Raphaël LECOQ

Reduced Order Models and Data Assimilation for power modules.

Nonlinear Compressed Reduced Basis Method for Data Assimilation

Reconstruction of sparse data with reduced basis methods using an ML autoencoder to reduce the online optimization procedure down to a few POD coefficients instead of all of them.

Error estimation for Discontinuous Galerkin methods

Implementation in MATLAB of an a posteriori error estimator for heterogeneous diffusion on TrioCFD. Enables local mesh refinement recovering optimal convergence for low-regularity solutions.

A posteriori error estimator for Finite Volume-based ROM in CFD

Proposed to use a Discontinuous Galerkin variational formulation of Finite Volumes hoping to enable a posteriori error estimators for Reduced Basis generation using a weak greedy algorithm defined in the Finite Elements framework.

Numerical analysis of branching processes

Modelling and statistical analysis of critical branching processes (Lévy flights, Brownian motion) and their clustering statistics in neutronic and avalanche cases.