This expansion gives rise to errors of the order of the cell size. It does not account for neutron leakage at the boundary of the core and yields unacceptable errors in practice. We derive a more accurate expansion of the eigenelements in the case of a symmetric and cubic domain. The analysis of a boundary layer allows us to derive modified boundary conditions for the diffusion eigenvalue problem. The resulting approximation for the leading transport eigenvalue is proven to be accurate to one order higher than previously.
Numerical experiments confirm the accuracy of the reconstructed eigenvectors in realistic settings.