A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions

Haochen Wang; Mingjie Liao; Ping Lin; Lei Zhang

doi:10.1137/17M1131106

A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions

Haochen Wang, Mingjie Liao, Ping Lin, Lei Zhang (Lead / Corresponding author)

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

221 Downloads (Pure)

Abstract

Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.

Original language	English
Pages (from-to)	A2087-A2119
Number of pages	33
Journal	SIAM Journal on Scientific Computing
Volume	40
Issue number	4
Early online date	5 Jul 2018
DOIs	https://doi.org/10.1137/17M1131106
Publication status	Published - 2018

Keywords

atomistic models
coarse graining
atomistic-to-continuum coupling
adaptive algorithm
a posteriori error estimate

Access to Document

10.1137/17M1131106

Author Accepted Manuscript
First Published in SIAM Journal on Scientific Computing, published by the Society for Industrial and Applied Mathematics (SIAM). Copyright © 2018 by SIAM. Unauthorized reproduction of this article is prohibited.
Accepted author manuscript, 666 KB

Lin, Ping
- p.lindundee.acuk
- Mathematics - Professor
Person: Academic

Cite this

@article{42e1d2f3fff64150baf6e7bbbbe64822,

title = "A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions",

abstract = "Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.",

keywords = "atomistic models, coarse graining, atomistic-to-continuum coupling, adaptive algorithm, a posteriori error estimate",

author = "Haochen Wang and Mingjie Liao and Ping Lin and Lei Zhang",

note = "HW was partially supported by NSFC grant 11501389, 11471214 and Sichuan University Starting Up Research Funding No. 2082204194117. PL and ML were partially supported by NSFC grant 91430106 and Fundamental Research Funds for Central Universities Nos. 06108038 and FRF-BR-13-023. PL and HW were partially supported by EMS RSF grant. LZ was partially supported by NSFC grant 11471214, 11571314 and the One Thousand Plan of China for young scientists.",

year = "2018",

doi = "10.1137/17M1131106",

language = "English",

volume = "40",

pages = "A2087--A2119",

journal = "SIAM Journal on Scientific Computing",

issn = "1064-8275",

publisher = "Society for Industrial and Applied Mathematics",

number = "4",

}

TY - JOUR

T1 - A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions

AU - Wang, Haochen

AU - Liao, Mingjie

AU - Lin, Ping

AU - Zhang, Lei

N1 - HW was partially supported by NSFC grant 11501389, 11471214 and Sichuan University Starting Up Research Funding No. 2082204194117. PL and ML were partially supported by NSFC grant 91430106 and Fundamental Research Funds for Central Universities Nos. 06108038 and FRF-BR-13-023. PL and HW were partially supported by EMS RSF grant. LZ was partially supported by NSFC grant 11471214, 11571314 and the One Thousand Plan of China for young scientists.

PY - 2018

Y1 - 2018

N2 - Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.

AB - Atomistic/continuum coupling methods aim to achieve optimal balance between accuracy and efficiency. Adaptivity is the key for the efficient implementation of such methods. In this paper, we carry out a rigorous a posteriori analysis of the residual, the stability constant, and the error bound, for a consistent atomistic/continuum coupling method in 2D. We design and implement the corresponding adaptive mesh refinement algorithm, and the convergence rate with respect to degrees of freedom is optimal compare with a priori error estimates.

KW - atomistic models

KW - coarse graining

KW - atomistic-to-continuum coupling

KW - adaptive algorithm

KW - a posteriori error estimate

U2 - 10.1137/17M1131106

DO - 10.1137/17M1131106

M3 - Article

SN - 1064-8275

VL - 40

SP - A2087-A2119

JO - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

IS - 4

ER -

A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions

Abstract

Keywords

Access to Document

Fingerprint

Profiles

Lin, Ping

Cite this