{"id":2761,"date":"2026-09-09T09:30:00","date_gmt":"2026-09-09T07:30:00","guid":{"rendered":"https:\/\/imag.umontpellier.fr\/?p=2761"},"modified":"2026-09-08T15:42:20","modified_gmt":"2026-09-08T13:42:20","slug":"le-projet-msca-effect-sacheve-apres-deux-annees-de-recherche-a-limag","status":"publish","type":"post","link":"https:\/\/imag.umontpellier.fr\/?p=2761","title":{"rendered":"Le projet MSCA EffECT s\u2019ach\u00e8ve apr\u00e8s deux ann\u00e9es de recherche \u00e0 l\u2019IMAG"},"content":{"rendered":"\n
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Le projet EffECT<\/a><\/strong>, financ\u00e9 par une bourse postdoctorale Marie Sk\u0142odowska-Curie et men\u00e9 par Silvano Pitassi<\/strong> \u00e0 l\u2019IMAG sous la supervision de Daniele Di Pietro<\/strong>, s\u2019est achev\u00e9 fin ao\u00fbt 2026 apr\u00e8s deux ann\u00e9es de recherche.
Con\u00e7u \u00e0 l\u2019origine pour d\u00e9velopper des m\u00e9thodes num\u00e9riques poly\u00e9driques pour des probl\u00e8mes \u00e9lectromagn\u00e9tiques, EffECT<\/strong> a fait \u00e9merger un axe th\u00e9orique plus g\u00e9n\u00e9ral. Celui-ci est consacr\u00e9 aux outils fonctionnels et topologiques pour l\u2019analyse de m\u00e9thodes num\u00e9riques pr\u00e9servant les structures diff\u00e9rentielles et topologiques des probl\u00e8mes continus.
Ce nouvel axe a donn\u00e9 lieu \u00e0 cinq pr\u00e9publications en libre acc\u00e8s. Les travaux ont port\u00e9 sur les in\u00e9galit\u00e9s de Poincar\u00e9 uniformes pour les complexes discrets de de Rham [1], la construction et la classification de g\u00e9n\u00e9rateurs topologiques sur des surfaces maill\u00e9es [2], la construction de repr\u00e9sentants conformes \u00e0 partir de donn\u00e9es discr\u00e8tes sur des maillages poly\u00e9driques (voir l\u2019illustration) [3], ainsi que sur la construction d\u2019op\u00e9rateurs d\u2019extension de Sobolev compatibles avec la structure diff\u00e9rentielle, sur des domaines de topologie g\u00e9n\u00e9rale [4].
Dans un cinqui\u00e8me travail, Silvano Pitassi introduit un nouveau cadre th\u00e9orique Hybrid High-Order (HHO) pour les formes diff\u00e9rentielles sur des maillages poly\u00e9driques g\u00e9n\u00e9raux. Ce travail \u00e9tablit \u00e9galement des in\u00e9galit\u00e9s de Poincar\u00e9 uniformes [5].
En parall\u00e8le, le volet applicatif engag\u00e9 pendant EffECT se poursuit dans un travail en cours de finalisation avec Raman Kumar et Aurelio Spadotto, postdoctorants de l\u2019\u00e9quipe NEMESIS \u00e0 l\u2019IMAG. Il d\u00e9veloppe une nouvelle m\u00e9thode d\u2019ordre \u00e9lev\u00e9 pour les courants de Foucault sur des maillages poly\u00e9driques, en s\u2019appuyant sur plusieurs outils d\u00e9velopp\u00e9s au cours du projet.
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Les r\u00e9sultats du projet et les publications associ\u00e9es sont disponibles sur le site EffECT<\/strong> :
https:\/\/silvano-pitassi.github.io\/EffECT<\/a><\/p>\n\n\n\n

R\u00e9f\u00e9rences<\/strong> :<\/strong><\/p>\n\n\n\n

[1] D. A. Di Pietro, J. Droniou, M.-L. Hanot, S. Pitassi,
Uniform Poincar\u00e9 inequalities for the discrete de Rham complex of differential forms<\/em>
https:\/\/arxiv.org\/abs\/2501.16116<\/a><\/p>\n\n\n\n

[2] S. Pitassi,
Generators of H\u00b9(\u0393, \u2202\u0393\u1d9c) with \u2202\u0393\u1d9c \u2282 \u2202\u0393 for Triangulated Surfaces \u0393: Construction and Classification of Global Loops<\/em>
https:\/\/arxiv.org\/abs\/2504.05124<\/a><\/p>\n\n\n\n

[3] D. A. Di Pietro, J. Droniou, S. Pitassi,
Conforming lifting and adjoint consistency for the Discrete de Rham complex of differential forms<\/em>
https:\/\/arxiv.org\/abs\/2509.21449<\/a><\/p>\n\n\n\n

[4] E. Nilsson, S. Pitassi,
Uniformly Bounded Cochain Extensions and Uniform Poincar\u00e9 Inequalities<\/em>
https:\/\/arxiv.org\/abs\/2604.04927<\/a><\/p>\n\n\n\n

[5] S. Pitassi,
Uniform discrete Poincar\u00e9 inequalities for Hybrid High-Order differential forms on polyhedral meshes<\/em>
https:\/\/arxiv.org\/abs\/2608.10713<\/a><\/p>\n<\/div><\/div>\n\n\n\n

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Le projet EffECT, financ\u00e9 par une bourse postdoctorale Marie Sk\u0142odowska-Curie et men\u00e9 par Silvano Pitassi \u00e0 l\u2019IMAG sous la supervision de Daniele Di Pietro, s\u2019est […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[190,91],"tags":[19,6],"class_list":["post-2761","post","type-post","status-publish","format-standard","hentry","category-doctorants","category-imag","tag-chercheurs","tag-imag"],"_links":{"self":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/posts\/2761","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2761"}],"version-history":[{"count":1,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/posts\/2761\/revisions"}],"predecessor-version":[{"id":2763,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=\/wp\/v2\/posts\/2761\/revisions\/2763"}],"wp:attachment":[{"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2761"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2761"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/imag.umontpellier.fr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}