In science, simulation is a key process for research or validation. Modern computer technology allows faster numerical experiments, which are cheaper than real models. In the field of neutron simulation, the calculation of eigenvalues is one of the key challenges. The complexity of these problems is such that a lot of computing power may be necessary. The work of this thesis is first the evaluation of new computing hardware such as graphics card or massively multicore chips, and their application to eigenvalue problems for neutron simulation. Then, in order to address the massive parallelism of supercomputers national, we also study the use of asynchronous hybrid methods for solving eigenvalue problems with this very high level of parallelism. Then we experiment the work of this research on several national supercomputers such as the Titane hybrid machine of the Computing Center, Research and Technology (CCRT), the Curie machine of the Very Large Computing Centre (TGCC), currently being installed, and the Hopper machine at the Lawrence Berkeley National Laboratory (LBNL). We also do our experiments on local workstations to illustrate the interest of this research in an everyday use with local computing resources.
