Response Matrix of Symmetric Nodes

Properties of a symmetric node's response matrix are discussed. The node may have an internal structure such that it remains invariant under the symmetry transformations of the considered node. A transformation diagonalizing the response matrix is given by means of symmetry considerations. The equivalence is demonstrated of the response matrix method to a finite difference scheme in which the dependent variables are of characteristic symmetry properties. Two applications are given with test results: The theory is implemented in coarse-mesh programs both in Cartesian and hexagonal geometries. An analytical few-group solution to the diffusion equation is presented.