K. N. Toosi University of TechnologyRadiation Physics and Engineering2645-63971120200101Three-dimensional solution of the forward and adjoint neutron diffusion equation using the generalized least squares finite element method19275788510.22034/rpe.2020.57885ENFarahnazSaadatian DerakhshandehMASNA engineering company, P.O. Box 1439951113, Tehran, IranJournal Article20170929Numerical 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.http://rpe.kntu.ac.ir/article_57885_71a444fdd987dd8f87e77a18249cbddc.pdf