Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method

S. Prudhomme; H. Ben Dhia; P. T. Bauman; N. Elkhodja; J. T. Oden

doi:10.1016/j.cma.2008.03.014

Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method

S. Prudhomme^*, H. Ben Dhia, P. T. Bauman, N. Elkhodja, J. T. Oden

^*Corresponding author for this work

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

64 Scopus citations

Abstract

We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden change in the spring properties. The surrogate model is obtained by the Arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using Lagrange multipliers. The objective of the present work is to show, via numerical experiments, that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and/or its size are increased.

Original language	English (US)
Pages (from-to)	3399-3409
Number of pages	11
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	197
Issue number	41-42
DOIs	https://doi.org/10.1016/j.cma.2008.03.014
State	Published - Jul 1 2008
Externally published	Yes

Bibliographical note

Funding Information:
S. Prudhomme would like to thank Denis Aubry for the kind invitation to visit Ecole Centrale de Paris, France, during the Springs of 2006 and 2007, where this work was initiated. P.T. Bauman acknowledges the support of the DOE Computational Science Graduate Fellowship. Support of this work by DOE under contract DE-FG02-05ER25701 is gratefully acknowledged.

Keywords

Atomistic-to-continuum coupling method
Error analysis
Homogenization
Modeling error in quantities of interest

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/j.cma.2008.03.014

Cite this

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title = "Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method",

abstract = "We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden change in the spring properties. The surrogate model is obtained by the Arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using Lagrange multipliers. The objective of the present work is to show, via numerical experiments, that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and/or its size are increased.",

keywords = "Atomistic-to-continuum coupling method, Error analysis, Homogenization, Modeling error in quantities of interest",

author = "S. Prudhomme and {Ben Dhia}, H. and Bauman, {P. T.} and N. Elkhodja and Oden, {J. T.}",

note = "Funding Information: S. Prudhomme would like to thank Denis Aubry for the kind invitation to visit Ecole Centrale de Paris, France, during the Springs of 2006 and 2007, where this work was initiated. P.T. Bauman acknowledges the support of the DOE Computational Science Graduate Fellowship. Support of this work by DOE under contract DE-FG02-05ER25701 is gratefully acknowledged.",

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doi = "10.1016/j.cma.2008.03.014",

language = "English (US)",

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T1 - Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method

AU - Prudhomme, S.

AU - Ben Dhia, H.

AU - Bauman, P. T.

AU - Elkhodja, N.

AU - Oden, J. T.

N1 - Funding Information: S. Prudhomme would like to thank Denis Aubry for the kind invitation to visit Ecole Centrale de Paris, France, during the Springs of 2006 and 2007, where this work was initiated. P.T. Bauman acknowledges the support of the DOE Computational Science Graduate Fellowship. Support of this work by DOE under contract DE-FG02-05ER25701 is gratefully acknowledged.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden change in the spring properties. The surrogate model is obtained by the Arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using Lagrange multipliers. The objective of the present work is to show, via numerical experiments, that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and/or its size are increased.

AB - We propose in this paper a 1D model problem to study the convergence of surrogate approximations, using an atomistic-to-continuum coupling method, towards the solution of a full particle model. The 1D problem consists of a collection of springs that exhibits a local defect, materialized by a sudden change in the spring properties. The surrogate model is obtained by the Arlequin approach which introduces an overlap region in which the continuum and particle models are coupled together using Lagrange multipliers. The objective of the present work is to show, via numerical experiments, that the modeling error does indeed converge to zero as the distance of the overlap region from the defect and/or its size are increased.

KW - Atomistic-to-continuum coupling method

KW - Error analysis

KW - Homogenization

KW - Modeling error in quantities of interest

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VL - 197

SP - 3399

EP - 3409

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

IS - 41-42

ER -

Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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