ABSTRACT
The field of nuclear science and engineering provided the earliest use of adjoint operators for performing sensitivity analysis of a large-scale linear system comprising many parameters. This chapter presents the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) for computing exactly and efficiently all of the first-order and the second-order functional derivatives of system responses to the system's model parameters. Dan Gabriel Cacuci conceived the generally applicable 2nd-ASAM for linear systems for computing exactly and most efficiently all of the second-order functional derivatives of model responses to parameters in models of linear systems. The general forward and adjoint sensitivity analysis methodology for computing exactly and efficiently the first-order sensitivities of nonlinear responses associated with general nonlinear systems was formulated and developed by Cacuci. The chapter shows that constructing and solving the Second-Level Adjoint Sensitivity System (2nd-LASS) requires very little additional effort beyond the construction of the 1st-LASS needed for computing the first-order sensitivities.
