Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues

TL;DR

This paper reviews the relationship between homogenization and nonlocal modeling, highlighting how insights from one can inform the other and discussing computational challenges and opportunities for advancing numerical methods.

Contribution

It explores the connection between homogenization and nonlocal models, proposing that cross-disciplinary insights can improve understanding and computational techniques.

Findings

Homogenization can characterize nonlocal interactions.

Nonlocal models can inform homogenization methods.

Discussion of computational issues in both fields.

Abstract

In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas from the different research fronts. We illustrate how homogenization may help characterizing the nature and the form of nonlocal interactions hypothesized in nonlocal models. We also offer some perspective on how studies of nonlocality may help the development of more effective numerical methods for homogenization.