Discontinuous Galerkin approximation of waves in conducting poro-elastic media
Magique3D proposes one Ph.D fellowship to begin in september 2017 on the modeling and simulation of wave propagation in conducting poro-elastic media. To apply to this fellowship, please send a cv and a cover letter to email@example.com.
The propagation of waves into conducting poro-elastic media is a physical phenomenon involving mechanical waves interacting with electromagnetic waves. This is thus a multi-scale problem of propagation of waves with very different wavelengths. This project deals with the development of numerical methods that are adapted to poro-elastic media in the perspective of a coupling with electromagnetic waves. Some important issues have to be addressed. First, the implementation of the solution of wave problems in porous media is a key step of the project which should last one year, including the validation of the numerical solution thanks to Gar6more (Diaz and Ezziani, 2010a; Diaz and Ezziani, 2010b), which provides analytical solutions in porous media. This is a considerable work of development that has to be carried out in the environment of our software package Hou10ni (https://team.inria.fr/magique3d/software/hou10ni/), which already allows for the solution of elastic and acoustic wave problems in heterogeneous media, using Discontinuous Galerkin methods. We will use in particular the Biot’s equations and for that purpose, the PhD student will draw upon the expertise of (Ezziani, 2005). The ultimate validation of the solver will be based on comparisons with published results, like for instance Morency and Tromp (2008). In particular, this work will provide interesting performance assessments by comparing DG-element with Spectral-element simulations. Once this first software brick is carried out, the question will be how to tackle the tricky problem of ensuring stable numerical approximations of wavefields with wavelengths that vary from the nanometer to the meter. One idea could be to begin with a quasi-static representation of the electric field in order to focus on the full discretization of the mechanical wavefield. This has been previously done in Imperial (2012) and following this former experience could be a good way to quickly begin with the electro-mechanical coupling, using what was formerly done during the first year. Regarding the quasi-static version of Maxwell’s equations, we intend to use the methodology proposed in Montjoie (https://www.math.u-bordeaux.fr/~durufle/montjoie/) and to extend it to Hou10ni in view of performing the coupling with the Biot’s equations. In the same time, our group will work on a way of achieving the coupling of the full equations. One idea consists in developing a multi-level method as it was suggesting in Glowinski et al. (2005) for elliptic problems. Recent results in Abdulle and Huber (2016) suggest that it is possible to develop a finite element approximation for electro-seismic coupling. The idea is to use a multiscale method that approximates the homogenized solution by using numerical upscaling which couples macro and micro finite elements. To the best of our knowledge, this approach has never been applied to the propagation of waves in conducting poro-elastic media.
As a member of the E2S (Energy and Environment Solution) consortium, Magique 3D is eligible to welcome Ph.D fellows from E2S. This year, twelve fellowships will be awarded after a three step selection
- 1st step:Candidates will be selected on the basis of the quality of their curriculum in relationship with the disciplinary fields of E2S-UPPA.
- 2nd step:Selected candidates will be directed to the appropriate laboratories corresponding to their competencies. They will participate in the development of a doctoral research proposal with the potential supervisor(s) and a three year work plan schedule. The purpose of this step is to prepare a thesis topic matching the competencies of the candidate, the expectations of the thesis supervisor and the challenges of E2S-UPPA. Applicants must be supported by one or several local host laboratory(ies).
- 3rd step:Interview – the candidate will be invited to defend his/her project in front of the selection board.
See http://e2s-uppa.eu/en/news-2/cfp-phdgrants.html for more details.
We encourage potential candidates interested by a Ph.D in Magique 3D on its main research themes (https://team.inria.fr/magique3d/research/) to contact us (firstname.lastname@example.org) and to apply to the E2S fellowship before June 10th, 2017.
The application file is to be sent email@example.com The required application documents should be gathered into a single pdf file:
- Cover letter – 1-3 pages where you introduce yourself and present your qualifications and achievements, and emphasis on future goals and research focus.
- Are there any specific projects and research issues you are primarily interested in ? To be indicated in the motivation letter
- Curriculum vitae
- Copies of certificates of any academic degrees and grade reports during their master studies
- Copies of certificates of French and/or English languages skills (for non French or English speaking applicants)
- Two letters of recommendation.
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