The APOLLO3® code developed at CEA/SERMA aims to provide users of reactor physics with the necessary tools allowing them to carry out their studies, and in particular, solvers of the neutron transport equation. The solvers available in the APOLLO3® code are specialized either for core calculations or for lattice calculations. The NYMO solver [Bourhrara 2019] recently introduced in APOLLO3® intended to be general and deal for both core calculations and lattice calculations.

The NYMO solver based on the spherical harmonics method also known as the PN method for the angular variable and the discontinuous finite element (DG) method for the spatial variable, see [Bourhrara 2019] for more details concerning the numerical scheme used by the solver. The NYMO solver implemented in C++ and already deals with 1D, 2D and 3D Cartesian geometries.

The objectives of the collaboration with the thesis candidate are:

1. Currently NYMO deals for 3D geometries but only in the cases of 2D extruded geometries, in order to deal with general 3D geometries, the doctoral student will extend the NYMO solver to tetrahedral meshes.
2. The doctoral student will also generalize the numerical scheme used in NYMO to RZ cylindrical geometries. Considering RZ geometries will allow the NYMO solver to deal with the neutron transport problem for all types of geometries used in application cases.
3. The NYMO solver based on a particular variational formulation introduced in [Bourhrara 2004]. As part of this thesis, we will also study the standard variational formulation of the transport problem.
4. The candidate will also participate in the optimization of the solver in terms of memory space and CPU time, by studying the possibility of other pre-conditioners for the matrix solvers.
5. Finally, we will study the parallelization using the GPU. NYMO already parallelized on shared memory using OpenMP and in distributed memory using MPI.