Finite elements in multidimensional nuclear diffusion

Although structural engineering has produced a large variety of element types only triangular and quadratic elements of the Lagrangian seem to have caught on in nuclear fields. In this report we wish to stress two topics. The first is, certain shortcomings of the triangular element, when used to model problems which are essentially one dimensional such as slab-geometry. This forced us to introduce rectangular elements into the finite element diffusion code FINELM. As far as ksub(eff) or reaction rates are concerned there is perhaps little to choose between the two but point flux behaviour is distinctly superior for rectangular elements. After the initial enthusiasm about finite elements the writing of finite element codes seems to be on the wane. This is largely due to the irregular wide band structure of the resulting system matrix which pose acute problems for core management. In FINELM, which has been operational for about two years, we considered the number of degrees of freedom as a given quantity and solved the core management problem by using basic graph-theoretic ideas. In QUFEM, the Yougoslavian code, which is still largely in the experimental stage the problem is attacked by using large high order general quadrilateral elements extending over spatially varying (smoothly) cross sections as would occur in pebble bed reactors. (orig./RW)