A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Marta D’Elia; Xingjie Li; Pablo Seleson; Xiaochuan Tian; Yue Yu

doi:10.1007/s42102-020-00038-7

A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Marta D’Elia, Xingjie Li, Pablo Seleson, Xiaochuan Tian, Yue Yu

Multiscale Methods

Research output: Contribution to journal › Review article › peer-review

31 Scopus citations

Abstract

Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. We present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.

Original language	English
Pages (from-to)	1-50
Number of pages	50
Journal	Journal of Peridynamics and Nonlocal Modeling
Volume	4
Issue number	1
DOIs	https://doi.org/10.1007/s42102-020-00038-7
State	Published - Mar 2022

Funding

M. D’Elia was supported by Sandia National Laboratories (SNL), SNL is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC-0000230927. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. X. Li was supported by NSF-DMS 1720245 and a UNC Charlotte faculty research grant. P. Seleson was supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the U. S. Department of Energy. This manuscript has been co-authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan ( http://energy.gov/downloads/doe-public-access-plan ). X. Tian was supported by NSF-DMS-2044945. Y. Yu was supported by NSF-DMS 1753031 and the Lehigh faculty research grant.

Funders	Funder number
U.S. Department of Energy
Directorate for Mathematical and Physical Sciences	1720245, 1819233
Division of Mathematical Sciences	DMS 1620434, NSF - DMS 1720245, DMS-1819233
Office of Science
National Nuclear Security Administration	DE-NA0003525
Advanced Scientific Computing Research	DE-SC-0000230927
Oak Ridge National Laboratory	Laboratory Directed Research, Development Program
Sandia National Laboratories
University of North Carolina at Charlotte
Charlotte Research Institute, University of North Carolina at Charlotte
Department of Physics and Optical Science, University of North Carolina at Charlotte
UT-Battelle	DE-AC05-00OR22725, 1753031, NSF-DMS-2044945
Energy Production and Infrastructure Center, University of North Carolina at Charlotte

Keywords

Coupling methods
Nonlocal diffusion
Nonlocal mechanics
Nonlocal models
Peridynamics

Access to Document

10.1007/s42102-020-00038-7

Cite this

@article{80d698a0773a45918023057c6e10e1e8,

title = "A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics",

abstract = "Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. We present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.",

keywords = "Coupling methods, Nonlocal diffusion, Nonlocal mechanics, Nonlocal models, Peridynamics",

author = "Marta D{\textquoteright}Elia and Xingjie Li and Pablo Seleson and Xiaochuan Tian and Yue Yu",

note = "Publisher Copyright: {\textcopyright} 2020, National Technology & Engineering Solutions of Sandia, LLC.",

year = "2022",

month = mar,

doi = "10.1007/s42102-020-00038-7",

language = "English",

volume = "4",

pages = "1--50",

journal = "Journal of Peridynamics and Nonlocal Modeling",

issn = "2522-896X",

publisher = "Springer",

number = "1",

}

TY - JOUR

T1 - A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

AU - D’Elia, Marta

AU - Li, Xingjie

AU - Seleson, Pablo

AU - Tian, Xiaochuan

AU - Yu, Yue

PY - 2022/3

Y1 - 2022/3

N2 - Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. We present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.

AB - Local-to-nonlocal (LtN) coupling refers to a class of methods aimed at combining nonlocal and local modeling descriptions of a given system into a unified coupled representation. This allows to consolidate the accuracy of nonlocal models with the computational expediency of their local counterparts, while often simultaneously removing nonlocal modeling issues such as surface effects. The number and variety of proposed LtN coupling approaches have significantly grown in recent years, yet the field of LtN coupling continues to grow and still has open challenges. This review provides an overview of the state of the art of LtN coupling in the context of nonlocal diffusion and nonlocal mechanics, specifically peridynamics. We present a classification of LtN coupling methods and discuss common features and challenges. The goal of this review is not to provide a preferred way to address LtN coupling but to present a broad perspective of the field, which would serve as guidance for practitioners in the selection of appropriate LtN coupling methods based on the characteristics and needs of the problem under consideration.

KW - Coupling methods

KW - Nonlocal diffusion

KW - Nonlocal mechanics

KW - Nonlocal models

KW - Peridynamics

UR - http://www.scopus.com/inward/record.url?scp=85130419789&partnerID=8YFLogxK

U2 - 10.1007/s42102-020-00038-7

DO - 10.1007/s42102-020-00038-7

M3 - Review article

AN - SCOPUS:85130419789

SN - 2522-896X

VL - 4

SP - 1

EP - 50

JO - Journal of Peridynamics and Nonlocal Modeling

JF - Journal of Peridynamics and Nonlocal Modeling

IS - 1

ER -

A Review of Local-to-Nonlocal Coupling Methods in Nonlocal Diffusion and Nonlocal Mechanics

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this