2019-01558 - PhD Position F/M [Campagne CORDI-S] Toward non-intrusive finite element approaches for multiscale problems
Le descriptif de l’offre ci-dessous est en Anglais

Type de contrat : CDD de la fonction publique

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

Contexte et atouts du poste

The PhD will be co-supervised by Claude Le Bris and Frédéric Legoll, both at Inria Paris (research team MATHERIALS, https://team.inria.fr/matherials/.) and Ecole des Ponts, the former in the applied mathematics laboratory (CERMICS), the latter in the mechanics laboratory (Navier). The PhD proposal is part of a long term project and collaborative work with different funding agencies and various scientists, in particular Alexei Lozinski (Besançon), Ulrich Hetmaniuk (Seattle) and others. The PhD will be held at CERMICS, Ecole des Ponts in Marne La Vallée (RER A station Noisy-champs).  It presumably includes some regular visits at other institutions of collaborators.

Mission confiée

It is a well recognized fact that, although sometimes mandatory when the problems considered are too expensive to attack directly, and although super effective in many situations, multi-scale approaches are definitely intrusive. For instance, the celebrated Multi-scale Finite Element Method (MsFEM)  requires to change the finite element basis set, and adjust it to the problem at hand. It is not always possible and it is therefore of major interest to investigate how computational multi-scale approaches can be adapted (possibly slightly simplified at the price of a marginal loss in their efficiency) so that they become as little intrusive as possible.
Several pathways can be followed. One of those is  to subdivide the computational domain in different computational areas, where different finite element are employed, including possibly a Multi-scale Finite Element, or many different such elements, in some of the areas.



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Bibliography:
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C. Le Bris, F. Legoll & A. Lozinski, MsFEM à la Crouzeix-Raviart for highly oscillatory
elliptic problems, Chinese Annals of Mathematics B,  34, no. 1,  (2013),   pp~113-138.
 http://hal.archives-ouvertes.fr/hal-00789102

C. Le Bris, F. Legoll & A. Lozinski, An MsFEM type approach for perforated domains, SIAM MMS, Volume 12, No. 3 (2014), pp 1046-1077.https://arxiv.org/abs/1307.0876
C. Le Bris, F. Legoll & F. Madiot, A numerical comparison of some MsFEM-type approaches for advection dominated problems in heterogeneous media, M2AN, 51, Issue 3 (2017), pp 851-888.https://arxiv.org/abs/1511.08453

C. Le Bris & F. Legoll, Examples of computational approaches for elliptic, possibly multiscale PDEs with random inputs, J. Comp. Phys., 328 (2017), pp 455 - 473. https://arxiv.org/abs/1604.05061

C. Le Bris, F. Legoll \& F. Madiot, Multiscale Finite Element methods à  la Crouzeix-Raviart for advection-dominated problems in a perforated domain,   https://arxiv.org/abs/1710.09331

Principales activités


The purpose of the proposed Phd work will be to investigate thoroughly this possibility. The first stages of the work will elaborate on previous elementary attempts to achieve the goal in simplistic academic settings and quickly move on to actually relevant settings.

Compétences

Applicant should have a Master degree in applied mathematics or mechanical engineering with a good knowledge of the discretization of partial differential equations. She/he should be familiar with a scientific programming language such as Fortran, C or C++, have a first experience in scientific computing and be interested in physical sciences and team working.

Avantages

  • Subsidized meals
  • Partial reimbursement of public transport costs
  • Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
  • Possibility of teleworking (after 6 months of employment) and flexible organization of working hours
  • Professional equipment available (videoconferencing, loan of computer equipment, etc.)
  • Social, cultural and sports events and activities
  • Access to vocational training
  • Social security coverage

Rémunération

1982 € la première et la deuxième année,  2085 € la troisième année.

1982 € during the first and second years, 2085 € the last year.