The simulation of the neutron transport inside a nuclear reactor leads to the computation of the lowest eigen pair of a simplified transport operator. Whereas the sequential solution at our disposal today is really efficient, we are not able to run some industrial cases due to the memory consumption and the computational time. This problem brings us to study parallel strategies. In order to re-use an important part of the solver and to bypass some limitations of conforming cartesian meshes, we propose a non overlapping domain decomposition based on the introduction of Lagrange multipliers. The method performs well on up to $100$ processors for an industrial test case.