Evaluation of the finite-element-synthesis model using the 3-D finite-element technique

For the solution of multi group diffusion theory equations a 3-D finite-element (FE) code finerc has been developed. 3-D element shapes with the base orthogonal to the third direction are considered in finerc. For these elements the 3-D element submatrices of the FE formulation are easily computed in terms of the corresponding lower-dimensional element submatrices. The 3-D problems are tackled in finerc with a degree of complexity equivalent to that of 2-D problems.The 3-D FE technique is still somewhat expensive for routine design computations. The method can, however, be used for assessing the accuracy of other faster calculational methods. In this paper we have compared the results of the 3-D FE method with those of the FE-synthesis method which was previously developed by the present author. It is noted that the FE-synthesis method gives, at negligible computational cost, accurate eigenvalue estimates and reasonably good predictions of reactor core power profiles for the 3-D benchmark problems. The FE-synthesis method may be used for a number of survey-type analyses with occasional counter-checking by the 3-D FE technique.