Dan Gabriel Cacuci
This work presents the Second-Order Sensitivity Analysis Methodology (2nd-ASAM) for nonlinear systems. This methodology yields exactly and efficiently the second-order functional derivatives of system responses (associated with physical, engineering, biological, etc., systems) to the system's model parameters.
Dan Gabriel Cacuci
This work presents an illustrative application of the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) developed by Cacuci (2015) to a paradigm nonlinear heat conduction benchmark, which models a conceptual experimental test section containing heated rods immersed in liquid lead-bismuth eutectic. This benchmark admits an exact solution, thereby making transparent the underlying mathematical derivations. For this illustrative problem, six large-scale adjoint computations sufficed to compute exactly all five 1st-order and fifteen distinct 2nd-order derivatives of the temperature response to the five model parameters. Very significantly, only the sources on the right-sides of the heat conduction differential operator need to be modified; the left-side of the differential equations (and hence the solver in large-scale practical applications) remains unchanged.