HIgh-order POlyhedral meTHods for Eddy Current testing simulations – HIPOTHEC

HIPOTHEC is a joint research project between EDF R&D and 4 academic partners, grouped into 2 geographical poles: Inria Lille and the UPHF (Valenciennes) in the North, and the Université de Montpellier and Université Côte d'Azur (Nice) in the South. The aim of the project is to devise, mathematically analyze, and practically implement high-order polyhedral (i.e. applicable on general meshes) methods for the simulation of non-destructive eddy current testing (ECT). ECT is used by EDF to assess the mechanical integrity of steam generator tubes in nuclear plants. In practice, in order to qualify the ECT devices that are employed, engineers rely on modeling and numerical simulation. HIPOTHEC aims at addressing at once 2 important issues faced by EDF in ECT simulations when using lowest-order standard finite element methods: (i) the significant noise on the control signal based on which the presence of a defect is inferred, and (ii) the great complexity of the 3D meshing process, especially when defects have to be accounted for. The project is structured in 3 work-packages (WP). The first WP is concerned with the devising and a priori analysis of (possibly enriched) Hybrid High-Order (HHO) methods for realistic ECT configurations. The second WP revolves around the development of reliable and efficient a posteriori error estimators as well as of efficient and robust multigrid linear solvers for the HHO methods developed in WP1. The third WP is concerned with the proof of concept of our methodology on a target industrial application. The expected outcomes for EDF are substantial: a noticeable gain in accuracy on the calculation of the quantities of interest, and an increased geometrical flexiblity in the 3D meshing process allowing, in particular, for the modeling of complex flaws and for the simplification of the remeshing stage inherent to the displacement of the ECT sensor. From an academic point of view, the project also embeds an important number of mathematical challenges, which justify the need for seasoned researchers expert in numerical analysis of PDEs and scientific computing, as well as for additional non-permanent human resources.