Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods

Rutger A. Biezemans; Claude Le Bris; Frédéric Legoll; Alexei Lozinski

doi:10.5802/crmeca.178

Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods

Rutger A. Biezemans ^1,² ; Claude Le Bris ^1,² ; Frédéric Legoll ^1,² ; Alexei Lozinski ^2,³

¹ École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
² MATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
³ Université de Franche-Comté, CNRS, LmB, F-25000 Besançon, France

Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 135-180.

Résumé

Multiscale Finite Element Methods (MsFEMs) are now well-established finite element type approaches dedicated to multiscale problems. They first compute local, oscillatory, problem-dependent basis functions that generate a suitable discretization space, and next perform a Galerkin approximation of the problem on that space. We investigate here how these approaches can be implemented in a non-intrusive way, in order to facilitate their dissemination within industrial codes or non-academic environments. We develop an abstract framework that covers a wide variety of MsFEMs for linear second-order partial differential equations. Non-intrusive MsFEM approaches are developed within the full generality of this framework, which may moreover be beneficial to steering software development and improving the theoretical understanding and analysis of MsFEMs.

Reçu le : 2022-11-30
Révisé le : 2023-02-01
Accepté le : 2023-02-06
Première publication : 2023-07-27
Publié le : 2024-04-26

DOI : 10.5802/crmeca.178

Mots clés : Partial differential equations, Finite element methods, Multiscale problems, Non-intrusive implementation

Affiliations des auteurs :

Rutger A. Biezemans ^{1, 2} ; Claude Le Bris ^{1, 2} ; Frédéric Legoll ^{1, 2} ; Alexei Lozinski ^{2, 3}

¹ École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, France
² MATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France
³ Université de Franche-Comté, CNRS, LmB, F-25000 Besançon, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Rutger A. Biezemans and Claude Le Bris and Fr\'ed\'eric Legoll and Alexei Lozinski},
     title = {Non-intrusive implementation of a wide variety of {Multiscale} {Finite} {Element} {Methods}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {135--180},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {351},
     number = {S1},
     year = {2023},
     doi = {10.5802/crmeca.178},
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Rutger A. Biezemans; Claude Le Bris; Frédéric Legoll; Alexei Lozinski. Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 135-180. doi : 10.5802/crmeca.178. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.178/

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