2020-03-Offer for a Thesis Allowance - Subject: Numerical resolution of magnetic diffusion issues in ferromagnetic materials

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Offer for a Thesis AllowanceSubject: Numerical resolution of magnetic diffusion issues in ferromagnetic materials

Scientific context

When considering two highly heterogeneous materials (Ω+, Ω−) with a common interface, contrasts of magnetic permeabilities (μr = μ−/μ+ ≫ 1) and conductivities may enter in competition. There are two asymptotic behaviors whether the contrast of conductivities or the contrast of permeabilities is predominant. The first case is well-known and it corresponds to methods of surface impedance. In this case, we have shown that the delta parameterization of the magnetic potentiel allows to derive a solution for any skin depth by using only a coarse mesh for the conductor body [1]. We propose to investigate the behavior when the permeability is dominating, that is the ferromagnetic case. Then it would be possible to use the same mesh for a large range of frequencies, which is usefull for instance in power electronics. A preliminary study has shown that a ferromagnetic conductor body behaves like a non-magnetic isolator body [2]. In the same way we propose to tackle the 3D eddy current problem for the electromagnetic field.

[1] L. Krähenbühl, V. Péron, R. Perrussel, and C. Poignard. On the asymptotic expansion of the magnetic potential in eddy-current problem: a practical use of asymptotics for numerical purposes. Rapport de Recherche Inria RR-8749, 2015.
[2] R. Perrussel, C. Poignard, V. Péron, R. Sabariego, P. Dular, and L. Krähenbühl. Asymptotic expansion for the magnetic potential in the eddy-current problem. In 10th International Symposium on Electric and Magnetic Fields (EMF 2016), Lyon, France, April 2016.


PhD project


We want to be able to solve eddy current problems by using the classical Finite Element Method (FEM) for the conception of industriel systems but without using any mesh adaptation to the skin depth. The FEM is well adapted to diffusion problems but mesh adaptation is very costly and time consuming, specificaly to solve 3D problems. The main goal of this thesis is to design a numerical method to solve efficiently eddy current problems minimizing numerical costs.

Work plan:

Our approach is based on the method of multi-scale expansion. The first part of this project concerns the asymptotic analysis of the diffusion problem. In the 2D problem, we aim at deriving an asymptotic expansion for the magnetic potential when the contrast of permeabilities is predominant. In 3D, we aim at deriving an asymptotic expansion for the electromagnetic (EM) field. This method could be validated by proving energy estimates for the EM field. The second part of this work is devoted to implement and to validate numerically the new asymptotic models using a finite element code. Analytic solutions could be also usefull at this step. In the last part, we want to derive delta parameterizations with respect to the relative permeability μr, for a large range of frequencies. This step will be realized by using the asymptotic expansion and a finite element solution computed for a sufficiently small skin depth together with a coarse mesh.


Working conditions

Hosting laboratories: Laboratoire de Mathématiques et de leurs Applications de Pau – UMR CNRS 5142

Localisation: Université de Pau et des Pays de l’Adour, France

PhD supervisor: Victor Péron

Collaborations: The PhD student will collaborate with Ronan Perrussel (CR CNRS, Laboratoire Laplace, INPT-ENSEEIHT, Toulouse) and with Laurent Krähenbühl (DR CNRS, Laboratoire Ampère, Ecole Centrale de Lyon) on all the numerical aspects of this project and on the physical interpretation of the results.

Starting date: October 2020

Length: 3 years

Employer: UPPA, doctoral school ED 211 Doctoral School of Exact Sciences and their Applications

Gross monthly salary: 1878 € for a PhD (UPPA doctoral contract, according to E2S UPPA project, including 96h of teaching during the three years)


Required skills and competences - Who can apply ?

Required knowledge : The candidate must have a Master in applied mathematics, engineering with scientific computing background. Knowledge on the method of multi-scale expansion would be a plus.

The candidate should have a strong predilection for laboratory work. Team working abilities are highly appreciated. 
He/She is rigorous, highly motivated, with the capacity to work autonomously.
Good knowledge in English and good writing skills are required.


Application - Evaluation criteria

Application files will be evaluated based on the following criteria:

  • Candidate's motivation, scientific maturity and curiosity
  • Academic results : grades and ranking in Licence/undergraduate, M1 and M2
  • English language proficiency
  • Oral and written communication skills
  • Candidate’s ability to present her/his work and results
  • Professional experience (e.g. internships in laboratory or other, any research work previously carried out, reports, publications ...)

Application file composition and submission deadline

To apply, please send an email to Victor PERON victor.peron@univ-pau.fr (ictor.peron @ univ-pau.fr) with [PhD offer] as its subject and the following documents attached:

  • CV
  • Cover letter detailing candidate's motivations
  • Copy of your Master diplomas and academic records (marks and ranking)
  • Letter(s) of recommendation
  • Contact details for 2 referees


Submission deadline : May 25th, 2020