The application of the finite element method to the solution of radiation-shielding problems

The three-dimensional energy-dependent steady-state diffusion equation is solved by a combination of the multigroup technique and the finite element method. A computer program (FE3DP0) has been developed to assemble and solve the resulting multigroup finite element equations. The code is aimed at radiation-shielding applications and in particular at providing a means of accelerating Monte Carlo calculations in situations of awkward geometry. With this aim in mind several methods of solving the multigroup equations have been investigated including factorized inversion, conjugate gradient, Gauss-Seidel and several types of two-grid techniques based upon two compatible linear and quadratic finite element meshes. Results indicate that iterative methods seem to offer more potential for shielding calculations due to their greater speed, smaller storage requirements and ability to give an estimate of the diffusion flux in situations not requiring too exact a solution. Problems involving over 9000 nodes and 5000 quadratic tetrahedral elements have been solved for a single finite element mesh but further work is required to extend the two-grid option to treat problems over approx. 6000 nodes and 3000 quadratic tetrahedral elements. (author)