PhD in applied maths:

Numerical analysis

Within the framework of the research project in association with the CEA (ATOMIC ENERGY COMMISSION), I developed a 3D code in finite elements to simulate a part of the industrial code already existing (MINOS) that numerically calculates the solution of the diffusion neutron equation. My code was validated and compared versus the benchmark's results. I then boosted the resolution of the handled problem: a complex system dependent on time ( the geometry is also time dependent) composed of two partial differential equations and six ordinary differential equations. The acceleration of the resolution is indeed made via an efficient algorithm for the parallelization in times of the evolution equations, namely the parareal in time algorithm.

Within the framework of the research project in association with EDF (Electricite de France), we are interested in the direct and inverse simulation of eddy current testing (ECT) experiments of SG tubes using monostatic probes composed of two coils introduced in the interior of the tubes. The generator coil creates an electromagnetic field, which in turn induces a current flow in the conductive material nearby. The presence of the default distorts the flow and change the current in the receiver coil, which is measured as ECT signals. Our goal is to estimate the shape of deposits with known electromagnetic parameters (permeability and conductivity) from these ECT signals. Although the tube and coils are axisymmetric, one has to address the problem in a 3D setting since in practice the deposits are located in the vicinity of the (non axi-symmetric) support plates (see Figure up left).

An animated reconstruction's results of non-axisymmetric deposit in four layers is presented in the figure below. We consider in this example one clogged opening of the TSP. The iterations of our algorithm is given in Figure (bottom), where we present the impedance signal fitting via a regularized steepest descent algorithm. We took twelve impedance mesurments for this case.