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

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.

Keywords

• Nonlocal diffusion
• Coupling method
• Optimization
• Nonlocal vector calculus