@article{kennedy_rabiti_abdel-khalik_2012, title={GENERALIZED PERTURBATION THEORY-FREE SENSITIVITY ANALYSIS FOR EIGENVALUE PROBLEMS}, volume={179}, ISSN={["1943-7471"]}, DOI={10.13182/nt179-169}, abstractNote={Generalized perturbation theory (GPT) has been recognized as the most computationally efficient approach for performing sensitivity analysis for models with many input parameters, which renders forward sensitivity analysis computationally overwhelming. In critical systems, GPT involves the solution of the adjoint form of the eigenvalue problem with a response-dependent fixed source. Although conceptually simple to implement, most neutronics codes that can solve the adjoint eigenvalue problem do not have a GPT capability unless envisioned during code development. We introduce in this manuscript a reduced-order modeling approach based on subspace methods that requires the solution of the fundamental adjoint equations but allows the generation of response sensitivities without the need to set up GPT equations, and that provides an estimate of the error resulting from the reduction. Moreover, the new approach solves the eigenvalue problem independently of the number or type of responses. This allows for an efficient computation of sensitivities when many responses are required. This paper introduces the theory and implementation details of the GPT-free approach and describes how the errors could be estimated as part of the analysis. The applicability is demonstrated by estimating the variations in the flux distribution everywhere in the phase space of a fast critical sphere and a high-temperature gas-cooled reactor prismatic lattice. The variations generated by the GPT-free approach are benchmarked to the exact variations generated by direct forward perturbations.}, number={2}, journal={NUCLEAR TECHNOLOGY}, author={Kennedy, Chris and Rabiti, Cristian and Abdel-Khalik, Hany}, year={2012}, month={Aug}, pages={169–179} }
 @article{el saghir_kennedy_shannon_2010, title={Electron Energy Distribution Function Extraction Using Integrated Step Function Response and Regularization Methods}, volume={38}, ISSN={0093-3813 1939-9375}, url={http://dx.doi.org/10.1109/TPS.2009.2036013}, DOI={10.1109/tps.2009.2036013}, abstractNote={Recently, electron energy distribution function (EEDF) extraction techniques have been evaluated using regularized solutions to the integral problem. These techniques do not assume any mathematical representation of the EEDF and solve the integral problem for any function that best represents the EEDF. Also, unlike the more widely used point-by-point extraction of the second-derivative relationship, the integrated relationship between electron current and the EEDF is used, instead of a relatively small fraction of the integrated data in the point-by-point method. In this paper, the electron current for an arbitrary distribution function is derived, assuming that the distribution is a sum of step functions representing such a function. This technique for EEDF extraction is validated by adding noise to numerically generated data and using a regularized least squares (RLS) method to calculate the original function by solving for the individual step function contribution to the total electron current. Comparisons are then made between the expected and the reconstructed solution to evaluate its accuracy with respect to EEDF reconstruction and integrated normalization of the electron density.}, number={2}, journal={IEEE Transactions on Plasma Science}, publisher={Institute of Electrical and Electronics Engineers (IEEE)}, author={El Saghir, A. and Kennedy, C. and Shannon, S.}, year={2010}, month={Feb}, pages={156–162} }