The deterministic solution of the neutron transport equation traditionally relies on the use of the multigroup approximation to discretize the energy variable. The energy domain is divided using a one-dimensional mesh, where the volume elements are called 'groups' in neutronics. Within each group, all physical quantities (neutron flux, cross sections, reaction rates, etc.) are projected using piecewise constant functions. This homogenization of cross sections, which are the input data of the transport equation, becomes particularly challenging in the presence of resonant nuclei, whose cross sections vary rapidly over several decades. Correcting for this requires computationally expensive on-the-fly treatments to improve the accuracy of the transport solution.

The goal of this thesis is to eliminate the need for the multigroup approximation in the resonant energy range by applying a Galerkin projection of the continuous energy equation onto an orthonormal wavelet basis. The candidate will develop a generic expansion method adapted to mixtures of resonant isotopes, including preprocessing of cross sections, selection of the wavelet basis, and determination of an efficient coefficient truncation strategy. A dedicated neutron transport solver will be developed, with a focus on efficient algorithmic implementation using advanced programming techniques suited to modern architectures (GPU, Kokkos). The results of this thesis research will be valorized through publications in peer-reviewed international journals and presentations at scientific conferences.