Post-Doctoral Research Visit F - M Two-Year Post-Doc Offer Taming Flaws In The Polyhedral Simulation Of Eddy Current Testing H/F INRIA

Post-Doctoral Research Visit F/M [Two-year post-doc offer] Taming flaws in the polyhedral simulation of eddy current testing
Le descriptif de l'offre ci-dessous est en Anglais
Type de contrat : CDD

Niveau de diplôme exigé : Thèse ou équivalent

Fonction : Post-Doctorant

A propos du centre ou de la direction fonctionnelle

The Inria University of Lille centre, created in 2008, employs 360 people including 305 scientists in 15 research teams. Recognised for its strong involvement in the socio-economic development of the Hauts-De-France region, theInria University of Lille centre pursues a close relationship with large companies and SMEs. By promoting synergies between researchers and industrialists, Inria participates in the transfer of skills and expertise in digital technologies and provides access to the best European and international research for the benefit of innovation and companies, particularly in the region.

For more than 10 years, theInria University of Lille centre has been located at the heart of Lille's university and scientific ecosystem, as well as at the heart of Frenchtech, with a technology showroom based on Avenue de Bretagne in Lille, on the EuraTechnologies site of economic excellence dedicated to information and communication technologies (ICT).

Contexte et atouts du poste

Post-doc framework:

Part of the ANR PRCE project («HIgh-order POlyhedral meTHods for Eddy Current testing simulations»), in partnership with the French National Power Company (EDF)

Practical aspects:

Secured two-year post-doc funding with flexible start date, located at INRIA Lille (France), endorsed with 2k EUR for light equipment and 2k EUR/year for missions.

Supervision:

(tenured researcher, INRIA Lille)

Mission confiée

Context of the project:

We are interested in the numerical simulation of eddy current testing (ECT). The target application is the non-invasive detection of flaws within highly conductive metallic components from the primary circuit of nuclear plants. In this project, we aim at devising polyhedral methods (that is, numerical methods that are applicable on general polyhedral meshes) for the simulation of the direct ECT problem. The direct ECT problem essentially consists in solving the 3D Maxwell equations, in the harmonic regime, within an heterogeneous medium. The medium, whose geometry may be complex, is composed of the metallic material to assess (along with its potential defects), of the testing probe, and of the surrounding medium. The class of polytopal methods we will focus on are the so-called hybrid high-order (HHO) methods [2], for which the curl-curl problem (magnetostatics) has been studied recently [1, 3]. The post-doc is essentially concerned, in the context of ECT simulation, with the physical and numerical modeling of the flaws.

Subject description:

The ECT problem is an interface problem by nature, since the domain of interest is composed of at least 3 different media (the material to assess, the testing probe, and the surrounding medium) with distinct electromagnetic properties. We are interested in the modeling of 3D defects, which may either consist in (i) a local, brutal variation of the material's properties, or (ii) a local alteration of the material's integrity (loss of matter, up to a through bore). The presence of defects within the conductive material may incidentally lead to the development of (possibly severe) singularities of the electromagnetic fields. Depending on their nature and their geometry, defects may also modify the topology of the conductive material. In the objective of simulating the complete ECT problem, 2 main challenges have to be faced, and will be investigated during the post-doc. First, the 3D meshing challenge. The difficulties include embedded interfaces (between the different media, or to account for defects), local mesh refinement (of the skin-depth region), and remeshing (at each new position of the testing probe). To tackle this difficulty, we will take full advantage of the flexibility offered by polyhedral grids. The second challenge to be faced is related to singularities. In the vicinity of sharp defects (e.g. with reentrant tips), the solution to approximate is expected to lack regularity, and thus the approximation to locally deteriorate. In addition to local mesh refinement, we aim to explore ad hoc space enrichment strategies. HHO methods offer a particularly versatile framework for local space enrichment, as recently showcased on a toy problem [4]. We envision to extend these ideas to electromagnetics.

All the implementations related to this project shall be carried out within the platform, which is a C++ library developed at INRIA for the 2D/3D polytopal approximation of PDEs.

Bibliographical references:

[1] J. Dalphin, J.-P. Ducreux, S. Lemaire, and S. Pitassi. Hybrid high-order approximations of div-curl systems on domains with general topology. To appear in SIAM J. Sci. Comput., 2025. Preprint .

[2] D. A. Di Pietro, A. Ern, and S. Lemaire. An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Comput. Methods Appl. Math., 14(4):461-472, 2014.

[3] S. Lemaire and S. Pitassi. Discrete Weber inequalities and related Maxwell compactness for hybrid spaces over polyhedral partitions of domains with general topology. Found. Comput. Math., 25(3):725-763, 2025.

[4]L. Yemm. Design and analysis of the extended Hybrid High-Order method for the Poisson problem. Adv. Comput. Math., 48(4):Paper No. 45, 25, 2022.

Principales activités
The post-doc will feature 3 principal activities:(i) the physical and numerical modeling of the flaws inside the conductive material;(ii) the numerical analysis of the (possibly enriched) resulting HHO methods;(iii) their implementation in a C++ platform supporting 3D polyhedral meshes.The research outcomes will be published in leading peer-reviewed journals in numerical analysis and scientific computing. The results will also be presented in international conferences.
Compétences

Profile of the candidate:

PhD in numerical analysis of PDEs and/or scientific computing, with strong programming skills in C++. The knowledge of the French language is welcome but not compulsory.

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 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

2 788€ gross per month