A Splice Method for Local-to-Nonlocal Coupling of Weak Forms

TL;DR

This paper introduces a splice method for effectively coupling local and nonlocal diffusion models using weak formulations, ensuring desirable mathematical properties and computational efficiency.

Contribution

It presents a novel coupling scheme that inherits key properties from existing methods, with proven well-posedness and demonstrated effectiveness in numerical tests.

Findings

The method maintains patch test consistency.

It demonstrates asymptotic compatibility.

It is computationally efficient and easy to implement.

Abstract

We propose a method to couple local and nonlocal diffusion models. By inheriting desirable properties such as patch tests, asymptotic compatibility and unintrusiveness from related splice and optimization-based coupling schemes, it enables the use of weak (or variational) formulations, is computationally efficient and straightforward to implement. We prove well-posedness of the coupling scheme and demonstrate its properties and effectiveness in a variety of numerical examples.