SUMMARY

The standard treatment of the energy variable in radiation transport is the multigroup method, which allows for the collapsing of reaction cross sections into a few coarse energy groups. This has been traditionally required to reduce the scope of problems to the level of available computing power, but the process makes use of several approximations which are known to introduce errors. These approximations include neglecting the coupling of the energy and angular dependence of the flux when generating the collapsed total cross section and the use of approximate boundary conditions (e.g., specular reflection) for subsets of the entire spatial domain (e.g. fuel assembly within a whole reactor core) to generate the weighting function used to collapse the cross sections. These approximations introduce an inconsistency in the coarse-group calculations. The objective of the proposed thesis is to develop a treatment of the energy variable which results in collapsed cross sections that explicitly account for the detailed energy spectrum as well as the coupling of the energy and angular variables. Previous work has shown that expanding the collapsed cross sections in orthogonal polynomials allows for much of the detailed information to be preserved, but without improvement in the coarse-group flux and global eigenvalue solutions. The primary focus of the thesis is to extend that work with more advanced expansion methods (e.g., wavelets, B-Splines) and to implement them in a consistent manner to eliminates the need for the standard approximations used in the collapsing process. This will allow for fine-group or continuous energy accuracy to be obtained within coarse-group calculations, which would represent a fundamental advancement in the methods available to solve radiation transport problems.