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.