A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

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

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Abstract

In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum model is discretized by P1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

Original languageEnglish
Pages (from-to)198-226
Number of pages29
JournalCommunications in Computational Physics
Volume27
Issue number1
Early online date31 Oct 2019
DOIs
Publication statusPublished - 2020

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continuums
estimates
interactions
stress tensors

Keywords

  • A posteriori error estimate
  • Atomistic models
  • Atomistic-to-continuum coupling
  • Coarse graining
  • Quasicontinuum method

Cite this

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title = "A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions",
abstract = "In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum model is discretized by P1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.",
keywords = "A posteriori error estimate, Atomistic models, Atomistic-to-continuum coupling, Coarse graining, Quasicontinuum method",
author = "Mingjie Liao and Ping Lin and Lei Zhang",
note = "Funding: ML and PL were partially supported by National Natural Science Foundation of China grant 11861131004, 11771040, 91430106. LZ was partially supported by Natural Science Foundation of China grant 11871339, 11861131004, 11571314, 11471214 and the One Thousand Plan of China for young scientists.",
year = "2020",
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pages = "198--226",
journal = "Communications in Computational Physics",
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A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions. / Liao, Mingjie; Lin, Ping; Zhang, Lei (Lead / Corresponding author).

In: Communications in Computational Physics, Vol. 27, No. 1, 2020, p. 198-226.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions

AU - Liao, Mingjie

AU - Lin, Ping

AU - Zhang, Lei

N1 - Funding: ML and PL were partially supported by National Natural Science Foundation of China grant 11861131004, 11771040, 91430106. LZ was partially supported by Natural Science Foundation of China grant 11871339, 11861131004, 11571314, 11471214 and the One Thousand Plan of China for young scientists.

PY - 2020

Y1 - 2020

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AB - In this paper, we develop the residual based a posteriori error estimates and the corresponding adaptive mesh refinement algorithm for atomistic/continuum (a/c) coupling with finite range interactions in two dimensions. We have systematically derived a new explicitly computable stress tensor formula for finite range interactions. In particular, we use the geometric reconstruction based consistent atomistic/continuum (GRAC) coupling scheme, which is quasi-optimal if the continuum model is discretized by P1 finite elements. The numerical results of the adaptive mesh refinement algorithm is consistent with the quasi-optimal a priori error estimates.

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KW - Coarse graining

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