The Application of the Finite Element Method to the Multigroup Neutron Diffusion Equation

The finite element method is applied to the multigroup neutron diffusion equations. The one-group inhomogeneous diffusion equation is first discretized using both triangular and rectangular elements. The finite element method is then extended to energy-dependent diffusion by treating the multigroup equations as a series of inhomogeneous one-group equations with sources arising from fission and group-to-group scattering. The resulting formalism is incorporated into a computer code for solving multigroup criticality problems by poweriteration techniques. Numerical results are presented for a two-group water reactor problem. Eigenvalues and flux distributions obtained from two finite element calculations using less than 500 simultaneous equations are in excellent agreement with an accurate PDQ calculation.