[NotiAMCA] Post Doc Position INRIA

[Victorio Sonzogni]

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INRIA-LORRAINE
INRIA 2008 POSTDOCTORAL FELLOWSHIP PROPOSAL
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City : Nancy

Title of Research Project: Domain decomposition for full wave simulation 
of cold plasma.

INRIA team in which the research would be effected: CALVI

Fellowship supervisor: Jean Roche

Description of Research:

Waves at a frequency close to the lower hybrid (LH) resonance are widely 
used in tokamaks for current drive. Modelling of LH waves is usually 
carried out using Ray-tracing code for computing the LH waves 
propagation and absorption. First “full wave” simulations based on 
spectral techniques have shown different results in comparison to RT 
model and inconistencies still remain.
The aim of this post doctoral fellowship is to develop a domain 
decomposition method for the full-wave simulation of electromagnetic 
wave propagation in plasma. This work is a collaboration between the 
INRIA team CALVI and the CEA Cadarache(ITER project).
The full-wave method allows us to study the electromagnetic wave 
propagation in cold plasma and the"whistler" modes for a frequency near 
the lower-hybrid frequency.
In the full wave simulation of wave propagation consider in this project 
we study a time harmonic formulation. In this formulation we solve the 
governing equation for the electric field.
The domain considered is as near as possible of the cavity fill by a 
tokomak plasma. Toroidal coordinates are introduced.
In our approach we consider Fourier decomposition in the angular 
coordinate to obtain stationary Maxwell equations in a cross-section of 
the tokamak cavity.
To consider finite element numerical method widely used to approximate 
the solution of this type of problems we introduce a mixed augmented 
variational (weak) formulation taking account the divergence constraint 
and natural boundary conditions (Costabel, Ciarlet Jr., Assous, Degond 
et al.). An evolution of this method due to Costabel and al. allows us 
to consider the anisotropic case.
A code was developed in the total domain case following these ideas in 
the team CALVI
The analysis of the weak formulation of our problem with a heterogeneous 
behaviour of the conductivity tensor presents some difficulties. We 
propose a domain decomposition to overcome this anisotropy.
The next objective is to develop the domain decomposition code, when we 
consider the mixed augmented formulation on each sub domains.
It's a non trivial work to identify the interface condition between sub 
domains. The postdoctoral fellow will first study interface conditions, 
a beginnig point for this research will be the papers of Alonso and 
Valli, Quarteroni and Valli, Collino, Ghanemi and Joly.
The domain decomposition must answer to two priorities. The first one is 
to take account of the anisotropy of the problem because of the magnetic 
field, with stiff behaviour of densities and gradients. We want to be 
able to adapt finite element discretization in each sub domains.
The second priority is to adapt the algorithm and the code to parallel 
computers. In that case we will be able to consider fine discretization 
and compare the results to ray-tracing ones.

Desired profile of candidate:

Ph. D. in Mathematics, Numerical analysis speciality, with good
experience in numerical resolution of PDE's, scientific computation,
and possible knowledge in domain decomposition or Ph.D in Physics,
possibly a specialization in Plasma Physics with a good knowledge of
scientific computation.

Contact: Jean Roche ,
IECN, Université Henri Poincaré
BP 239-54506 Vandoeuvre les Nancy
roche en iecn.u-nancy.fr
Ph. : (33) 3 83 68 45 82
http://www-math.u-strasbg.fr/calvi/
PLEASE Apply at : 
http://www.inria.fr/travailler/opportunites/postdoc/postdoc.en.html