couple local and nonlocal continuum models by formulating it as a control problem, with numerical examples demonstrating its theoretical soundness.

Contribution

It presents a novel control-based coupling approach for local and nonlocal models, specifically applied to diffusion, with theoretical analysis and numerical validation.

Findings

The method successfully minimizes model mismatch on overlapping domains.

Numerical examples confirm the theoretical properties of the coupling approach.

The approach provides a systematic way to couple local and nonlocal diffusion models.

Abstract

We present an optimization-based coupling method for local and nonlocal continuum models. Our approach couches the coupling of the models into a control problem where the states are the solutions of the nonlocal and local equations, the objective is to minimize their mismatch on the overlap of the local and nonlocal problem domains, and the virtual controls are the nonlocal volume constraint and the local boundary condition. We present the method in the context of Local-to-Nonlocal diffusion coupling. Numerical examples illustrate the theoretical properties of the approach.