Solutions of the diffusion equation with zero average boundary values

Abstract

The response matrix method as used in reactor physics deals mostly with face averaged quantities. When homogenizing a region we use position independent boundary conditions. In both problems we neglect those solutions of the equation to be solved that belong to the zero average value along the boundary. In the case of the diffusion equation those solutions — called overtones — are studied on two examples. First the entering current distribution of an efficient analytical coarse- mesh model is assessed, then the widely applied quadratic entering current distribution.