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

Document Type: Original Article


MASNA engineering company‎, ‎P.O‎. ‎Box 1439951113‎, ‎Tehran‎, ‎Iran


‎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.


  • Multi-group static 3-D neutron di usion equation is solved using the nite element method.
  • Generalized least squares FEM, through a variational approach is applied for solving the NDE.
  • GELES code is developed based on the tetrahedral elements for an arbitrary shaped system.
  • To validate the approach, output of GELES were compared against the DONJON computer code.

 Acceptable accuracy for the neutron multiplication factor and the power distribution was achieved.