Applications of finite groups to iterative problems in reactor physics

In the calculation of nuclear reactor cores, the solution of the emerging boundary value problem is often based on the so called response matrix iteration. The response matrix relates the solution at boundary points to the gradient of the solution at boundary points. In the first part of the present work, a procedure is presented to decompose the response matrix and the material distribution into irreducible components of the automorphism group of a finite volume Ω. lution is usually a numerical one, where an approximation is used at the boundary and inside. In the second part, we provide compatibility conditions for the approximations inside Ω and on the boundary ∂Ω. The present work addresses an observed convergence problem in the iterative solution in the application of a number of coarse mesh methods to boundary value problems. We use point group theory to clarify the cause of the non-convergence, and give rules for choosing the appropriate and consistent orders of approximation on the boundary and within the volume so as to avoid non-convergence. nk between the solutions to the mentioned problem is group theory, which has proved rather effective.