Three-dimensional solution of the forward and adjoint neutron diffusion equation using the generalized least squares finite element method

‎Numerical solution of the multi-group static forward and adjoint neutron diffusion equation (NDE) using the Finite Elements Method (FEM) is investigated in detail‎. ‎A finite element approach based on the generalized least squares method is applied for the spatial discretization of the NDE in 3D-XYZ geometry‎. ‎A computer code called GELES was also developed based on the described methodology covering linear or quadratic tetrahedral elements generated via the mesh generator for an arbitrary shaped system‎. ‎A number of test cases are also studied to validate the proposed approach‎. ‎Moreover‎, ‎to assess the output dependency to the number of elements‎, ‎a sensitivity analysis is carried out at the end‎.