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A multiscale virtual element method for the analysis of heterogeneous media

Sreekumar, Abhilash; Triantafyllou, Savvas P.; B�cot, Fran�ois?Xavier; Chevillotte, Fabien

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Authors

Abhilash Sreekumar

Savvas P. Triantafyllou

Fran�ois?Xavier B�cot

Fabien Chevillotte



Abstract

We introduce a novel heterogeneous multiscale method for the elastic analysis of two-dimensional domains with a complex microstructure. To this end, the multiscale finite element method is revisited and originally upgraded by introducing virtual element discretizations at the microscale, hence allowing for generalized polygonal and nonconvex elements. The microscale is upscaled through the numerical evaluation of a set of multiscale basis functions. The solution of the equilibrium equations is performed at the coarse scale at a reduced computational cost. We discuss the computation of the multiscale basis functions and corresponding virtual projection operators. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples.

Citation

Sreekumar, A., Triantafyllou, S. P., Bécot, F., & Chevillotte, F. (2020). A multiscale virtual element method for the analysis of heterogeneous media. International Journal for Numerical Methods in Engineering, 121(8), 1791-1821. https://doi.org/10.1002/nme.6287

Journal Article Type Article
Acceptance Date Nov 26, 2019
Online Publication Date Jan 8, 2020
Publication Date Apr 30, 2020
Deposit Date Nov 18, 2021
Publicly Available Date Mar 29, 2024
Journal International Journal for Numerical Methods in Engineering
Print ISSN 0029-5981
Electronic ISSN 1097-0207
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 121
Issue 8
Pages 1791-1821
DOI https://doi.org/10.1002/nme.6287
Keywords General Engineering; Applied Mathematics; Numerical Analysis
Public URL https://nottingham-repository.worktribe.com/output/3611427
Publisher URL https://onlinelibrary.wiley.com/doi/10.1002/nme.6287
Additional Information This is the peer reviewed version of the following article: Sreekumar, A, Triantafyllou, SP, Bécot, F-X, Chevillotte, F. A multiscale virtual element method for the analysis of heterogeneous media. Int J Numer Methods Eng. 2020; 121: 1791– 1821, which has been published in final form at https://doi.org/10.1002/nme.6287. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. This article may not be enhanced, enriched or otherwise transformed into a derivative work, without express permission from Wiley or by statutory rights under applicable legislation. Copyright notices must not be removed, obscured or modified. The article must be linked to Wiley’s version of record on Wiley Online Library and any embedding, framing or otherwise making available the article or pages thereof by third parties from platforms, services and websites other than Wiley Online Library must be prohibited.

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