Exact-to-precision generalized perturbation theory for eigenvalue problems

摘要

This manuscript extends the exact-to-precision generalized perturbation theory (E_PGPT), introduced previously, to eigenvalue problems whereby previous developments focused on source driven problems only. The E_PGPT collectively denotes new developments in generalized perturbation theory (GPT) that place high premium on computational efficiency in order to render GPT a standard analysis tool in routine design and safety reactor calculations. Unlike GPT, E_PGPT defines a small number of what is referred to as the 'active' responses which are solely dependent on the physics model rather than on the responses of interest, the number of input parameters, or the number of points in the state phase space. The active responses are captured by determining all possible state variations resulting from all possible parameters perturbations. If r (the number of active responses) is much smaller than n (the size of the state space), one can show that by recasting GPT equations in terms of the active responses, all higher order responses variations can be determined to a user-defined accuracy criterion. In addition to presenting the mathematical theory of E_PGPT to eigenvalue problems, illustrative numerical experiments will be conducted serving as proof of principle.