Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods
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 th...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-07-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.178/ |
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| author | Biezemans, Rutger A. Le Bris, Claude Legoll, Frédéric Lozinski, Alexei |
| author_facet | Biezemans, Rutger A. Le Bris, Claude Legoll, Frédéric Lozinski, Alexei |
| author_sort | Biezemans, Rutger A. |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-08d093d7d710448a855fe650ecaff1c0 |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-08d093d7d710448a855fe650ecaff1c02025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-07-01351S113518010.5802/crmeca.17810.5802/crmeca.178Non-intrusive implementation of a wide variety of Multiscale Finite Element MethodsBiezemans, Rutger A.0Le Bris, Claude1Legoll, Frédéric2Lozinski, Alexei3https://orcid.org/0000-0003-0745-0365MATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, FranceMATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, FranceMATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; École Nationale des Ponts et Chaussées, 6 et 8 avenue Blaise Pascal, 77455 Marne-La-Vallée Cedex 2, FranceMATHERIALS project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; Université de Franche-Comté, CNRS, LmB, F-25000 Besançon, FranceMultiscale 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.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.178/Partial differential equationsFinite element methodsMultiscale problemsNon-intrusive implementation |
| spellingShingle | Biezemans, Rutger A. Le Bris, Claude Legoll, Frédéric Lozinski, Alexei Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods Comptes Rendus. Mécanique Partial differential equations Finite element methods Multiscale problems Non-intrusive implementation |
| title | Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods |
| title_full | Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods |
| title_fullStr | Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods |
| title_full_unstemmed | Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods |
| title_short | Non-intrusive implementation of a wide variety of Multiscale Finite Element Methods |
| title_sort | non intrusive implementation of a wide variety of multiscale finite element methods |
| topic | Partial differential equations Finite element methods Multiscale problems Non-intrusive implementation |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.178/ |
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