Feasibility of a wavelet expansion method to treat energy in cell calculations

This paper discusses the application of the Discrete Wavelet Transform (DWT) for the functional expansion of the energy variable in a cell calculation. The motivation of the work is the desire to obtain a self-shielding methodology in which the treatment of the energy variable in a given material region can be automatically adapted to the complexity of the cross section in that region. Unfortunately, the work presented in this paper shows that it is generally not possible to obtain the desired adaptivity. The most fundamental reason is that in a multi-region system, the energy dependence of the flux in a given material region is a function of the energy dependent cross sections and sources in all material regions through which the neutrons have crossed before entering into the present material. The complexity of the energy dependence of the cross section in a material region is thus not necessarily linked to the energy dependence of the flux in that region. If one sacrifices the objective of adaptivity, then an accurate method can be obtained using the DWT as a functional expansion. However, the resulting system of equations is more complicated than the direct solution of a hyper-fine group calculation. The conclusion is thus that the DWT approach is not very practical. (authors)