An Efficient Algorithm to Solve the GITT-Transformed 2-D Neutron Diffusion Equation

In the last few years special attention has been devoted to searching analytic solutions for the diffusion equation. We are aware of literature for this sort of solution for specialized topics dealing with the simulation of pollutant dispersion in the atmosphere. For illustration we cite the works of (Buske et al. in Atmosphere Environment 2007), (Buske et al. in Environmental Fluid Mechanics 2007), (Moreira et al. 2009). On the other hand, the literature is scarce regarding analytical solutions for the neutron diffusion equation, except for very specialized problems (Maiorino et al. 2007). Work on analytical solutions to the one-dimensional and two-dimensional two-group neutron diffusion equation for either homogeneous or heterogeneous sheets by the well-known GITT technique (Moreira et al. 2009) has recently emerged in the literature. The key feature of this methodology is that is it uses an expansion of the fast and thermal fluxes in a series written in terms of a set of orthogonal eigenfunctions. Replacing these expansions in the original equation and taking moments, yields a second-order matrix differential equation, known in the framework of this methodology as the GITT transformed problem.