A Timing Comparison Study for Some High Order Finite Element Approximation Procedures and a Low Order Finite Difference Approximation Procedure for the Numerical Solution of the Multigroup Neutron Diffusion Equation

Abstract

This paper contains the results of detailed comparison studies of the efficiency of high order finite element approximations vs low order finite difference approximations, for the numerical solution of the static multigroup diffusion equation in two dimensions. The comparisons are based on the execution times for a keff calculation with a prescribed precision for two particular computer programs— HOD (finite elements) and DARC2D (finite differences). The calculations were performed for three different types of reactor configurations: a simple two-zone configuration with two energy groups, a multizone configuration [1000-MW(e) LMFBR mockup] with four energy groups, and a loosely coupled configuration with two energy groups.The conclusions are: The use of high order approximation procedures based on finite element methods leads to substantial execution time savings and offers not just a viable alternative to the use of low order approximation procedures based on finite difference methods; it is, indeed, a significant advancement in computational capability.With high order approximation procedures based on finite element methods it is possible to obtain, at reasonable cost, solutions to the multigroup diffusion equation which are sufficiently accurate that any errors can be attributed to either the diffusion theory approximation or other approximations in the reactor model, rather than to the numerical approximation procedure.Solutions obtained with the finite element method provide as much accuracy in the flux inventories as in the multiplication factor.