A method for obtaining an approximate solution of the group-diffusion equations for geometrically complex reactors is described and tested for a two-group two-dimensional situation. The basic idea of the scheme is to represent the group fluxes throughout a given subassembly as the product of a precomputed normalized “shape function” that accounts for local geometrical detail and a smooth finite element function that specifies the overall magnitude of the fluxes within the subassembly and the gross leakage effects between a given subassembly and its neighbors. These composite fluxes for each subassembly are then stitched together by the application of a variational principle.